Student Handbook. Prerequisite Skills Extra Practice Mixed Problem Solving Preparing for Standardized Tests...

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1 Student Handbook Built-In Workbooks Prerequisite Skills Etra Practice Mied Problem Solving Preparing for Standardized Tests Reference English-Spanish Glossar R Selected Answers R Photo Credits R0 Inde R0 Formulas and Smbols Inside Back Cover 7 Eclipse Studios

2 The Student Handbook is the additional skill and reference material found at the end of the tet. This handbook can help ou answer these questions. What if I Forget What I Learned Last Year? Use the Prerequisite Skills section to refresh our memor about things ou have learned in other math classes. Here s a list of the topics covered in our book.. The FIL Method. Factoring Polnomials. Congruent and Similar Figures. Pthagorean Theorem. Mean, Median, and Mode. Bar and Line Graphs 7. Frequenc Tables and Histograms. Stem-and-Leaf Plots 9. Bo-and-Whisker Plots What If I Need More Practice? You, or our teacher, ma decide that working through some additional problems would be helpful. The Etra Practice section provides these problems for each lesson so ou have ample opportunit to practice new skills. What If I Have Trouble with Word Problems? The Mied Problem Solving portion of the book provides additional word problems that use the skills presented in each lesson. These problems give ou real-world situations where math can be applied. What If I Need to Practice for a Standardized Test? You can review the tpes of problems commonl used for standardized tests in the Preparing for Standardized Tests section. This section includes eamples and practice with multiple-choice, griddable or grid-in, and etended-response test items. What If I Forget a Vocabular Word? The English-Spanish Glossar provides a list of important or difficult words used throughout the tetbook. It provides a definition in English and Spanish as well as the page number(s) where the word can be found. What If I Need to Check a Homework Answer? The answers to odd-numbered problems are included in Selected Answers. Check our answers to make sure ou understand how to solve all of the assigned problems. What If I Need to Find Something Quickl? The Inde alphabeticall lists the subjects covered throughout the entire tetbook and the pages on which each subject can be found. What if I Forget a Formula? Inside the back cover of our math book is a list of Formulas and Smbols that are used in the book. Student Handbook 7

3 Prerequisite Skills Prerequisite Skills The FIL Method The product of two binomials is the sum of the products of F the first terms, the outer terms, I the inner terms, and L the last terms. EXAMPLE Find ( + )( ). F L ( + ) ( )= + ( ) + + ( ) I First uter Inner Last = + = EXAMPLE Find ( + )( + ). ( + )( + ) = = = + + Eercises Find each product.. (a + )(a + ) a + a +. (v - 7)(v - ) v - v + 7. (h + )(h - ) h -. (d - )(d + ) d -. (b + )(b - ) b + b -. (s - 9)(s + ) s + s (r + )(r - ) r + r. (k - )(k + ) k + k (p + )(p + ) p + p + 0. ( - )( - ) (c + )(c - ) c - 9c -. (7n - )(n + ) 7 n + 9n -. (m + )(m - ) m - 7m - 0. (g + )(g + 9) 0 g + g + 9. (q - 7)(q + ) q - q -. (t - 7)(t - ) t - 9t + NUMBER For Eercises 7 and, use the following information. I m thinking of two integers. ne is 7 less than a number, and the other is greater than the same number. 7. Write epressions for the two numbers. n - 7, n +. Write a polnomial epression for the product of the numbers. n - n - FFICE SPACE For Eercises 9, use the following information. Monica s current office is square. Her office in the compan s new building will be feet wider and feet longer. 9. Write epressions for the dimensions of Monica s new office. +, + 0. Write a polnomial epression for the area of Monica s new office Suppose Monica s current office is 7 feet b 7 feet. How much larger will her new office be? 7 sq. ft 7 Prerequisite Skills

4 Factoring Polnomials Some polnomials can be factored using the Distributive Propert. EXAMPLE Factor a + a. Find the GCF of a and a. a = a a a = a GCF: a or a a + a = a(a) + a() Rewrite each term using the GCF. = a(a + ) Distributive Propert Prerequisite Skills To factor quadratic trinomials of the form + b + c, find two integers m and n with a product of c and with a sum of b. Then write + b + c using the pattern ( + m)( + n). EXAMPLE Factor each polnomial. a. + + Both b and c are positive. In this trinomial, b is and c is. Find two numbers with a product of and a sum of. Factors of Sum of Factors, 7, The correct factors are and. + + = ( + m)( + n) Write the pattern. = ( + )( + ) m = and n = CHECK Multipl the binomials to check the factorization. ( + )( + ) = () FIL = + + b. - + b is negative and c is positive. In this trinomial, b = - and c =. This means that m + n is negative and mn is positive. So m and n must both be negative. Factors of Sum of Factors -, - - -, - - The correct factors are - and = ( + m)( + n) Write the pattern. = [ + (-)][ + (-)] m = - and n = - = ( - )( - ) Simplif. c. + - b is positive and c is negative. In this trinomial, b = and c = -. This means that m + n is positive and mn is negative. So either m or n must be negative, but not both. Factors of Sum of Factors, - - -, The correct factors are - and. + - = ( + m)( + n) Write the pattern. = [ + (-)]( + ) m = - and n = = ( - )( + ) Simplif. Prerequisite Skills 77

5 Prerequisite Skills To factor quadratic trinomials of the form a + b + c, find two integers m and n whose product is equal to ac and whose sum is equal to b. Write a + b + c using the pattern a + m + n + c. Then factor b grouping. EXAMPLE Factor In this trinomial, a =, b = 7 and c = -. Find two numbers with a product of (-) or - and a sum of 7. Factors of - Sum of Factors, , 7, , 9 7 The correct factors are - and = + m + n - Write the pattern. = + (-) m = - and n = 9 = ( ) + (9 - ) Group terms with common factors. = ( - ) + ( - ) Factor the GCF from each group. = ( + )( - ) Distributive Propert Here are some special products. Perfect Square Trinomials Difference of Squares ( a + b) = (a + b)(a + b) (a - b) = (a - b)(a - b) a - b = (a + b)(a - b) = a + ab + b = a - ab + b EXAMPLE Factor each polnomial. a The first and last terms are perfect squares. The middle term is equal to ()(). This is a perfect square trinomial of the form (a + b) = () + ()() + Write as a + ab + b. = ( + ) Factor using the pattern. b. - This is a difference of squares. - = - () Write in the form a - b. = ( + )( - ) Factor the difference of squares. Eercises Factor the following polnomials ab - ab a - 0ab + b a + ab + 9b c a - 9 b 7 Prerequisite Skills

6 Congruent and Similar Figures Congruent figures have the same size and the same shape. Two polgons are congruent if their corresponding sides are congruent and their corresponding angles are congruent. A B D C ABC EFD F E Congruent Angles A E B F C D Congruent Sides AB EF BC FD AC ED Prerequisite Skills The order of the vertices indicates the corresponding parts. Read the smbol as is congruent to. EXAMPLE The corresponding parts of two congruent triangles are marked on the figure. Write a congruence statement for the two triangles. D List the congruent angles and sides. A D AB DE B E AC DC B ACB DCE BC EC C E Match the vertices of the congruent angles. Therefore, ABC DEC. A Similar figures have the same shape, but not necessaril the same size. In similar figures, corresponding angles are congruent, and the measures of corresponding sides are proportional. (The have equivalent ratios.) A B EXAMPLE C ABC DEF Congruent Angles A D, B E, C F Proportional Sides _ AB DE = _ BC EF = _ AC DF Read the smbol as is similar to. Determine whether the polgons are similar. Justif our answer. a. Since _ = _ = _ = _, the measures of the sides of the polgons are proportional. However, the corresponding angles are not congruent. The polgons are not similar. b. Since 7_ 0. = _. = 7_ 0. = _, the measures. of the sides of the polgons are proportional. The corresponding angles are congruent. Therefore, the polgons are similar. D E F Prerequisite Skills 79

7 Prerequisite Skills EXAMPLE CIVIL ENGINEERING The cit of Mansfield plans to build a bridge across Pine Lake. Use the information in the diagram to find the distance across Pine Lake. ABC ADE _ AB AD = _ BC Definition of similar polgons DE _ 00 0 = _ AB = 00, AD = = 0, BC = DE 00DE = 0() Cross products 00DE =,00 Simplif. D E B 0 m m C 00 m A DE = Divide each side b 00. The distance across the lake is meters. Eercises Determine whether each pair of figures is similar, congruent, or neither Each pair of polgons is similar. Find the values of and SHADWS n a sunn da, Jason measures the length of his shadow and the length of a tree s shadow. Use the figures at the right to find the height of the tree.. m. m? m 7. m. PHTGRAPHY A photo that is inches wide b inches long must be reduced to fit in a space inches wide. How long will the reduced photo be?. SURVEYING Surveors use instruments to measure objects that are too large or too far awa to measure b hand. The can use the shadows that objects cast to find the height of the objects without measuring them. A surveor finds that a telephone pole that is feet tall is casting a shadow 0 feet long. A nearb building is casting a shadow feet long. What is the height of the building? 0 Prerequisite Skills

8 Pthagorean Theorem The Pthagorean Theorem states that in a right triangle, the square of the length of the hpotenuse c is equal to the sum of the squares of the lengths of the legs a and b. That is, in an right triangle, c = a + b. EXAMPLE Find the length of the hpotenuse of each right triangle. a c b Prerequisite Skills a. in. c in. b. c = a + b Pthagorean Theorem c = + Replace a with and b with. c = + Simplif. c = 9 Add. c = 9 Take the square root of each side. c = in. The length of the hpotenuse is inches. cm c cm c = a + b Pthagorean Theorem c = + 0 Replace a with and b with 0. c = + 00 Simplif. c = Add. c = Take the square root of each side. c.7 0 cm Use a calculator. To the nearest tenth, the length of the hpotenuse is.7 centimeters. EXAMPLE Find the length of the missing leg in each right triangle. a. 7 ft ft a ft c = a + b Pthagorean Theorem = a + 7 Replace c with and b with 7. = a + 9 Simplif. - 9 = a Subtract 9 from each side. 7 = a Simplif. 7 = a Take the square root of each side. = a The length of the leg is feet. Prerequisite Skills

9 Prerequisite Skills b. c = a + b Pthagorean Theorem b m m m = + b Replace c with and a with. = + b Simplif. = b Subtract from each side. = b Take the square root of each side.. b Use a calculator to find the square root of. Round to the nearest tenth. To the nearest tenth, the length of the leg is. meters. EXAMPLE The lengths of the three sides of a triangle are, 7, and 9 inches. Determine whether this triangle is a right triangle. Since the longest side is 9 inches, use 9 as c, the measure of the hpotenuse. c = a + b Pthagorean Theorem Replace c with 9, a with, and b with Evaluate 9,, and 7. 7 Simplif. Since c a + b, the triangle is not a right triangle. Eercises Find each missing measure. Round to the nearest tenth, if necessar ft km a km m in. c ft ft in. c in. 7. a =, b =, c =?. a =?, b =, c = 9. a =, b =?, c = 0 0. a =, b = 9, c =? 9.. a =, b =?, c =.. a =?, b = 7, c =. The lengths of three sides of a triangle are given. Determine whether each triangle is a right triangle.. in., 7 in., in. no. 9 m, m, m es. cm, 7 cm, cm no. ft, ft, ft no 7. 0 d, d, d es. km, 0 km, km es 9. FLAGPLES Mai-Lin wants to find the distance from her feet to the top of the flagpole. If the flagpole is 0 feet tall and Mai-Lin is standing a distance of feet from the flagpole, what is the distance from her feet to the top of the flagpole? about. ft b m 0. CNSTRUCTIN The walls of the Downtown Recreation Center are being covered with paneling. The doorwa into one room is ft 0.9 meter wide and. meters high. What is the width of the widest rectangular panel that can be taken through this doorwa? about. m 0 km m cm d b cm d? ft 0 cm c d 0 ft Prerequisite Skills

10 Mean, Median, and Mode Mean, median, and mode are measures of central tendenc that are often used to represent a set of data. To find the mean, find the sum of the data and divide b the number of items in the data set. (The mean is often called the average.) To find the median, arrange the data in numerical order. The median is the middle number. If there is an even number of data, the median is the mean of the two middle numbers. The mode is the number (or numbers) that appears most often in a set of data. If no item appears most often, the set has no mode. Prerequisite Skills EXAMPLE Michelle is saving to bu a car. She saved $00 in June, $00 in Jul, $00 in August, and $0 in September. What was her mean (or average) monthl savings? mean = sum of monthl savings/number of months $00 + $00 + $00 + $0 = = _ $00 or $.0 Michelle s mean monthl savings was $.0. EXAMPLE Find the median of the data. To find the median, order the numbers from least to greatest. The median is in the middle. The two middle numbers are.7 and =.9 There is an even number of data. Find the mean of the middle two. Peter s Best Running Times Week Minutes to Run a Mile EXAMPLE GLF Four plaers tied for first in the 00 PGA Tour Championship. The scores for each plaer for each round are shown in the table below. What is the mode score? Plaer Round Round Round Round Mike Weir David Toms 7 7 Sergio Garcia 9 7 Ernie Els 9 Source: ESPN The mode is the score that occurred most often. Since the score of occurred times, it is the mode of these data. Prerequisite Skills

11 Prerequisite Skills The range of a set of data is the difference between the greatest and the least values of the set. It describes how a set of data varies. EXAMPLE Find the range of the data. {,,,, 9,,, } The greatest value is and the least value is. So, the range is - or. Eercises Find the mean, median, mode, and range for each set of data. Round to the nearest tenth if necessar.. 0.; 0.; 0 and 0;. {,,,, } 0; ; no mode;. {, 7, 7,,, } ; 7; 7;. {7, 9,, 9, 00, } 9.; ; no mode;. {99, 00,, 9, 9, 99} 9., 97., 99,. {9.9, 9.9, 0, 9.9,., 9., 9.} 9.; 9.9; 9.9;.. {0, 0, 0, 0, 0, 0, 0, 0} 7. {7, 9,,,, 7, 9} ; ; no mode;. {,,,,,,, }.; 0; no mode; 9. {0., 0.0, 0.9,., 0.} 0.; 0.; no mode; 0. _ {, _ 7, _, _, } ; _ ; no mode; _ 7.0. CHARITY The table shows the amounts. SCHL The table shows Pilar s grades collected b classes at Jackson High in chemistr class for the semester. Find School. Find the mean, median, mode, her mean, median, and mode scores, and and range of the data. the range of her scores. 9.; 9; 9; Amounts Collected for Charit Class Amount Class Amount A $0 E $0 B $00 F $ C $ G $00 D $0 H $00 $0; $77.0; no mode; $90 Chemistr Grades Assignment Grade (out of 00) Homework 00 Electron Project 9 Test I 7 Atomic Mass Project 9 Test II Phase Change Project 90 Test III 9. WEATHER The table shows the precipitation for the month of Jul in Cape Hatteras, North Carolina, in various ears. Find the mean, median, mode, and range of the data..0;.; no mode; 9.77 Jul Precipitation in Cape Hatteras, North Carolina Year Inches Source: National Climatic Data Center. SCHL Kaitln s scores on her first five algebra tests are, 90, 9, 9, and 9. What test score must Kaitln earn on the sith test so that her mean score will be at least 90? at least 90. GLF Colin s average for three rounds of golf is 9. What is the highest score he can receive for the fourth round to have an average (mean) of 9?. SCHL Mika has a mean score of on his first four Spanish quizzes. If each quiz is worth points, what is the highest possible mean score he can have after the fifth quiz?. 7. SCHL To earn a grade of B in math, Latisha must have an average (mean) score of at least on five math tests. Her scores on the first three tests are, 9, and. What is the lowest total score that Latisha must have on the last two tests to earn a B test average? Prerequisite Skills

12 Bar and Line Graphs A bar graph compares different categories of data b showing each as a bar whose length is related to the frequenc. A double bar graph compares two sets of data. Another wa to represent data is b using a line graph. A line graph usuall shows how data changes over a period of time. EXAMPLE MARRIAGE The table shows the average age at which Americans marr for the first time. Make a double bar graph to displa the data. Step Draw a horizontal and a vertical ais and label them as shown. Step Draw side-b-side bars to represent each categor. Average Age to Marr Year Men 7 Women Source: U.S. Census Bureau Prerequisite Skills Average Age to Marr The legend indicates that the blue bars refer to men and the red bars refer to women. Age Men Women Year The side-b-side bars compare the age of men and women for each ear. EXAMPLE HEALTH The table shows Mark s height at -ear intervals. Make a line graph to displa the data. Age 0 Height (feet) Step Draw a horizontal and a vertical ais. Label them as shown. Step Plot the points. Step Draw a line connecting each pair of consecutive points. Height (feet) 7 0 Mark s Height 0 Age (ears) Eercises -. See Student Handbook Answer Appendi.. HEALTH The table below shows the life epectanc for Americans born in each ear listed. Make a double-bar graph to displa the data. Life Epectanc Year of Birth Male Female MNEY The amount of mone in Beck s savings account from August through March is shown in the table below. Make a line graph to displa the data. Month Amount Month Amount August $00 December $70 September $00 Januar $00 ctober $700 Februar $90 November $70 March $900 Prerequisite Skills

13 Prerequisite Skills 7 Frequenc Tables and Histograms A frequenc table shows how often an item appears in a set of data. A tall mark is used to record each response. The total number of marks for a given response is the frequenc of that response. Frequencies can be shown in a bar graph called a histogram. A histogram differs from other bar graphs in that no space is between the bars and the bars usuall represent numbers grouped b intervals. EXAMPLE TELEVISIN Use the frequenc table of Brad s data. a. How man more chose sports programs than news? b. Which two programs together have the same frequenc as adventures? a. Seven people chose sports. Five people chose news. 7 =, so more people chose sports than news. b. As man people chose adventures as the following pairs of programs. sports and music videos msteries and news msteries and soap operas comedies and music videos Favorite Television Shows Program Tall Frequenc Sports IIII II 7 Msteries IIII Soap operas IIII News IIII Quiz shows IIII I Music videos II Adventure IIII IIII 9 Comedies IIII II 7 EXAMPLE FITNESS A gm teacher tested the number of sit-ups students in two classes could do in minute. The results are shown. a. Make a histogram of the data. Title the histogram. b. How man students were able to do 9 sit-ups in minute? c. How man students were unable to do 0 sit-ups in minute? d. Between which two consecutive intervals does the greatest increase in frequenc occur? What is the increase? Number of Sit-Ups Frequenc a. Use the same intervals as those in the frequenc table on the horizontal ais. Label the vertical ais with a scale that includes the frequenc numbers from the table. b. Ten students were able to do 9 sit-ups in minute. c. Add the students who did 0 sit-ups and 9 sit-ups. So +, or 0, students were unable to do 0 sit-ups in minute. d. The greatest increase is between intervals 9 and 0. These frequencies are and. So the increase is =. Prerequisite Skills

14 Eercises ART For Eercises, use the following information. The prices in dollars of paintings sold at an art auction are shown Make a frequenc table of the data. See Student Handbook Answer Appendi.. What price was paid most often for the artwork? $00. What is the average price paid for artwork at this auction? $9.. How man works of art sold for at least $00 and no more than $00? Prerequisite Skills PETS For Eercises 9, use the following information. Number of Pets per Famil Use a frequenc table to make a histogram of the data. See Student Handbook Answer. How man families own two to three pets? Appendi. 7. How man families own more than three pets?. To the nearest percent, what percent of families own no pets? 9% 9. Name the median, mode, and range of the data. median =, mode =, range = TREES For Eercises 0, use the histogram shown. 0. Which interval contains the most evergreen seedlings? 0 9. Which intervals contain an equal See Student number of trees? Handbook Answer Appendi.. Which intervals contain 9% of the data? See Student Handbook Answer Appendi.. Between which two consecutive intervals does the greatest increase in frequenc occur? What is the increase? See Student Handbook Answer Appendi.. MARKET RESEARCH A civil engineer is studing traffic patterns. She counts the number of cars that make it through one rush hour green light ccle. rganize her data into a frequenc table, and then make a histogram See Student Handbook Answer Appendi. Prerequisite Skills 7

15 Prerequisite Skills Stem-and-Leaf Plots In a stem-and-leaf plot, data are organized in two columns. The greatest place value of the data is used for the stems. The net greatest place value forms the leaves. Stem-and-leaf plots are useful for organizing long lists of numbers. EXAMPLE SCHL Isabella has collected data on the GPAs (grade point average) of the students in the art club. Displa the data in a stem-and-leaf plot. {.0,.9,.,.9,.,.7,.,.,.0,.9,.,.,.9,.,.,.} Step Find the least and the greatest number. Then identif the greatest place-value digit in each number. In this case, ones. least data:. greatest data:.0 The least number has The greatest number in the ones place. has in the ones place. Step Draw a vertical line and write the stems from to to the left of the line. Step Write the leaves to the right of the line, with the corresponding stem. For eample, write 0 to the right of for.0. Step Rearrange the leaves so the are ordered from least to greatest. Step Include a ke or an eplanation. Stem Stem Leaf Leaf =. Eercises GAMES For Eercises, use the following information. The stem-and-leaf plot at the right shows Charmaine s scores for her favorite computer game.. What are Charmaine s highest and lowest scores? 0; 90. Which score(s) occurred most frequentl? 90, 9. How man scores were above?. Has Charmaine ever scored? no. SCHL The class scores on a 0-item test are shown in the table at the right. Make a stem-and-leaf plot of the data.. See Student Handbook Answer Appendi.. GEGRAPHY The table shows the land area of each count in Woming. Round each area to the nearest hundred square miles and organize the data in a stem-and-leaf plot. Prerequisite Skills Stem Leaf = Test Scores Count Area (mi) Count Area (mi) Count Area (mi) Alban 7 Hot Springs 00 Sheridan Big Horn 7 Johnson Sublette Campbell 797 Laramie Sweetwater 0, Carbon 79 Lincoln 09 Teton 00 Converse Natrona 0 Unita 0 Crook 9 Niobrara Washakie 0 Fremont 9 Park 9 Weston 9 Goshen Platte 0 Source: The World Almanac

16 9 Bo-and-Whisker Plots In a set of data, quartiles are values that divide the data into four equal parts. median lower half upper half } } The median of the lower half of a set The median of the upper half of a set of data is the lower quartile, or LQ. of data is the upper quartile, or UQ. Prerequisite Skills To make a bo-and-whisker plot, draw a bo around the quartile values, and lines or whiskers to represent the values in the lower fourth of the data and the upper fourth of the data EXAMPLE MNEY The amount spent in the cafeteria b 0 students is shown. Displa the data in a bo-and-whisker plot. Step Find the least and greatest number. Then draw a number line that covers the range of the data. In this case, the least value is and the greatest value is.. Amount Spent $.00 $.00 $.00 $.00 $.00 $.0 $.0 $.00 $.0 $.00 $.00 $.0 $.0 $.00 $.00 $.0 $.00 $.00 $.0 $.0 Step Find the median, the etreme values, and the upper and lower quartiles. Mark these points above the number line.,,,.,,,,,.,.,.,.,.,,.,,,,,. LQ = _ + or M = least value: $ $ $ $ $ $ $ lower quartile: $ median: $ $ $ $ $ $ $ Step Draw a bo and the whiskers. upper quartile: $.7 or. UQ =. + or.7 greatest value: $.0 $ $ $ $ $ $ The interquartile range (IQR) is the range of the middle half of the data and contains 0% of the data in the set. Interquartile range = UQ - LQ The interquartile range of the data in Eample is.7 - or.7. An outlier is an element of a set that is at least. interquartile ranges less than the lower quartile or greater than the upper quartile. The whisker representing the data is drawn from the bo to the least or greatest value that is not an outlier. Prerequisite Skills 9

17 Prerequisite Skills EXAMPLE SCHL The number of hours José studied each da for the last month is shown in the bo-and-whisker plot below. 0 a. What percent of the data lies between. and.? The value. is the lower quartile and. is the upper quartile. The values between the lower and upper quartiles represent 0% of the data. b. What was the greatest amount of time José studied in a da? The greatest value in the plot is, so the greatest amount of time José studied in a da was hours. c. What is the interquartile range of this bo-and-whisker plot? The interquartile range is UQ - LQ. For this plot, the interquartile range is. -. or.7 hours. d. Identif an outliers in the data. An outlier is at least.(.7) less than the lower quartile or more than the upper quartile. Since. + (.)(.7) =.7, and >.7, the value is an outlier, and was not included in the whisker. Eercises DRIVING For Eercises, use the following information. Tler surveed 0 randoml chosen students at his school about how man miles the drive in an average da. The results are shown in the bo-and-whisker plot What percent of the students drive more than 0 miles in a da? %. What is the interquartile range of the bo-and-whisker plot? 7 mi. Does a student at Tler s school have a better chance to meet someone who drives the same mileage the do if the drive 0 miles in a da or miles in a da? Wh?. See Student Handbook Answer Appendi.. SFT DRINKS Carlos surveed his friends to find the number of cans of soft drink the drink in an average week. Make a bo-and-whisker plot of the data. {0, 0, 0,,,,,,,,,,, 7, 0, 0, 0,, }. BASEBALL The table shows the number of sacrifice hits made b teams in the National Baseball League in one season. Make a bo-andwhisker plot of the data.. ANIMALS The average life span of some animals commonl found in a zoo are as follows: {, 7, 7, 0,,,,,, 0, 0, 0,, 0, 00}. Make a bo-and-whisker plot of the data. Team Home Runs Team Home Runs Arizona 7 Milwaukee Atlanta Montreal Chicago 7 New York Cincinnati Philadelphia 7 Colorado Pittsburgh 0 Florida 0 San Diego 9 Houston 7 San Francisco 7 Los Angeles 7 St. Louis Source: ESPN 90 Prerequisite Skills

18 Etra Practice Lesson - (pages 0) _ Evaluate each epression if q =, r =., s = -, and t =.. qr - st. qr st. qrst. qr + st. _ q s. _ qr t 7. r(s - ) t Evaluate each epression if a = -0., b =, c =, and d = -.. q s + t - 9. b + d 0. ab + c. bc + d a. 7ab - d. ad + b - c. a + c b. ab - d a. a + ad bc Lesson - (pages 7) Name the sets of numbers to which each number belongs. (Use N, W, Z, Q, I, and R.) _ Name the propert illustrated b each equation. 7. ( + 9a)b = b( + 9a). _ ( = ) 9. a( - ) = a - a 0. (-b) + b = 0. jk + 0 = jk. (a)b = (ab) Etra Practice Simplif each epression.. 7s + 9t + s - 7t. (a + b) + (a - b). ( - ) - ( + ). 0.(m - ) + 0.( - m) 7. _ (7p + q) + _ (p - q). _ (v - w) - _ (7v - w) Lesson - (pages ) Write an algebraic epression to represent each verbal epression.. twelve decreased b the square of. twice the sum of a number and a number negative nine. the product of the square of a number. the square of the sum of a number and and Name the propert illustrated b each statement.. If a + =, then (a + ) = ().. If + ( + ) =, then + 9 =. 7. If 7 =, then 7 - = -.. If + = and =, then + =. Solve each equation. Check our solution. 9. t + = = -. _ = _ +. s - = (s + ). (k - ) = k +. 0.z + 0 = z +. q - _ q =. - _ 7 r + _ 7 = 7. d - = _ (d - ) Solve each equation or formula for the specified variable.. C = πr; for r 9. I = Prt, for t 0. m = _ n - n, for n Etra Practice 9

19 Lesson - (pages 7 ) Evaluate each epression if = -, =, and z = z. - + z z Etra Practice Solve each equation. Check our solutions. 9. d + = 7 0. a - = 0. - =. t =. p =. g - =. + =. b - 0 = b = 0. c + - = m - = 0. + z + = 0. d =. t = 0. d - = d = 7 +. b + - = b +. t + = t + Lesson - (pages 9) Solve each inequalit. Then graph the solution set on a number line.. z + 7. r - > b <. - >. (f + ). - > g ( - ) -9. 7a + > a (b - ) b ( - ) < ( - ). (c - ) > c +. (d + ) - (d + ). - t < ( - t). - _ +. _ a + _ 7 + a 7. - < _ + 7. ( - ) - ( - ). s - (s + 7) > - s Define a variable and write an inequalit for each problem. Then solve. 9. The product of 7 and a number is greater than. 0. The difference of twice a number and is at most.. The product of -0 and a number is greater than or equal to 0.. Thirt increased b a number is less than twice the number plus three. Lesson - (pages ) Write an absolute value inequalit for each of the following. Then graph the solution set on a number line.. all numbers less than -9 and greater than 9. all numbers between -. and.. all numbers greater than or equal to - and less than or equal to Solve each inequalit. Graph the solution set on a number line.. m - < 7 or m + >. < n + < 7. - s - 7. t + -7 or t < or - > p. 7d -. a + <. t - >. - <. d <. v + > 9. r + < 0. w - 9. z q < 0. h + < 0. n - 9 Etra Practice

20 Lesson - (pages ) State the domain and range of each relation. Then determine whether each relation is a function. Write es or no.. Year Population 970,0 90, 990,0 000,0.. Graph each relation or equation and find the domain and range. Then determine whether the relation or equation is a function and state whether discrete or continuous.. {(, ), (, ), (, ), (, )}. {(0, ), (0, ), (0, ), (0, 0)}. = - 7. = -. = 9. = - Find each value if f() = + 7 and g() = ( + ). 0. f(). f(-). f(a + ). g(). g(-). f(0.). g(b - ) 7. g(c) Etra Practice Lesson - (pages 70) State whether each equation or function is linear. Write es or no. If no, eplain our reasoning.. _ - = 7. = +. g() = _. f() = 7 - Write each equation in standard form. Identif A, B, and C =. = - 7. = 7 +. = _ = = - Find the -intercept and the -intercept of the graph of each equation. Then graph the equation.. + =. - = -. = -. =. _ - =. = - Lesson - (pages 7 77) Find the slope of the line that passes through each pair of points.. (0, ), (, 0). (, ), (, 7). (, ), (, -). (., -), (,.). _ (-, _, _ ) ( 0, - _. (-, c), (, c) ) Graph the line passing through the given point with the given slope. 7. (0, );. (, ); 0 9. (-, ); - _ Graph the line that satisfies each set of conditions. 0. passes through (0, ), parallel to a line with a slope of -. passes through (, -), perpendicular to the graph of - + = Etra Practice 9

21 Lesson - (pages 79 ) Write an equation in slope-intercept form for each graph... (, ) (, ) (,) Etra Practice Write an equation in slope-intercept form for the line that satisfies each set of conditions.. slope -, passes through (7, ). slope _, passes through the origin. passes through (, -) and (-, ). -intercept -, -intercept 7. passes through (, ), parallel to the graph of + =. passes through (0, 0), perpendicular to the graph of + = Lesson - (pages 9) Complete parts a c for each set of data in Eercises. a. Draw a scatter plot and describe the correlation. b. Use two ordered pairs to write a prediction equation. c. Use our prediction equation to predict the missing value.. Telephone Costs. Washington. Federal Minimum Minutes Cost ($) Year Population Wage ,, Year Wage ,, 9 $ ,, 990 $ ,,9 99 $ ,9, 99 $.7? 00? 997 $. 0? Source: The World Almanac Source: The World Almanac Lesson - (pages 9 0) Identif each function as S for step, C for constant, A for absolute value, or P for piecewise... Graph each function. Identif the domain and range.. f() = +. g() = -. f() = -. h() = - 7. h() = -. g() = + 9. h() = { if < - 0. f() = if - { - if - if > 9 Etra Practice

22 Lesson -7 (pages 0 0) Graph each inequalit.. -. < > < - 7. > _ _ _ -. - < > < < _ - Lesson - (pages ) Solve each sstem of equations b graphing or b completing a table.. + =. - =. + = - + = 7 - = 0 _ + =. + = 0. - = 7. = _ + + = _ - _ = - = + Graph each sstem of equations and describe it as consistent and independent, consistent and dependent, or inconsistent =. - = 9. = = - = - = = 7. _ - = 0. _ = _. -. =. _ + _ = - = 0 Etra Practice Lesson - (pages 9) Solve each sstem of equations b using substitution.. + = 0. = = -7 + = + = - + = -7 Solve each sstem of equations b using elimination = 9. r + s = -7. p + q = 0 - = r - s = - p - q = - Solve each sstem of equations b using either substitution or elimination = 7. a + b = - 9. c + d = - + = a - b = c - d = =. m + n =. = - = - 9 m - n = - - =.. +. = -. _ + _ =. _ 7 c - _ d = = _ - = -7 _ 7 c + _ d = - Etra Practice 9

23 Lesson - (pages 0 ) Solve each sstem of inequalities... <. + <. + < < < _ > + 9. > Etra Practice Find the coordinates of the vertices of the figure formed b each sstem of inequalities _ + _ 7 -_ _ + _ Lesson - (pages ) A feasible region has vertices at (-, ), (, ), (, ), and (, -). Find the maimum and minimum values of each function.. f(, ) = -. f(, ) = +. f(, ) = -. f(, ) = - +. f(, ) = -. f(, ) = - Graph each sstem of inequalities. Name the coordinates of the vertices of the feasible region. Find the maimum and minimum values of the given function for this region f(, ) = + f(, ) = + f(, ) = f(, ) = f(, ) = + f(, ) = + Lesson - (pages ) For each sstem of equations, an ordered triple is given. Determine whether or not it is a solution of the sstem z = -. u + v + w =. + = z = - u - v + w = -9 + z = z = ; u - v - w = -; + z = ; (-,, ) (,, -) (-, -, ) Solve each sstem of equations.. a =. s + t =. u - v = b - c = 7r - s + t = 0 v + w = - a + 7c = - t = u - w = 7. a + b - c =. + - z = z = 7 a + b - c = z = z = a - b + c = + + z = - + z = 9 Etra Practice

24 Lesson - (pages 7) Solve each matri equation.. [ -z] = [ -z ]. + - =. - w + - z = z. = 0-0 z. - = z = = - +. = 0 z - - Lesson - (pages 9 7) Perform the indicated matri operations. If the matri does not eist, write impossible [0 - ] [- 9] - [ -7 ] Etra Practice Use matrices A, B, C, D, and E to find the following. A = A + B. C + D 9. A - B 0. B. D - C. E + A. D - B. A + E - D Lesson - (pages 77 ) Find each product, if possible.. [- ] Etra Practice 97

25 Lesson - (pages 9) For Eercises, use the following information. The vertices of quadrilateral ABCD are A(, ), B(-, ), C(-, -), and D(, -). The quadrilateral is dilated so that its perimeter is times the original perimeter.. Write the coordinates for ABCD in a verte matri.. Find the coordinates of the image A'B'C'D'.. Graph ABCD and A'B'C'D'. Etra Practice For Eercises 0, use the following information. The vertices of MQN are M(, ), Q(, -), and N(, -).. Write the coordinates of MQN in a verte matri.. Write the reflection matri for reflecting over the line =.. Find the coordinates of M'Q'N' after the reflection. 7. Graph MQN and M'Q'N'.. Write a rotation matri for rotating MQN 90 counterclockwise about the origin. 9. Find the coordinates of M'Q'N' after the rotation. 0. Graph MQN and M'Q'N'. Lesson - (pages 9 00) Evaluate each determinant using epansion b minors Evaluate each determinant using diagonals Lesson - (pages 0 07) Use Cramer s Rule to solve each sstem of equations.. - = 9. p - q =. - + = 7 + = p + q = 0 + =. _ - _ = -. _ c + _ d =. 0.a +.b = 0. _ + _ = - _ c - _ d = - 0.a +.b = z =. a + b - c = - 9. r + s - t = z = - a - b + c = -r + s + t = + - z = - -a - b + c = r - s + t = -9 9 Etra Practice

26 Lesson -7 (pages 0 ) Determine whether each pair of matrices are inverses.. A = -7. X = 0-7, B = -7 0, Y = C = -. N = 0 -, D = - - 0, M = - - Find the inverse of each matri, if it eists Lesson - (pages ) Write a matri equation for each sstem of equations.. a + b =. + = -. m + n = a - b = 9 - = m - n = c - d = z =. a - b - c = c - d = z = a + b + c = + + z = a - b - c = - Etra Practice Solve each matri equation or sstem of equations = = = = 7. m + n =. c + d = 7. a - b = + = m + n = c - 0d = - a + b =. r - 7s =. + = -. m - n = 7. + = -r + s = = -m + 9n = - - = - Lesson - (pages ) For Eercises, complete parts a c for each quadratic function. a. Find the -intercept, the equation of the ais of smmetr, and the -coordinate of the verte. b. Make a table of values that includes the verte. c. Use this information to graph the function.. f() =. f() = -. f() = +. f() = - -. f() = +. f() = f() = + -. f() = f() = f() = + -. f() = f() = Determine whether each function has a maimum or a minimum value and find the maimum or minimum value. Then state the domain and range of the function.. f() = 9. f() = 9 -. f() = - +. f() = f() = - 9. f() = f() = f() = - + _. f() = - + _ + _ Etra Practice 99

27 Lesson - (pages ) Use the related graph of each equation to determine its solutions = 0. - = = 0 f () f() f () f () f() f() Etra Practice Solve each equation b graphing. If eact roots cannot be found, state the consecutive integers between which the roots are located.. - = = = = = = = 0. + =. = = = = 0 Lesson - (pages ) Solve each equation b factoring = 0. = = 9. = - 0. = 0. - = =. = = 0. - = =. - = = =. + 7 =. - = Write a quadratic equation with the given roots. Write the equation in the form a + b + c = 0, where a, b, and c are integers. 7.,. -, 9. -, , _. -, _. - _, - _ Lesson - (pages 9 ) Simplif _. -b. t -_ 7s. (7i). (i)(-i)(i) 7. ( -)( -). -i 9. i 7 i i 0. ( - i) + (- + 9i). (7i) - ( + i). ( + i) - ( + i). (7 + i)(7 - i). ( - i)( + i). ( + i). 7. i. - 7i - i + i + i Solve each equation = 0. _ 9 + =. + =. - 9 = =. _ + = Etra Practice

28 Lesson - (pages 7) Find the value of c that makes each trinomial a perfect square. Then write the trinomial as a perfect square c c. - + c. - _ + c c. + _ + c 7. - _ + c. - + c Solve each equation b completing the square = = = = = = = = = = = = = = = = = = = = = 0 Etra Practice Lesson - (pages 7 ) For Eercises, complete parts a c for each quadratic equation. a. Find the value of the discriminant. b. Describe the number and tpe of roots. c. Find the eact solutions b using the Quadratic Formula = = = = = 0. = = = = =. 7 =. = = = = 0 Solve each equation b using the method of our choice. Find eact solutions = = 0. + = 9 9. = =. + + = = = 0. = 0 Lesson -7 (pages 9) Write each quadratic function in verte form, if not alread in that form. Then identif the verte, ais of smmetr, and direction of opening.. = ( + ) -. = ( - ) -. = -( + ) + 7. = -9( - 7) +. = = Graph each function. 7. = - +. = = = = _ = = + +. = = Etra Practice 90

29 Lesson - (pages 9 0) Graph each inequalit > > Etra Practice Use the graph of the related function of each inequalit to write its solutions < 0 Solve each inequalit algebraicall < > > Lesson - (pages ) Simplif. Assume that no variable equals m m m (-) (-). _ t t. -_ 7. _. _ p q 7 p q 9. -(m ) 0. ( ) (abc). ( ). (b ). (- ) ( ) -. (-) ( ). ( a7 b c). Evaluate. Epress the result in scientific notation. _ - _ 7. a + a -. ( )(. 0 7 ). (. 0 )( ) 7. (. 0 )( ) (. 0 ) Lesson - (pages 0 ) Simplif.. ( ) + ( ). ( - + ) + (7 + - ). ( ) + (- - + ). ( ) - (- - + ). 7_ uw ( u w - uw + _ 7u) w ( ) 7. ( - )( + 7). ( - )(- - ) 9. ( - )( - ) 0. ( + )( - ). ( - 7)( + 7). ( + w)( - w). (a + )(a - ). (- + 0)(- - 0). ( - ). ( + ) 7. (- + ). _ ( + + ) 9. - _ a (a - a + a) 90 Etra Practice

30 Lesson - (pages 0) Find p() and p(-) for each function.. p() = 7 -. p() = p() = + -. p() = - +. p() = -. p() = _ + 7. p() = p() = p() = - If p() = and q() = -, find each value. 0. q(n). p(b). q(z ). p(m ). q( + ). p( - ). q(a - ) 7. q(h - ). [p(c - )] 9. q(n - ) + q(n ) 0. -p(a) - p(a). [q(d + )] + q(d) Lesson - (pages ) For Eercises, complete each of the following. a. Graph each function b making a table of values. b. Determine the values of between which the real zeros are located. c. Estimate the -coordinates at which the relative maima and relative minima occur.. f() = + -. f() = f() = f() = f() = f() = f() = f() = f() = f() = f() = f() = f() = f() = f() = f() = Etra Practice Lesson - (pages 9 ) Factor completel. If the polnomial is not factorable, write prime.. a b c - a b c + 7a b c. 0a - - ab + b p - pq - q t a - b. a + a - a ac - bd - 7ad + bc. h - 0hj + h - j Simplif. Assume that no denominator is equal to Etra Practice 90

31 Etra Practice Lesson - (pages 9 ) Simplif.. r s + r s 9r s. v w - v w -v w (bh + ch) (b + c). (c d + 0c d - cd) cd. (f + 0f 9 - f ) f 7. (m + mn - m )(m) -. (g + 9g - g + 9) (g + ) 9. (p + p + p 7 - )(p 7 + ) - 0. (k - k + 9) (k - 7). (r + r - ) (r + ). (n + ) (n + ). ( ) ( - ). (q + q + q + 7) (q + ). (v + v - v + ) (v - ). ( ) ( + ) 7. (s + s - 7) (s + ). (t - t + t - t + ) (t - ) 9. (z - z - z - z - ) (z - ) 0. (r - r - r + r - ) (r + ). (b - b + b + 9) (b - ) Lesson -7 (pages ) Use snthetic substitution to find f() and f(-) for each function.. f() = - +. f() = + -. f() = f() = f() = f() = 0 + Given a polnomial and one of its factors, find the remaining factors of the polnomial. Some factors ma not be binomials. 7. ( ); ( + ). ( ); ( - ) 9. ( ); ( - ) 0. ( - ); ( - ). ( + + ); ( + ). ( ); ( + ). ( ); ( - 7). ( ); ( - ). ( ); ( + ). ( ); ( - ) 7. ( ); ( - 7). ( ); ( + ) Lesson - (pages ) Solve each equation. State the number and tpe of roots = = 0. - = - 0 State the number of positive real zeros, negative real zeros, and imaginar zeros for each function.. f() = f() = f() = f() = f() = f() = Find all of the zeros of the function. 0. f() = f() = f() = f() = f() = f() = Etra Practice

32 Lesson -9 (pages 9 7) List all of the possible rational zeros for each function.. f() = f() = f() = 9-7 Find all of the rational zeros for each function.. f() = f() = f() = f() = f() = f() = Find all of the zeros of each function. 0. f() = f() = f() = Lesson 7- (pages 90) Find (f + g)(), (f - g)(), (f g)(), and ( f _ g ) () for each f() and g().. f() = +. f() =. f() = -. f() = + g() = - g() = g() = + g() = + Etra Practice For each set of ordered pairs, find f g and g f, if the eist.. f = {(-, ), (, -), (-, )}. f = {(0, ), (, -), (-9, )} g = {(, -), (-, ), (, -)} g = {(-, ), (, ), (, )} 7. f = {(, ), (, ), (-, ), (, 0)}. f = {(0, ), (-, ), (, ), (-, 0)} g = {(, ), (, ), (, -), (0, )} g = {(-, 0), (, -9), (-7, ), (-, -)} Find [g h]() and [h g](). 9. g() = - 0. g() = - 7. g() = + 7. g() = + h() = h() = + h() = _ - 7 h() = - If f() = +, g() =, and h() = -, find each value.. g[ f()]. [f h](). [h f ](). [g f ](-) 7. g[h(-0)]. f[h(-)] 9. g[ f(a)] 0. [f (g f)](c) Lesson 7- (pages 9 9) Find the inverse of each relation.. {(-, 7), (, 0), (, -)}. {(-, 9), (-, ), (, 9), (-, )} Find the inverse of each function. Then graph the function and its inverse.. f() = - 7. = +. g() = -. = = -. g() = - 9. h() = _ + 0. h() = - _. = _ -. = _ -. f() = +. g() = - Determine whether each pair of functions are inverse functions.. f() = -. f() = - 7. f() = -. f() = - 7 g() = - g() = _ + g() = - _ g() = _ + 7 Etra Practice 90

33 Lesson 7- (pages 97 0) Graph each function. State the domain and range of the function.. = -. = + 7. = - 0. = +. = + -. = -. = +. = + -. = _ +. = 9. = -. = - + Graph each inequalit.. >. < < - + Etra Practice Lesson 7- (pages 0 0) Use a calculator to approimate each value to three decimal places Simplif. 9. 9h _ ,000. -d 9. ). _ (- 9 a b. ± p q r s 0 ( - ). ± m n. - ( - ) (r + s). 9a + a ± a + a + a + Lesson 7- (pages 0 ) Simplif r ( - ). - ( - ). ( + )( + ). ( + )( - ). ( + ) 7. ( + )( - ). ( + ) 9. ( - 7 )( + 7 ) 0. ( - 7 ). _ m _.. _ a Etra Practice. _ r s t. _ _ 7 n

34 Lesson 7- (pages ) Write each epression in radical form.. 0 _. _. a _. (b ) _ Write each radical using rational eponents a. ab c Evaluate each epression _ 0. 7 _. (-) _. - _ 7) -. (-) - _. _ _. - _ _. ( Simplif each epression _ 9 7 _ 9. _ _ 9. ( k _ ) 0. _ _. m _ m _. ( p _ q 7_. 9. _ t 9_ 9a 0. _ ). a - _ ( 9_ c _ ). 7 r_ r 7_. v _ 7 - v _ 7 v _ _ + _ Etra Practice Lesson 7-7 (pages 7) Solve each equation or inequalit.. =. s - =.. z + = 7. m = 9 a + =. d + d - = 7. g + = g +. - = > 0. n -. w < c < -. + >. c > 0 7. n + -. z - - = (n - ) _ = 0 0. (7 - ) _ + =. (a - ) _ Lesson - (pages 9) Simplif each epression.. _. _ - _ _ _ 7 0. _ 9u v _ 7u v.. -a b ab. (-cd ) c d. _ - _ 0 7. _ u _ u. _ _ a a _ _ (ab) _ c. _ a b c Etra Practice 907

35 Lesson - (pages 0 ) Find the LCM of each set of polnomials.. a b, ab, 0a. - -, Etra Practice Simplif each epression.. _ 7d - _. _ + d -_ _ +. 7_ + _ 7. _ - + _ ( - ). _ - _ _. m + - m. _ - m _ -. a - - a. 7. c + a + c _ + + _ 9. - z - z + z _ - _ v + _ uv + _ u c + c _ _ - Lesson - (pages 7 ) Determine the equations of an vertical asmptotes and the values of for an holes in the graph of each rational function.. f() = _. f() = _ -. f() = + + ( + )( - ). f() = _. f() = -. f() = Graph each rational function. 7. f() = _. f() = _ 9. f() = f() = _. f() = - ( - ). f() = ( + )( - ). f() = + -. f() = _ + +. f() = Lesson - (pages 7) State whether each equation represents a direct, joint, or inverse variation. Then name the constant of variation.. = 0. _ 7 =. _ = -. = _. A = lw 7. _ b = - _. 0 = c. D = rt 9. If varies directl as and = when =, find when =. 0. If varies inversel as and = when = -, find when = -.. If m varies directl as w and m = - when w =., find m when w =... If varies jointl as and z and = 0 when z = and =, find when = and z =.. If varies inversel as and = _ when =, find when = _. 90 Etra Practice

36 Lesson - (pages 7 7) Identif the tpe of function represented b each graph.... Identif the function represented b each equation. Then graph the equation.. = 7. = -. = _ 0. = - +. = + -. = _. = =. = - Etra Practice Lesson - (pages 79 ) Solve each equation or inequalit. Check our solutions.. _ - = _. _ + _ = _. _ b - <. _ a + >. _ - = _ _ - n < n 7. _ d + _ d - = = 0 9. _ n + + _ n - = n - 0. p_ p + + _ + = 0. z + p - z - = _ -z - z + _. _ z = _ +. m - = m. + m _ - =. n + _ n + = _ n n - Lesson 9- (pages 9 0) Sketch the graph of each function. Then state the function s domain and range.. = (). = 0.(). = ( _ ). = (.) Determine whether each function represents eponential growth or deca.. = (). = 0-7. = ( _ ). = ( _ ) Write an eponential function for the graph that passes through the given points. 9. (0, ) and (, ) 0. (0, -) and (-, -). (0,.) and (, 0.) Solve each equation or inequalit. Check our solution = < +. + = > _ ( ) - =. + = 9. = - Etra Practice 909

37 Lesson 9- (pages 09 7) Write each equation in logarithmic form.. =. 0 = = _ Write each equation in eponential form.. log _ = -. log = _. log 7 _ 7 = - Etra Practice Evaluate each epression. 7. log. log 0 0, log _ 0. log 9 0. log. log _. log. log 0 Solve each equation or inequalit. Check our solutions.. log b =. log < 7. log _ n = - _ 9. log 7 = 9. log _ a < 0. log ( - 9) = Lesson 9- (pages 0 ) Use log. and log 7.77 to approimate the value of each epression.. log 7 _. log. log Solve each equation. Check our solutions.. log + log ( - ) = log. log = log + log. log ( + 7) = _ log 7. log ( - 9) =. log ( + ) + log = 9. log + log ( - ) = 0. log ( + ) = log - log. log - log ( - ) =. log = _ log 9 + log. log ( + ) + log ( - ) =. log + log = log. log 0 = _ log 0 Lesson 9- (pages ) Use a calculator to evaluate each epression to four decimal places.. log. log.7. log.. log 0.0. log 9.9. log 0. Solve each equation or inequalit. Round to four decimal places. 7. =. a > 9. 7 = 0. + > 7.. a - 7 = 9.. b =. 7 c < c -. m + = < +. 9 n - = n + 7. t + t +. a - = a + Epress each logarithm in terms of common logarithms. Then approimate its value to four decimal places. 9. log 0. log. log. log 90 Etra Practice

38 Lesson 9- (pages ) Use a calculator to evaluate each epression to four decimal places.. e. e 0.7. e -. e -.. ln. ln 7. ln.. ln 0. Write an equivalent eponential or logarithmic equation. 9. e = 0 0. ln.0. e = 9. ln 0. = Solve each equation or inequalit.. e = 000. e 0.07 >. e <.. -e + = 7. + e = 7. e - 9. ln 7 = 0 0. ln =. ln 9. ln ( + ) =. ln ( + ) > 0. ln ( - ) = Lesson 9- (pages 0). FARMING Mr. Rogers purchased a combine for $7,000 for his farming operation. It is epected to depreciate at a rate of % per ear. What will be the value of the combine in ears?. REAL ESTATE The Jacksons bought a house for $,000 in 99. Houses in the neighborhood have appreciated at the rate of.% a ear. How much is the house worth in 00?. PPULATIN In 90, the population of a cit was 0,000. Since then, the population has increased b.% per ear. If it continues to grow at this rate, what will the population be in 00?. BEARS In a particular state, the population of black bears has been decreasing at the rate of 0.7% per ear. In 990, it was estimated that there were 00 black bears in the state. If the population continues to decline at the same rate, what will the population be in 00? Etra Practice Lesson 0- (pages ) Find the midpoint of the line segment with endpoints at the given coordinates.. (7, -), (-, ). (, 9), (-7, ). (, -), (-7, -) ). _ (-, _, _ ) (-, - _. (-7.,.), (.9, -9.). ( _, _ ), ( _, _ Find the distance between each pair of points with the given coordinates. 7. (, 7), (, 9). (-, -), (, ) 9. (-, ), (7, -) 0. (, -), (-, -9). (.9, -0.), (.0, -0.). (, ), (-, - ). _ (, 0 ), _ (-,. ) (, -, _ ) (-, ). A circle has a radius with endpoints at (-, ) and (, -). Find the circumference and area of the circle. Write the answer in terms of π.. Triangle ABC has vertices A(0, 0), B(-, ), and C(, ). Find the perimeter of the triangle. ) Etra Practice 9

39 Lesson 0- (pages 7 7) Write each equation in standard form.. = = = - + Etra Practice Identif the coordinates of the verte and focus, the equations of the ais of smmetr and directri, and the direction of opening of the parabola with the given equation. Then find the length of the latus rectum and graph the parabola.. + =. = ( + ). ( + ) = ( - ) 7. + =. = = ( - ) = ( + ). = ( + ) = 0. = - _ + _ - 7. = =. = = - +. = + + Write an equation for each parabola described below. Then graph. 9. focus (, ), directri = - 0. verte (-, ), directri = - Lesson 0- (pages 7 79) Write an equation for the circle that satisfies each set of conditions.. center (, ), r = units. center (-, ), r = units. center (, -), r = _ units. center (0, 7), tangent to -ais. center (-, -), tangent to -ais. endpoints of a diameter at (-9, 0) 7. endpoints of a diameter at (, ) and (, -) and (-, ). center (, -0), passes through origin 9. center (0., 0.), passes through (, ) Find the center and radius of the circle with the given equation. Then graph =. ( - ) + ( + ) = = = -. + = ( - ) ( - ) =. + = = = Lesson 0- (pages ) Write an equation for the ellipse that satisfies each set of conditions.. endpoints of major ais at (-, 7) and (, 7), endpoints of minor ais at (, ) and (, 9). endpoints of minor ais at (, -) and (, ), endpoints of major ais at (-, 0.) and (, 0.). major ais units long and parallel to the -ais, minor ais units long, center at (0, ) Find the coordinates of the center and foci and the lengths of the major and minor aes for the ellipse with the given equation. Then graph the ellipse.. _ + _ =. _ ( - ) + =. ( + ) ( + ) + = 7. + =. 7 + = = = = -. + = ( + ) = 0 9 Etra Practice

40 Lesson 0- (pages 90 97) Find the coordinates of the vertices and foci and the equations of the asmptotes for the hperbola with the given equation. Then graph the hperbola.. _ - _ =. _ 9 - _ =. _ 9 - _ = ( - ). ( + ) - ( - 7) =. - ( - ) =. ( + ) ( + ) - = =. - 9 = = = ,9. ( + ) - 0( - ) = 00 Write an equation for the hperbola that satisfies each set of conditions.. vertices (-, 0) and (, 0); conjugate ais of length units. vertices (0, -7) and (0, 7); conjugate ais of length units. center (0, 0); horizontal transverse ais of length units and a conjugate ais of length 0 units Lesson 0- (pages 9 0) Write each equation in standard form. State whether the graph of the equation is a parabola, circle, ellipse, or hperbola. Then graph the equation = = = 0. 9 = = 0. + = = = = + ( - ) 0. - ( + ) = =. - = Etra Practice Without writing the equation in standard form, state whether the graph of each equation is a parabola, circle, ellipse, or hperbola.. ( + ) = ( + ) =. - + = 0. ( - ) + ( + ) = 9 Lesson 0-7 (pages 0 0) Solve each sstem of inequalities b graphing.. _ - _ ( - ) < + Find the eact solution(s) of each sstem of equations.. _ + _ =. = 7. _ = + ( + ) + =. ( + ) - = = + ( - ) + _ = 9. + = 0. _ - _ = = + - = - = -. + = =. + = 0 + = - = = Etra Practice 9

41 Lesson - (pages ) Find the net four terms of each arithmetic sequence.. 9, 7,,....,.,,.... 0,, 0,....,,,... Find the first five terms of each arithmetic sequence described.. a =, d = 7. a = -, d = 7. a =., d =.7. a = - _, d = - _ Find the indicated term of each arithmetic sequence. 9. a =, d =, n = 0 0. a = -0, d = -, n =. a = -, d =, n = Etra Practice Write an equation for the nth term of each arithmetic sequence..,, 7, 9,...., -, -, -7,.... 0,,,,... Find the arithmetic means in each sequence..,?,?,?,. 0,?,?,?, ,?,?,?, Lesson - (pages 9 ) Find S n for each arithmetic series described.. a =, a n = 0, n =. a = 90, a n = -, n = 0. a =, a n =, n =. a = -, d = 0, n = 0. a =, d = -, n =. a =, d = - _, n = 7 Find the sum of each arithmetic series. 7. (n + ) 0. (n - ) 9. (0 - k) n= n= k= 0. ( - k). (0n + ) 0. ( + n) k= n= n= Find the first three terms of each arithmetic series described.. a =, a n =, S n =. n =, a n =, S n = -. n =, a n =, S n = 0 Lesson - (pages ) Find the net two terms of each geometric sequence..,,,...., 0, 0,....,,, , 7, -, , 0.7,.,.... _, - _, _ 9,... Find the first five terms of each geometric sequence described. 7. a = -, r =. a =, r = - 9. a = 0., r =. 0. a = - _, r = - _ Find the indicated term of each geometric sequence.. a =, r = 7, n =. a = 00, r = - _, n = 0. a = 0, r = -, n = Write an equation for the nth term of each geometric sequence.. 0, 0, 0, _, - _, - _,... Find the geometric means in each sequence..,?,?,?, 7.,?,?,?, 0 9 Etra Practice

42 Lesson - (pages 9) Find S n for each geometric series described.. a = _, r =, n =. a =, r = -, n = 7. a =, r =, n =. a = -7, r = - _, n =. a = 000, r = _, n = 7. a =, r = - _, n = 7. a = 0, r =, n =. a = 0, r = - _, n = 9. a =, r = _, n = 0. a =, r = _, n =. a = 7, r =, n = 7. a = - _, r = - _, n = Find the sum of each geometric series.. k. -n. ( n ). -(-) k - k= n=0 n=0 k= Find the indicated term for each geometric series described. 7. S n = 00, a n = 0,. S n = -7, n = 9, 9. S n = -7, a n = -9, r = ; a r = -; a r = ; a Etra Practice Lesson - (pages 0 ) Find the sum of each infinite geometric series, if it eists.. a =, r = _. a = 7, r = _ _ 0. n= ( _. a =, r = -. a = 000, r = _ + _ + _ _ -... ) n -. n= _ (- 0) n -. - (- Write each repeating decimal as a fraction n= ) n - Lesson - (pages ) Find the first five terms of each sequence.. a =, a n + = a n +. a =, a n + = a n + 7. a =, a n + = a n + (n + ). a =, a n + = n_ n + a n. a = - _, a n + = a n + _. a = _, a = _, a n + = a n + a n - Find the first three iterates of each function for the given initial value. 7. f() = -, 0 =. f() = -, 0 = - 9. f() = +, 0 = 0 0. f() = +, 0 =. f() = + +, 0 =. f() = + 9, 0 =. f() = + +, 0 = - _. f() = + -, 0 = _ Etra Practice 9

43 Lesson -7 (pages 9) Evaluate each epression..!.!. _!!!. _. _ 7! 7. _ 9!!0!!!! Epand each power... _ 0!!7! _ 0! 0!0! 9. (z - ) 0. (m + ). ( + ). (z - ). (m + n). (a - b). (n + ). (n - ) 7. (n - m) 0. ( - a) 9. (r - s) 0. ( b _ - ) Etra Practice Find the indicated term of each epansion.. sith term of ( + ). fourth term of ( - ) 7. fifth term of (a + b). fourth term of ( - ) 9. sith term of ( + ) 7. fifth term of ( + ) 0 Lesson - (pages 70 7) Prove that each statement is true for all positive integers n = n + n (n - ) = n (n - ). _ + _ + _ n(n + ) = n(n + ) (n + )(n + ) n(n + ) =. _ _ + 7_ _ + 9_ _ n + n(n + )(n + 7) n(n + ) _ n = - n (n + ) Find a countereample for each statement.. n + n - is divisible b. 7. n + n is prime.. n - + n = n + - n for all integers n 9. n - n = n - n for all integers n Lesson - (pages 9) For Eercises, state whether the events are independent or dependent.. tossing a penn and rolling a number cube. choosing first and second place in an academic competition. choosing from three pairs of shoes if onl two pairs are available. A comed video and an action video are selected from the video store.. The numbers 0 are written on pieces of paper and are placed in a hat. Three of them are selected one after the other without replacement.. In how man different was can a 0-question true-false test be answered? 7. A student council has seniors, juniors, and sophomore as members. In how man was can a -member council committee be formed that includes one member of each class?. How man license plates of smbols can be made using a letter for the first smbol and digits for the remaining smbols? 9 Etra Practice

44 Lesson - (pages 90 9) Evaluate each epression.. P(, ). P(, ). P(0, ). P(, ). P(, ). P(7, ) 7. C(, ). C(0, 7) 9. C(9, ) C(, ) 0. C(, ) C(, ). C(0, ) C(, ). C(7, ) C(, ) Determine whether each situation involves a permutation or a combination. Then find the number of possibilities.. choosing a team of 9 plaers from a group of 0. selecting the batting order of 9 plaers in a baseball game. arranging the order of songs on a CD. finding the number of -card hands that include diamonds and club Lesson - (pages 97 70) A jar contains red, green, and orange marbles. If three marbles are drawn at random and not replaced, find each probabilit.. P(all green). P( red, then not red) Etra Practice Find the odds of an event occurring, given the probabilit of the event.. _. _. _ 9 0 Find the probabilit of an event occurring, given the odds of the event.. _ 7. _. _ 7 9 The table shows the number of was to achieve each product when two dice are tossed. Find each probabilit. Product Was 9. P() 0. P(). P(not ). P(not ) Lesson - (pages ) An octahedral die is rolled twice. The sides are numbered. Find each probabilit.. P(, then ). P(two different numbers). P(, then an number) Two cards are drawn from a standard deck of cards. Find each probabilit if no replacement occurs.. P(jack, jack). P(heart, club). P(two diamonds) 7. P( of hearts, diamond). P( red cards) 9. P( black aces) Determine whether the events are independent or dependent. Then find the probabilit. 0. According to the weather reports, the probabilit of rain on a certain da is 70% in Yellow Falls and 0% in Copper Creek. What is the probabilit that it will rain in both cities?. The odds of winning a carnival game are to. What is the probabilit that a plaer will win the game three consecutive times? Etra Practice 97

45 Lesson - (pages 70 7) An octahedral die is rolled. The sides are numbered. Find each probabilit.. P(7 or ). P(less than ). P(greater than ). P(not prime). P(odd or prime). P(multiple of or odd) Ten slips of paper are placed in a container. Each is labeled with a number from through 0. Determine whether the events are mutuall eclusive or inclusive. Then find the probabilit. 7. P( or 0). P( or odd) 9. P( or less than 7) Etra Practice 0. Two letters are chosen at random from the word GEESE and two are chosen at random from the word PLEASE. What is the probabilit that all four letters are Es or none of the letters is an E?. Three dice are rolled. What is the probabilit the all show the same number?. Two marbles are simultaneousl drawn at random from a bag containing red, blue, and green marbles. Find each probabilit. a. P(at least one red marble) c. P(two marbles of the same color) b. P(at least one green marble) d. P(two marbles of different colors) Lesson - (pages 77 7) Find the mean, median, mode, and standard deviation of each set of data. Round to the nearest hundredth, if necessar.. [,,,, ]. [, 7, 7,,,, 7]. [, 0,,,,,, 0, 9]. [.,.7, 0.9,.,.,.0,.7]. [,,,,,,,,,, 7,,, 0,, 7,,,, ]. [, 0, 0,,, 0,,, 0, 0, 70, 0, 70, 0, 90, 0,,,, 0, 7,, 0,,, 0, 0] 7. [, 0, 7,, 0,,, 9, 7,,,, 0,,, 0,,,,, 99] Lesson -7 (pages 7 7) For Eercises, use the following information. The diameters of metal fittings made b a machine are normall distributed. The diameters have a mean of 7. centimeters and a standard deviation of 0. centimeters.. What percent of the fittings have diameters between 7.0 and.0 centimeters?. What percent of the fittings have diameters between 7. and.0 centimeters?. What percent of the fittings have diameters greater than. centimeters?. f 00 fittings, how man will have a diameter between.0 and. centimeters? For Eercises 7, use the following information. A college entrance eam was administered at a state universit. The scores were normall distributed with a mean of 0, and a standard deviation of 0.. What percent would ou epect to score above 0?. What percent would ou epect to score between 0 and 90? 7. What is the probabilit that a student chosen at random scored between 0 and 70? 9 Etra Practice

46 Lesson - (pages 79 7) HRSES For Eercises and, use the following information. The average lifespan of a horse is 0 ears.. What is the probabilit that a randoml selected horse will live more than ears?. What is the probabilit that a randoml selected horse will live less than 0 ears? MINIATURE GLF For Eercises and, use the following information. The probabilit of reaching in a basket of golf balls at a miniature golf course and picking out a ellow golf ball is 0... If golf balls are drawn, what is the probabilit that at least will be ellow?. What is the epected number of ellow golf balls if golf balls are drawn? Lesson -9 (pages 7 79) Find each probabilit if a coin is tossed times.. P(0 heads). P(eactl heads). P(eactl tails) Etra Practice Ten percent of a batch of toothpaste is defective. Five tubes of toothpaste are selected at random from this batch. Find each probabilit.. P(0 defective). P(eactl one defective). P(at least three defective) 7. P(less than three defective) n a 0-question true-false test, ou guess at ever question. Find each probabilit.. P(all answers correct) 9. P(eactl 0 correct) Lesson -0 (pages 7 7) Determine whether each situation would produce a random sample. Write es or no and eplain our answer.. finding the most often prescribed pain reliever b asking all of the doctors at a hospital. taking a poll of the most popular bab girl names this ear b studing birth announcements in newspapers from different cities across the countr. polling people who are leaving a pizza parlor about their favorite restaurant in the cit For Eercises, find the margin of sampling error to the nearest percent.. p = %, n =. p = %, n = 0. p = %, n = A poll conducted on the favorite breakfast choice of students in our school showed that 7% of the 0 students asked indicated oatmeal as their favorite breakfast. Etra Practice 99

47 Lesson - (pages 79 77) Find the values of the si trigonometric functions for angle θ Etra Practice 9 Solve ABC using the diagram at the right and the given measurements. Round measures of sides to the nearest tenth and measures of angles to the nearest degree.. B =, c = 0. A =, a =. B = 9, b = 7. A = 7, c =. b =, c = 9. a =, c = 0. cos B = _, a =. tan A = _, b = Lesson - (pages 7 77) Draw an angle with the given measure in standard position b A C a c B Rewrite each degree measure in radians and each radian measure in degrees π. _ 9π. _ 9π. _ 7π 7. _ 7π 0 0. π _. - 7π_ _ Find one angle with positive measure and one angle with negative measure coterminal with each angle π. -π 7. π _. _ π 9. 0 Lesson - (pages 77 7) Find the eact values of the si trigonometric functions of θ if the terminal side of θ in standard position contains the given point.. P(, -). P (, ). P(0, ). P(-, -). P (, - Find the eact value of each trigonometric function.. cos 7. sin _ (- π ). tan _ 7π 9. tan (-00 ) 0. cos 7π _ Suppose θ is an angle in standard position whose terminal side is in the given quadrant. For each function, find the eact values of the remaining five trigonometric functions of θ.. cos θ = -_ ; Quadrant III. sec θ = ; Quadrant IV. sin θ = _ ; Quadrant II. tan θ = -; Quadrant IV. csc θ = -; Quadrant III. cot θ = -; Quadrant II 7. tan θ = _ ; Quadrant III. cos θ = _ ; Quadrant I 9. csc θ = - _ ; Quadrant IV ) 90 Etra Practice

48 Lesson - (pages 7 79) Find the area of ABC. Round to the nearest tenth.. a = m, b = m, C =. a = ft, b = ft, C = 90. a = cm, b = cm, C = 0 Solve each triangle. Round to the nearest tenth.. A =, B = 7, a =. A = 0, C =, c =. B = 0, C =, b = 0 7. B = 0, C =, c =. A =, B = 0, b = 9. A =, C =, a = 0 Determine whether each triangle has no solution, one solution, or two solutions. Then solve each triangle. Round to the nearest tenth. 0. A = 0, B = 0, c = 0. B = 70, C =, a =. A = 0, a =, b =. A =, a =, b = 9. A =, B =, c =. A = 0, a =, b =. A = 7, a =, b = 9 7. A =, a =, b = 0. C = 9, a =, c = A = 0, B = 0, c = 0 0. A =, a =, b = 0. A =, a =, b = 79 Lesson - (pages 79 79) Determine whether each triangle should be solved b beginning with the Law of Sines or Law of Cosines. Then solve each triangle.. C. C C. Etra Practice 0 0 A B A A B 0 B. a =, b =, c =. B =, C =, c = 7. a = 9, b =., c =. 7. A =, a =, c = 0. b =, c = 7, A = 9. a =, b =, c = 7 0. C =, a =, b = 9. a =, A = 9, B =. A =, b = 0, c = 0. c = 0, A =, C =. a = 0, b =, c = 9. B =, a = 0, c =. B = 00, a = 0, c = 7. A = 0, B =, c =. A = 0, b = 00, c = Lesson - (pages 799 0) The given point P is located on the unit circle. Find sin θ and cos θ.. P _ (, _. P _ ) (, - _. P _ ) (- 7, - _. P 7) (_ 7, _ 0 7 ). P _ (-, _ ) Find the eact value of each function.. sin 0 7. cos 0. cos ( ) 9. cos 0. sin 70. sin 90. sin _ 7π_ π. cos - sin 0 + cos 0. cos 0 + cos 0. (sin )(cos ). 7. cos 0 + sin 0 Determine the period of each function Etra Practice 9

49 Etra Practice Lesson 7 (pages 0 ) Write each equation in the form of an inverse function.. Sin m + n. Tan =. Cos = _. Sin = a. Tan 0 =. Sin = _ Solve each equation. 7. = Sin - -_. Tan - () = 9. a = Arccos (_ 0. Arcsin (0) =. = Cos - _ Find each value. Round to the nearest hundredth.. Arccos (-_. tan [ Sin - ( 9. sin [ Tan - ( _. = Sin - () ). Sin - (-). cos [ ( Arcsin _ )] _ ) ] 7. sin [ Arccos _ ]. sin [ Arccos _ ( 7) ] ) ] 0. tan [ ( Arccos - _ ) ]. sin - [Cos - () - ]. Cos - [ tan π _ ]. cos [ Sin- _ ]. sin [Cos- (0)] Lesson - (pages ) Find the amplitude, if it eists, and period of each function. Then graph each function.. = cos θ. = _ sin θ. = sin θ. = sec θ. = sec _ θ. = csc θ 7. = tan θ. = sin _ θ 9. = sin _ θ 0. = sin θ. = _ cos _ θ. = csc θ. = cot θ. = csc θ. = tan _ θ ) Lesson - (pages 9 ) State the phase shift for each function. Then graph the function.. = sin (θ + 0 ). = cos (θ - 90 ). = tan ( θ + _ π ). = sin θ + _ π State the vertical shift and the equation of the midline for each function. Then graph the function.. = cos θ +. = sin θ - 7. = sec θ +. = csc θ - 9. = sin θ - 0. = _ sin θ + 7 State the vertical shift, amplitude, period, and phase shift of each function. Then graph the function.. = cos [(θ + 0 )] +. = tan [(θ - 0 )] -. = _ sin [(θ + )] +. = _ cos [(θ + )] -. = - sin [ ( θ + π _ ) ]. = + cos [ ( θ - π _ 9 Etra Practice ) ]

50 Lesson - (pages 7 ) Find the value of each epression.. sin θ, if cos θ = _ ; 0 θ 90. tan θ, if sin θ = _ ; 0 θ 90. csc θ, if sin θ = _ ; 90 θ 0. cos θ, if tan θ = ; 90 θ 0. sec θ, if tan θ = ; 90 θ 0. sin θ, if cot θ = - _ ; 70 θ 0 7. tan θ, if sec θ = ; 90 θ 0. sin θ, if cos θ = _ ; 70 θ 0 9. cos θ, if sin θ = - _ ; 70 θ 0 0. csc θ, if cot θ = - _ ; 90 θ 0. csc θ, if sec θ = - _ ; 0 θ 70. cos θ, if tan θ = ; 0 θ 70 Simplif each epression.. csc θ - cot θ. sin θ tan θ csc θ. tan θ csc θ. sec θ cot θ cos θ 7. cos θ ( - cos θ). sin θ cos θ 9. sin θ + cos θ cos 0. + tan θ + cot θ. + sin θ + - sin θ Lesson - (pages ) Verif that each of the following is an identit.. sin θ + cos θ + tan θ = sec θ. _ tan θ sin θ = sec θ _ tan θ. cot θ = tan θ. csc θ ( - cos θ) =. - cot θ = csc θ - csc θ. sin θ - cos θ = sin θ - cos θ 7. sin θ + cot θ sin θ =. _ cos θ csc θ - _ csc θ sec θ = - _ cos θ 9. _ cos θ sin θ sec θ - + cos θ sec θ + = cot θ 0. + cos θ = sin θ. sec θ + tan θ = cos θ. tan θ + cot θ = csc θ sec θ sin θ - cos θ - sin θ cot. θ + cot θ = - sin tan θ sin θ θ. = sin θ. sin θ( - cos θ) = sin θ sec θ + cos θ. sin θ + sin θ tan θ = tan θ 7. sec θ - sec θ + + cos θ - cos θ + = 0. tan θ( - sin θ) = sin θ cos θ 9. tan θ + + sin θ = sec θ 0. tan θ sec θ + = - cos θ. csc θ - sin θ sin θ + cos θ = cot θ Etra Practice Lesson - (pages ) Find the eact value of each epression.. sin 9. cos. sin. sin 0. cos. sin 7. cos 7. sin 9. sin (- ) 0. cos (-0 ). cos (- ). sin (-0 ). sin 0. sin. cos (-0 ) Verif that each of the following is an identit.. sin (90 + θ) = cos θ 7. cos (0 - θ) = -cos θ. sin (p + θ) = -sin θ 9. sin (θ + 0 ) + sin (θ + 0 ) = + _ (sin θ + cos θ) 0. cos (0 - θ) + cos (0 + θ) = cos θ Etra Practice 9

51 Lesson - (pages 9) θ_ Find the eact value of sin θ, cos θ, sin, and cos θ_ for each of the following.. cos θ = _ 7 ; 0 < θ < 90. sin θ = _ 7 ; 0 < θ < 90. cos θ = - _ ; 0 < θ < 70 Etra Practice. sin θ = - _ ; 70 < θ < 0. sin θ = _ ; 0 < θ < 90. cos θ = - 7_ ; 90 < θ < 0 Find the eact value of each epression b using the half-angle formulas. 7. sin 7. cos 7 9. sin π _ 0. cos _ π. cos.. cos π _ Verif that each of the following is an identit. sin θ. sin θ = cot θ. + cos θ = + tan θ. csc θ sec θ = csc θ. sin θ (cot θ + tan θ) = 7. - tan θ + tan θ csc θ + sin θ = cos θ. csc θ - sin θ + sin θ = cos θ Lesson -7 (pages ) Find all the solutions for each equation for 0 θ < 0.. cos θ = -_. sin θ = -_. cos θ = - sin θ. sin θ + cos θ =. sin θ + sin θ = 0. sin θ = cos θ Solve each equation for all values of θ if θ is measured in radians. 7. cos θ sin θ =. sin _ θ + cos _ θ = 9. cos θ + cos θ = - 0. sin _ θ + cos θ =. tan θ - tan θ = 0. sin θ cos θ = - Solve each equation for all values of θ if θ is measured in degrees.. sin θ - = 0. cos θ - cos θ sin θ = 0. cos θ sin θ =. (tan θ - )( cos θ + ) = 0 7. cos θ = 0.. sin θ tan θ - tan θ = 0 Solve each equation for all values of θ. 9. tan θ = 0. cos θ =. sin θ + = cos θ. sin θ cos θ =. cos θ = + sin θ. cos θ = cos θ 9 Etra Practice

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53 Mied Problem Solving Chapter Equations and Inequalities (pp. ) Mied Problem Solving GEMETRY For Eercises and, use the following information. The formula for the surface area of a sphere is SA = πr, and the _ formula for the volume of a sphere is V = πr. (Lesson -). Find the volume and surface area of a sphere with radius inches. Write our answer in terms of π.. Is it possible for a sphere to have the same numerical value for the surface area and volume? If so, find the radius of such a sphere.. CNSTRUCTIN The Birtic famil is building a famil room on their house. The dimensions of the room are feet b feet. Show how to use the Distributive Propert to mentall calculate the area of the room. (Lesson -) GEMETRY For Eercises, use the following information. The formula for the surface area of a clinder is SA = πr + πrh. (Lesson -). Use the Distributive Propert to rewrite the formula b factoring out the greatest common factor of the two terms.. Find the surface area for a clinder with radius centimeters and height 0 centimeters using both formulas. Leave the answer in terms of π.. Which formula do ou prefer? Eplain our reasoning. PPULATIN For Eercises 7 and, use the following information. In 00, the population of Ba Cit was 9,. For each of the net five ears, the population decreased b an average of 7 people per ear. (Lesson -) 7. What was the population in 009?. If the population continues to decline at the same rate as from 00 to 009, what would ou epect the population to be in 00? ASTRNMY For Eercises 9 and 0, use the following information. The planets in our solar sstem travel in orbits that are not circular. For eample, Pluto s farthest distance from the Sun is 9 million miles, and its closest distance is 7 million miles. (Lesson -) 9. What is the average of the two distances? 0. Write an equation that can be solved to find the minimum and maimum distances from the Sun to Pluto. HEALTH For Eercises and, use the following information. The National Heart Association recommends that less than 0% of a person s total dail Caloric intake come from fat. ne gram of fat ields nine Calories. Jason is a health -earold male whose average dail Caloric intake is between 00 and 00 Calories. (Lesson -). Write an inequalit that represents the suggested fat intake for Jason.. What is the greatest suggested fat intake for Jason? TRAVEL For Eercises and, use the following information. Bonnie is planning a -da trip to a convention. She wants to spend no more than $000. The plane ticket is $7, and the hotel is $ per night. (Lesson -). Let f represent the cost of food for one da. Write an inequalit to represent this situation.. Solve the inequalit and interpret the solution.. PAINTING Phil owns and operates a home remodeling business. He estimates that he will need gallons of paint for a particular project. If each gallon of paint costs $.99, write and solve a compound inequalit to determine what the cost c of the paint could be. (Lesson -) 9 Mied Problem Solving

54 Chapter Linear Relations and Functions (pp. ) AGRICULTURE For Eercises, use the following information. The table shows the average prices received b farmers for a bushel of corn. (Lesson -) Year Price Year Price 90 $0. 90 $. 90 $. 990 $. 90 $ $. 970 $. Source: The World Almanac. Write a relation to represent the data.. Graph the relation.. Is the relation a function? Eplain. MEASUREMENT For Eercises and, use the following information. The equation = 0.97 can be used to convert an number of centimeters to inches. (Lesson -). Find the number of inches in 00 centimeters.. Find the number of centimeters in inches. PPULATIN For Eercises and 7, use the following information. The table shows the growth in the population of Miami, Florida. (Lesson -) Year Population Year Population 90 9,7 990, 970,9 000,7 90, 00 7, Source: The World Almanac. Graph the data in the table. 7. Find the average rate of change. HEALTH For Eercises 0, use the following information. In 9, 9% of people in the United States age and over reported using cigarettes. The percent of people using cigarettes has decreased about.7% per ear following 9. Source: The World Almanac (Lesson -). Write an equation that represents how man people use cigarettes in ears. 9. If the percent of people using cigarettes continues to decrease at the same rate, what percent of people would ou predict to be using cigarettes in 00? 0. If the trend continues, when would ou predict there to be no people using cigarettes in the U.S.? How accurate is our prediction? EMPLYMENT For Eercises, use the table that shows unemploment statistics for 99 to 999. (Lesson -) Year Number Unemploed Percent Unemploed 99,90, ,99, ,0, ,, ,79, ,0, ,0,000. Source: The World Almanac. Draw two scatter plots of the data. Let represent the ear.. Use two ordered pairs to write an equation for each scatter plot.. Compare the two equations.. Predict the percent of people that will be unemploed in 00.. In 999, what was the total number of people in the United States?. EDUCATIN At Madison Elementar, each classroom can have at most students. Draw a graph of a step function that shows the relationship between the number of students and the number of classrooms that are needed. (Lesson -) CRAFTS For Eercises 7 9, use the following information. Priscilla sells stuffed animals at a local craft show. She charges $0 for the small and $ for the large ones. To cover her epenses, she needs to sell at least $0. (Lesson -7) 7. Write an inequalit for this situation.. Graph the inequalit. 9. If she sells 0 small and large animals, will she cover her epenses? Mied Problem Solving Mied Problem Solving 97

55 Chapter Sstems of Equations and Inequalities (pp. 9) Mied Problem Solving EXERCISE For Eercises, use the following information. At Everbod s Gm, ou have two options for becoming a member. You can pa $00 per ear or ou can pa $0 per ear plus $ per visit. (Lesson -). For each option, write an equation that represents the cost of belonging to the gm.. Graph the equations. Estimate the breakeven point for the gm memberships.. Eplain what the break-even point means.. If ou plan to visit the gm at least once per week during the ear, which option should ou choose?. GEMETRY Find the coordinates of the vertices of the parallelogram whose sides are contained in the lines whose equations are =, = 7, =, and = -. (Lesson -) EDUCATIN For Eercises 9, use the following information. Mr. Gunlikson needs to purchase equipment for his phsical education classes. His budget for the ear is $0. He decides to purchase cross-countr ski equipment. He is able to find skis for $7 per pair and boots for $0 per pair. He knows that he should bu more boots than skis because the skis are adjustable to several sizes of boots. (Lesson -). Let be the number of pairs of boots and be the number of pairs of skis. Write a sstem of inequalities for this situation. (Remember that the number of pairs of boots and skis must be positive.) 7. Graph the region that shows how man pairs of boots and skis he can bu.. Give an eample of three different purchases that Mr. Gunlikson can make. 9. Suppose Mr. Gunlikson wants to spend all of the mone. What combination of skis and boots should he bu? Eplain. MANUFACTURING For Eercises 0, use the following information. A shoe manufacturer makes outdoor and indoor soccer shoes. There is a two-step process for both kinds of shoes. Each pair of outdoor shoes requires hours in step one, hour in step two, and produces a profit of $0. Each pair of indoor shoes requires hour in step one, hours in step two, and produces a profit of $. The compan has 0 hours of labor per da available for step one and 0 hours available for step two. (Lesson -) 0. Let represent the number of pairs of outdoor shoes and let represent the number of indoor shoes that can be produced per da. Write a sstem of inequalities to represent the number of pairs of outdoor and indoor soccer shoes that can be produced in one da.. Draw the graph showing the feasible region.. List the coordinates of the vertices of the feasible region.. Write a function for the total profit.. What is the maimum profit? What is the combination of shoes for this profit? GEMETRY For Eercises 7, use the following information. An isosceles trapezoid has shorter base of measure a, longer base of measure c, and congruent legs of measure b. The perimeter of the trapezoid is inches. The average of the bases is 9 inches and the longer base is twice the leg plus 7. (Lesson -). Write a sstem of three equations that represents this situation.. Find the lengths of the sides of the trapezoid. 7. Find the area of the trapezoid.. EDUCATIN The three American universities with the greatest endowments in 000 were Harvard, Yale, and Stanford. Their combined endowments are $. billion. Harvard had $0. billion more in endowments than Yale and Stanford together. Stanford s endowments trailed Harvard s b $0. billion. What were the endowments of each of these universities? (Lesson -) 9 Mied Problem Solving

56 Chapter Matrices (pp. 0 ) AGRICULTURE For Eercises and, use the following information. In 00, the United States produced,90,000 metric tons of wheat, 9,0,000 metric tons of rice, and,90,000 metric tons of corn. In that same ear, Russia produced,0,000 metric tons of wheat, 0,000 metric tons of rice, and,,000 metric tons of corn. Source: The World Almanac (Lesson -). rganize the data in two matrices.. What are the dimensions of the matrices? LIFE EXPECTANCY For Eercises, use the life epectanc table. (Lesson -) Year Male Female Source: The World Almanac. rganize all the data in a matri.. Show how to organize the data in two matrices in such a wa that ou can find the difference between the life epectancies of males and females for the given ears. Then find the difference.. Does addition of an two of the matrices make sense? Eplain. CRAFTS For Eercises and 7, use the following information. Mrs. Long is selling crocheted items. She sells large afghans for $0, bab blankets for $0, doilies for $, and pot holders for $. She takes the following number of items to the fair: afghans, bab blankets, doilies, and 0 pot holders. (Lesson -). Write an inventor matri for the number of each item and a cost matri for the price of each item. 7. Suppose Mrs. Long sells all of the items. Find her total income as a matri. GEMETRY For Eercises, use the following information. A trapezoid has vertices T(, ), R(-, ), A(-, -), and P(, -). (Lesson -). Show how to use a reflection matri to find the vertices of TRAP after a reflection over the -ais. 9. The area of a trapezoid is found b multipling one-half the sum of the bases b the height. Find the areas of TRAP and T R A P. How do the compare? 0. Show how to use a matri and scalar multiplication to find the vertices of TRAP after a dilation that triples its perimeter.. Find the areas of TRAP and T R A P in Eercise 0. How do the compare? AGRICULTURE For Eercises and, use the following information. A farm has a triangular plot defined b the coordinates _ (-, - _, ) ( _, _, and ) ( _, - _, ) where units are in square miles. (Lesson -). Find the area of the region in square miles.. ne square mile equals 0 acres. To the nearest acre, how man acres are in the triangular plot? ART For Eercises and, use the following information. Small beads sell for $.0 per pound, and large beads sell for $.0 per pound. Bernadette bought a bag of beads for $ that contained times as man pounds of the small beads as the large beads. (Lesson -). Write a sstem of equations using the information given.. How man pounds of small and large beads did Bernadette bu? MATRICES For Eercises and 7, use the following information. Two inverse matrices have a sum of - 0. The value of each entr is no less 0 - than - and no greater than. (Lesson -7). Find the two matrices that satisf the conditions. 7. Eplain our method.. CNSTRUCTIN Alan charges $70 to build a small deck and $0 to build a large deck. During the spring and summer, he built more small decks than large decks. If he earned $,70, how man of each tpe of deck did he build? (Lesson -) Mied Problem Solving Mied Problem Solving 99

57 Chapter Quadratic Functions and Inequalities (pp. 09) Mied Problem Solving PHYSICS For Eercises, use the following information. A model rocket is shot straight up from the top of a 00-foot building at a velocit of 00 feet per second. (Lesson -). The height h(t) of the model rocket t seconds after firing is given b h(t) = -t + at + b, where a is the initial velocit in feet per second and b is the initial height of the rocket above the ground. Write an equation for the rocket.. Find the maimum height of the rocket and the time that the height is reached.. Suppose a rocket is fired from the ground (initial height is 0). Find values for a, initial velocit, and t, time, if the rocket reaches a height of,000 feet at time t. RIDES For Eercises and, use the following information. An amusement park ride carries riders to the top of a -foot tower. The riders then freefall in their seats until the reach 0 feet above the ground. (Lesson -). Use the formula h(t) = -t + h 0, where the time t is in seconds and the initial height h 0 is in feet, to find how long the riders are in free-fall.. Suppose the designer of the ride wants the riders to eperience free-fall for seconds before stopping 0 feet above the ground. What should be the height of the tower? CNSTRUCTIN For Eercises and 7, use the following information. Nicole s new house has a small deck that measures feet b feet. She would like to build a larger deck. (Lesson -). B what amount must each dimension be increased to triple the area of the deck? 7. What are the new dimensions of the deck? NUMBER THERY For Eercises and 9, use the following information. Two comple conjugate numbers have a sum of and a product of 0. (Lesson -). Find the two numbers. 9. Eplain the method ou used. CNSTRUCTIN For Eercises 0 and, use the following information. A contractor wants to construct a rectangular pool with a length that is twice the width. He plans to build a two-meter-wide walkwa around the pool. He wants the area of the walkwa to equal the surface area of the pool. (Lesson -) 0. Find the dimensions of the pool to the nearest tenth of a meter.. What is the surface area of the pool to the nearest square meter? PHYSICS For Eercises, use the following information. A ball is thrown into the air verticall with a velocit of feet per second. The ball was released feet above the ground. The height above the ground t seconds after release is modeled b the equation h(t) = -t + t +. (Lesson -). When will the ball reach 0 feet?. Will the ball ever reach 0 feet? Eplain.. In how man seconds after its release will the ball hit the ground? WEATHER For Eercises 7, use the following information. The normal monthl high temperatures for Alban, New York, are,,,,, 7, 7, 70,, 0, 0, and 7 degrees Fahrenheit, respectivel. Source: The World Almanac (Lesson -7). Suppose Januar =, Februar =, and so on. A graphing calculator gave the following function as a model for the data: = Graph the points in the table and the function on the same coordinate plane.. Identif the verte, ais of smmetr, and direction of opening for this function. 7. Discuss how well ou think the function models the actual temperature data.. MDELS John is building a displa table for model cars. He wants the perimeter of the table to be feet, but he wants the area of the table to be no more than 0 square feet. What could the width of the table be? (Lesson -) 90 Mied Problem Solving

58 Chapter Polnomial Functions (pp. 0 ). EDUCATIN In 00 in the United States, there were,0,0 classroom teachers and,0,0 students. An average of $77 was spent per student. Find the total amount of mone spent for students in 00. Write the answer in both scientific and standard notation. Source: The World Almanac (Lesson -) PPULATIN For Eercises, use the following information. In 000, the population of Meico Cit was,,000, and the population of Bomba was,0,000. It is projected that, until the ear 0, the population of Meico Cit will increase at the rate of 0.% per ear and the population of Bomba will increase at the rate of % per ear. Source: The World Almanac (Lesson -). Let r represent the rate of increase in population for each cit. Write a polnomial to represent the population of each cit in 00.. Predict the population of each cit in 0.. If the projected rates are accurate, in what ear will the two cities have approimatel the same population? PPULATIN For Eercises, use the following information. The table shows the percent of the U.S. population that was foreign-born during various ears. The -values are ears since 900 and the -values are the percent of the population. Source: The World Almanac (Lesson - and -) U.S. Foreign-Born Population Graph the function.. Describe the turning points of the graph and its end behavior. 7. What do the relative maima and minima represent?. If this graph were modeled b a polnomial equation, what is the least degree the equation could have? GEMETRY For Eercises 9 and 0, use the following information. Hero s formula for the area of a triangle is given b A = s(s - a)(s - b)(s - c), where a, b, and c are the lengths of the sides of the triangle and s = 0.(a + b + c). (Lesson -) 9. Find the lengths of the sides of the triangle given in this application of Hero s formula: A = s - s + 7s - 0s. 0. What tpe of triangle is this? GEMETRY For Eercises and, use the following information. The volume of a rectangular bo can be written as , and the height is alwas +. (Lesson -). What are the width and length of the bo?. Will the ratio of the dimensions of the bo alwas be the same regardless of the value of? Eplain. SALES For Eercises and, use the following information. The sales of items related to information technolog can be modeled b S() = , where is the number of ears since 99 and is billions of dollars. Source: The World Almanac (Lesson -7). Use snthetic substitution to estimate the sales for 00 and 00.. Do ou think this model is useful in estimating future sales? Eplain.. MANUFACTURING A bo measures inches b inches b inches. The manufacturer will increase each dimension of the bo b the same number of inches and have a new volume of 9 cubic inches. How much should be added to each dimension? (Lesson -). CNSTRUCTIN A picnic area has the shape of a trapezoid. The longer base is more than times the length of the shorter base and the height is more than times the shorter base. What are the dimensions if the area is 0 square feet? (Lesson -9) Mied Problem Solving Mied Problem Solving 9

59 Mied Problem Solving Chapter 7 Radical Equations and Inequalities (pp. 7) EMPLYMENT For Eercises and, use the following information. From 99 to 999, the number of emploed women and men in the United States, age and over, can be modeled b the following equations, where is the number of ears since 99 and is the number of people in thousands. Source: The World Almanac (Lesson 7-) women: = 0. +,0 men: = ,0. Write a function that models the total number of men and women emploed in the United States during this time.. If f is the function for the number of men, and g is the function for the number of women, what does ( f - g)() represent?. HEALTH The average weight of a bab born at a certain hospital is 7 _ pounds, and the average length is 9. inches. ne kilogram is about. pounds, and centimeter is about 0.97 inches. Find the average weight in kilograms and the length in centimeters. (Lesson 7-) SAFETY For Eercises and, use the following information. The table shows the total stopping distance, in meters, of a vehicle and the speed, in meters per second. (Lesson 7-) LAW ENFRCEMENT For Eercises 7 and, use the following information. The approimate speed s in miles per hour that a car was traveling if it skidded d feet is given b the formula s =. kd, where k is the coefficient of friction. (Lesson 7-) 7. For a dr concrete road, k = 0.. If a car skids 0 feet on a dr concrete road, find its speed in miles per hour to the nearest whole number.. Another formula using the same variables is s = kd. Compare the results using the two formulas. Eplain an variations in the answers. PHYSICS For Eercises 9, use the following information. Kepler s Third Law of planetar motion states that the square of the orbital period of an planet, in Earth ears, is equal to the cube of the planet s distance from the Sun in astronomical units (AU). Source: The World Almanac (Lesson 7-) 9. The orbital period of Mercur is 7.97 Earth das. What is Mercur s distance from the Sun in AU? 0. Pluto s period of revolution is 7. Earth ears. What is Pluto s distance from the Sun?. What is Earth s distance from the Sun in AU? Eplain our result. Distance 9 9 Speed 9 0. Graph the data in the table.. Graph the function = on the same coordinate plane. How well do ou think this function models the given data? Eplain.. PHYSICS The speed of sound in a liquid is s = B_, where B is known as the bulk d modulus of the liquid and d is the densit of the liquid. For water, B =. 0 9 N/m and d = 0 kg/m. Find the speed of sound in water to the nearest meter per second. (Lesson 7-) PHYSICS For Eercises and, use the following information. The time T in seconds that it takes a pendulum to make a complete swing back and forth is given b the formula T = π L_ g, where L is the length of the pendulum in feet and g is the acceleration due to gravit, feet per second squared. (Lesson 7-7). In Toko, Japan, a huge pendulum in the Shinjuku building measures 7 feet 9.7 inches. How long does it take for the pendulum to make a complete swing? Source: The Guinness Book of Records. A clockmaker wants to build a pendulum that takes 0 seconds to swing back and forth. How long should the pendulum be? 9 Mied Problem Solving

60 Chapter Rational Epressions and Equations (pp. 0 9) MANUFACTURING For Eercises, use the following information. The volume of a shipping container in the shape of a rectangular prism can be represented b the polnomial + +, where the height is. (Lesson -). Find the length and width of the container.. Find the ratio of the three dimensions of the container when =.. Will the ratio of the three dimensions be the same for all values of? PHTGRAPHY For Eercises, use the following information. The formula _ q = _ f - _ p can be used to determine how far the film should be placed from the lens of a camera. The variable q represents the distance from the lens to the film, f represents the focal length of the lens, and p represents the distance from the object to the lens. (Lesson -). Solve the formula for _ p.. Write the epression containing f and q as a single rational epression.. If a camera has a focal length of centimeters and the lens is 0 centimeters from the film, how far should an object be from the lens so that the picture will be in focus? PHYSICS For Eercises 7 and, use the following information. The Inverse Square Law states that the relationship between two variables is related to the equation = _ (Lesson -). 7. Graph = _.. Give the equations of an asmptotes. PHYSICS For Eercises 9 and 0, use the following information. The formula for finding the gravitational force between two objects is F = G _ m Am B, where d F is the gravitational force between the objects, G is the universal constant, m A is the mass of the first object, m B is the mass of the second object, and d is the distance between the centers of the objects. (Lesson -) 9. If the mass of object A is constant, does Newton s formula represent a direct or inverse variation between the mass of object B and the distance? 0. The value of G is N m /kg. If two objects each weighing kilograms are placed so that their centers are 0. meter apart, what is the gravitational force between the two objects? EDUCATIN For Eercises, use the table that shows the average number of students per computer in United States public schools for various ears. (Lesson -) Year Students Year Students Source: The World Almanac. Let represent ears where 9 =, 99 =, and so on. Let represent the number of students. Graph the data.. What tpe of function does the graph most closel resemble?. Use a graphing calculator to find an equation that models the data. TRAVEL For Eercises and, use the following information. A trip between two towns takes hours under ideal conditions. The first 0 miles of the trip is on an interstate, and the last 0 miles is on a highwa with a speed limit that is 0 miles per hour less than on the interstate. (Lesson -). If represents the speed limit on the interstate, write epressions for the time spent at that speed and for the time spent on the other highwa.. Write and solve an equation to find the speed limits on the two highwas. Mied Problem Solving Mied Problem Solving 9

61 Mied Problem Solving Chapter 9 Eponential and Logarithmic Relations (pp. 9 9) PPULATIN For Eercises, use the following information. In 90, the world population was about. billion. B 90, it had increased to about. billion. Source: The World Almanac (Lesson 9-). Write an eponential function of the form = ab that could be used to model the world population in billions for 90 to 90. Write the equation in terms of, the number of ears since 90. (Round the value of b to the nearest ten-thousandth.). Suppose the population continued to grow at that rate. Estimate the population in In 000, the population of the world was about.0 billion. Compare our estimate to the actual population.. Use the equation ou wrote in Eercise to estimate the world population in the ear 00. How accurate do ou think the estimate is? Eplain our reasoning. EARTHQUAKES For Eercises, use the following information. The table shows the Richter scale that measures earthquake intensit. Column shows the increase in intensit between each number. For eample, an earthquake that measures 7 is 0 times more intense than one measuring. (Lesson 9-) Richter Number Increase in Magnitude ,000 00,000 7,000,000 0,000,000 Source: The New York Public Librar. Graph this function.. Write an equation of the form = b - c for the function in Eercise. (Hint: Write the values in the second column as powers of 0 to see a pattern and find the value of c.) 7. Graph the inverse of the function in Eercise.. Write an equation of the form = log 0 + c for the function in Eercise 7. 9 Mied Problem Solving EARTHQUAKES For Eercises 9 and 0, use the table showing the magnitude of some major earthquakes. (Lesson 9-) Year/Location Magnitude 99/Turke.0 9/Yugoslavia.0 970/Peru 7. 9/Armenia /Morocco. Source: The World Almanac 9. For which two earthquakes was the intensit of one 0 times that of the other? For which two was the intensit of one 00 times that of the other? 0. What would be the magnitude of an earthquake that is 000 times as intense as the 9 earthquake in Yugoslavia?. Suppose ou know that log 7 0. and log Describe two different methods that ou could use to approimate log 7.. (You can use a calculator, of course.) Then describe how ou can check our result. (Lesson 9-) WEATHER For Eercises and, use the following information. The atmospheric pressure P, in bars, of a given height on Earth is given b using the formula P = s e - k_ H. In the formula, s is the surface pressure on Earth, which is approimatel bar, h is the altitude for which ou want to find the pressure in kilometers, and H is alwas 7 kilometers. (Lesson 9-). Find the pressure for,, and 7 kilometers.. What do ou notice about the pressure as altitude increases? AGRICULTURE For Eercises, use the following information. An equation that models the decline in the number of U.S. farms is =,9,0(0.9), where is ears since 90 and is the number of farms. Source: Wall Street Journal (Lesson 9-). How can ou tell that the number is declining?. B what annual rate is the number declining?. Predict when the number of farms will be less than. million.

62 Chapter 0 Conic Sections (pp. 0 7) GEMETRY For Eercises, use the following information. Triangle ABC has vertices A(, ), B(-, ), and C(-, -). (Lesson 0-). An isosceles triangle has two sides with equal length. Is ABC isosceles? Eplain.. An equilateral triangle has three sides of equal length. Is ABC equilateral? Eplain.. Triangle EFG is formed b joining the midpoints of the sides of ABC. What tpe of triangle is EFG? Eplain.. Describe an relationship between the lengths of the sides of the two triangles.. ENERGY For Eercises, use the following information. A parabolic mirror can be used to collect solar energ. The mirrors reflect the ras from the Sun to the focus of the parabola. The latus rectum of a particular mirror is 0 feet long. (Lesson 0-). Write an equation for the parabola formed b the mirror if the verte of the mirror is 9.7 feet below the origin.. ne foot is eactl 0.0 meter. Rewrite the equation in terms of meters. 7. Graph one of the equations for the mirror.. Which equation did ou choose to graph? Eplain. CMMUNICATIN For Eercises 9, use the following information. The radio tower for KCGM has a circular radius for broadcasting of miles. The radio tower for KVCK has a circular radius for broadcasting of miles. (Lesson 0-) 9. Let the radio tower for KCGM be located at the origin. Write an equation for the set of points at the maimum broadcast distance from the tower. 0. The radio tower for KVCK is 0 miles south and miles west of the KCGM tower. Let each mile represent one unit. Write an equation for the set of points at the maimum broadcast distance from the KVCK tower.. Graph the two equations and show the area where the radio signals overlap. ASTRNMY For Eercises, use the table that shows the closest and farthest distances of Venus and Jupiter from the Sun in millions of miles. (Lesson 0-) Planet Closest Farthest Venus. 7.7 Jupiter Source: The World Almanac. Write an equation for the orbit of each planet, assuming that the center of the orbit is the origin, the center of the Sun is a focus, and the Sun lies on the -ais.. Find the eccentricit for each planet.. Which planet has an orbit that is closer to a circle? Eplain our reasoning.. A comet follows a path that is one branch of a hperbola. Suppose Earth is the center of the hperbolic curve and has coordinates (0, 0). Write an equation for the path of the comet if c =,,000 miles and a =,00,000 miles. Let the -ais be the transverse ais. (Lesson 0-) AVIATIN For Eercises, use the following information. The path of a militar jet during an air show can be modeled b a conic section with equation ,0 -,00 = 0, where distances are in feet. (Lesson 0-). Identif the shape of the path of the jet. Write the equation in standard form. 7. If the jet begins its ascent at (0, 0), what is the horizontal distance traveled b the jet from the beginning of the ascent to the end of the descent?. What is the maimum height of the jet? SATELLITES For Eercises 9 and 0, use the following information. The equations of the orbits of two satellites are _ (00) + _ (900) = and _ (00) + _ (90) =, where distances are in km and Earth is the center of each curve. (Lesson 0-7) 9. Solve each equation for. 0. Use a graphing calculator to estimate the intersection points of the two orbits. Mied Problem Solving Mied Problem Solving 9

63 Mied Problem Solving Chapter Sequences and Series (pp. 0 ) CLUBS For Eercises and, use the following information. A quilting club consists of 9 members. Ever week, each member must bring one completed quilt square. (Lesson -). Find the first eight terms of the sequence that describes the total number of squares that have been made after each meeting.. ne particular quilt measures 7 inches b inches and is being designed with -inch squares. After how man meetings will the quilt be complete? ART For Eercises and, use the following information. Alberta is making a beadwork design consisting of rows of colored beads. The first row consists of 0 beads, and each consecutive row will have more beads than the previous row. (Lesson -). Write an equation for the number of beads in the nth row.. Find the number of beads in the design if it contains rows. GAMES For Eercises and, use the following information. An audition is held for a TV game show. At the end of each round, one half of the prospective contestants are eliminated from the competition. n a particular da, contestants begin the audition. (Lesson -). Write an equation for finding the number of contestants that are left after n rounds.. Using this method, will the number of contestants that are to be eliminated alwas be a whole number? Eplain. SPRTS For Eercises 7 9, use the following information. Caitlin is training for a marathon (about miles). She begins b running miles. Then, when she runs ever other da, she runs one and a half times the distance she ran the time before. (Lesson -) 7. Write the first five terms of a sequence describing her training schedule.. When will she eceed miles in one run? 9. When will she have run 00 total miles? GEMETRY For Eercises 0, use a square of paper at least inches on a side. (Lesson -) 0. Let the square be one unit. Cut awa one half of the square. Call this piece Term. Net, cut awa one half of the remaining sheet of paper. Call this piece Term. Continue cutting the remaining paper in half and labeling the pieces with a term number as long as possible. List the fractions represented b the pieces.. If ou could cut squares indefinitel, ou would have an infinite series. Find the sum of the series.. How does the sum of the series relate to the original square of paper? BILGY For Eercises, use the following information. In a particular forest, scientists are interested in how the population of wolves will change over the net two ears. ne model for animal population is the Verhulst population model, p n + = p n + rp n ( - p n ), where n represents the number of time periods that have passed, p n represents the percent of the maimum sustainable population that eists at time n, and r is the growth factor. (Lesson -). To find the population of the wolves after one ear, evaluate p = 0. +.(0.)( - 0.).. Eplain what each number in the epression in Eercise represents.. The current population of wolves is. Find the new population b multipling b the value in Eercise.. PASCAL S TRIANGLE Stud the first eight rows of Pascal s triangle. Write the sum of the terms in each row as a list. Make a conjecture about the sums of the rows of Pascal s triangle. (Lesson -7) 7. NUMBER THERY Two statements that can be proved using mathematical induction are _ + _ + _ _ n = _ - ( _ ) n and _ + _ + _ _ n = _ - ( _ ) n. Write and prove a conjecture involving _ that is similar to the statements. (Lesson -) 9 Mied Problem Solving

64 Chapter Probabilit and Statistics (pp. 7) NUMBER THERY For Eercises, use the following information. According to the Rational Zero Theorem, if _ p q is a rational root, then p is a factor of the constant of the polnomial, and q is a factor of the leading coefficient. (Lesson -). What is the maimum number of possible rational roots that ou ma need to check for the polnomial ? Eplain our answer.. Wh ma ou not need to check the maimum number of possible roots?. Are choosing the numerator and the denominator for a possible rational root independent or dependent events?. GARDENING A gardener is selecting plants for a special displa. There are varieties of pansies from which to choose. The gardener can onl use 9 varieties in the displa. How man was can 9 varieties be chosen from the varieties? (Lesson -) SPEED LIMITS For Eercises and, use the following information. Speed Limit Number of States Source: The World Almanac The table shows the number of states having each maimum speed limit for their rural interstates. (Lesson -). If a state is randoml selected, what is the probabilit that its speed limit is 7? 0?. If a state is randoml selected, what is the probabilit that its speed limit is 0 or greater? 7. LTTERIES A lotter number for a particular state has seven digits, which can be an digit from 0 to 9. It is advertised that the odds of winning the lotter are to 0,000,000. Is this statement about the odds correct? Eplain our reasoning. (Lesson -) For Eercises and 9, use the table that shows the most popular colors for luur cars in 00. (Lesson -) Color % of cars Color % of cars gra. red.9 silver. blue. wh. metallic 7. gold. white. lt. blue. black 0.9 other. Source: The World Almanac. If a car is randoml selected, what is the probabilit that it is gra or silver? 9. In a parking lot of 000 cars sold in 00, how man cars would ou epect to be white or black? EDUCATIN For Eercises 0, use the following information. The list shows the average scores for each state for the ACT for (Lesson -) 0.,.,., 0.,., 0.,.,., 7., 0., 0.0,.7,., 0.,.,.0,., 0., 9.,., 0.,.,.,.,.,.,.7,.7,.,.,., 0.,., 0.,.,., 0.,.,.,.9, 9.,., 0., 0.,.,.7, 0.9,.,.,. 0. Compare the mean and median of the data.. Find the standard deviation of the data. Round to the nearest hundredth.. Suppose the state with an average score of 0.0 incorrectl reported the results. The score for the state is actuall.. How are the mean and median of the data affected b this data change?. HEALTH The heights of students at Madison High School are normall distributed with a mean of inches and a standard deviation of inches. f the 00 students in the school, how man would ou epect to be less than inches tall? (Lesson -7). SURVEY A poll of 70 people shows that 7% enjo travel. Find the margin of the sampling error for the surve. (Lesson -9) Mied Problem Solving Mied Problem Solving 97

65 Mied Problem Solving Chapter Trigonometric Functions (pages 7 9) CABLE CARS For Eercises and, use the following information. The longest cable car route in the world begins at an altitude of 79 feet and ends at an altitude of,9 feet. The ride is -miles long. Source: The Guinness Book of Records (Lesson -). Draw a diagram to represent this situation.. To the nearest degree, what is the average angle of elevation of the cable car ride? RIDES For Eercises and, use the following information. In 000, a gigantic Ferris wheel, the London Ee, opened in England. The wheel has cars evenl spaced around the circumference. (Lesson -). What is the measure, in degrees, of the angle between an two consecutive cars?. If a car is located such that the measure in standard position is 0, what are the measures of one angle with positive measure and one angle with negative measure coterminal with the angle of this car?. BASKETBALL A person is selected to tr to make a shot at a distance of feet from the basket. The formula R = _ V 0 sin θ gives the distance of a basketball shot with an initial velocit of V 0 feet per second at an angle of u with the ground. If the basketball was shot with an initial velocit of feet per second at an angle of 7, how far will the basketball travel? (Lesson -). CMMUNICATINS A telecommunications tower needs to be supported b two wires. The angle between the ground and the tower on one side must be and the angle between the ground and the second tower must be 7. The distance between the two wires is 0 feet. wire 0 ft tower wire 7 To the nearest foot, what should be the lengths of the two wires? (Lesson -) 9 Mied Problem Solving SURVEYING For Eercises 7 and, use the following information. A triangular plot of farm land measures 0.9 b 0. b. miles. (Lesson -) 7. If the plot of land is fenced on the border, what will be the angles at which the fences of the three sides meet? Round to the nearest degree.. What is the area of the plot of land? (Hint: Use the area formula in Lesson -.) 9. WEATHER The monthl normal temperatures, in degrees Fahrenheit, for New York Cit are given in the table. Januar is assigned a value of, Februar a value of, and so on. (Lesson -) Month Temperature Month Temperature A trigonometric model for the temperature T in degrees Fahrenheit of New York Cit at t months is given b T =. sin _ ( π -. ) +.. A quadratic model for the same situation is T = Which model do ou think best fits the data? Eplain our reasoning. PHYSICS For Eercises 0, use the following information. When light passes from one substance to another, it ma be reflected and refracted. Snell s law can be used to find the angle of refraction as a beam of light passes from one substance to another. ne form of the formula for Snell s law is n sin θ = n sin θ, where n and n are the indices of refraction for the two substances and θ and θ are the angles of the light ras passing through the two substances. (Lesson -7) 0. Solve the equation for sin θ.. Write an equation in the form of an inverse function that allows ou to find θ.. If a light beam in air with inde of refraction of.00 hits a diamond with inde of. at an angle of 0, find the angle of refraction.

66 Chapter Trigonometric Graphs and Identities (pages 0 7). TIDES The world s record for the hightest tide is held b the Minas Basin in Nova Scotia, Canada, with a tidal range of. feet. A tide is at equilibrium when it is at its normal level halfwa between its highest and lowest points. Write an equation to represent the height h of the tide. Assume that the tide is at equilibrium at t = 0, that the high tide is beginning, and that the tide completes one ccle in hours. (Lesson -) RIDES For Eercises and, use the following information. The Cosmoclock is a huge Ferris wheel in Yokohama Cit, Japan. The diameter is feet. Suppose that a rider enters the ride at 0 feet and then rotates in 90 increments counterclockwise. The table shows the angle measures of rotation and the height above the ground of the rider. (Lesson -) ft 90 ft Angle Height Angle Height TRIGNMETRY Using the eact values for the sine and cosine functions, show that the identit cos θ + sin θ = is true for angles of measure 0,, 0, 90, and 0. (Lesson -). RCKETS In the formula h = _ v sin θ = h is the g maimum height reached b a rocket, θ is the angle between the ground and the initial path of the object, v is the rocket s initial velocit, and g is the acceleration due to gravit. Verif the identit _ v sin θ = _ v cos θ. g g cot (Lesson -) θ WEATHER For Eercises and 7, use the following information. The monthl high temperatures for Minneapolis, Minnesota, can be modeled b the equation =. sin ( _ π -.09 ) +., where the months are Januar =, Februar =, and so on. The monthl low temperatures for Minneapolis can be modeled b the equation = 0. sin _ ( π -.09 ) +.9. (Lesson -). Write a new function b adding the epressions on the right side of each equation and dividing the result b. 7. What is the meaning of the function ou wrote in Eercise?. Begin with one of the Pthagorean Identities. Perform equivalent operations on each side to create a new trigonometric identit. Then show that the identit is true. (Lesson -) 9. TELEVISIN The tallest structure in the world is a television transmitting tower located near Fargo, North Dakota, with a height of 0 feet. Mied Problem Solving. A function that models the data is (sin ( 90 )). Identif the vertical shift, amplitude, period, and phase shift of the graph.. Write an equation using the sine that models the position of a rider on the Vienna Giant Ferris Wheel in Vienna, Austria, with a diameter of 00 feet. Check our equation b plotting the points and the equation with a graphing calculator. 0 ft tower shadow What is the measure of θ if the length of the shadow is mile? Source: The Guinness Book of Records (Lesson -7) Mied Problem Solving 99

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68 Becoming a Better Test-Taker At some time in our life, ou will probabl have to take a standardized test. Sometimes this test ma determine if ou go on to the net grade or course, or even if ou will graduate from high school. This section of our tetbook is dedicated to making ou a better test-taker. TYPES F TEST QUESTINS In the following pages, ou will see eamples of four tpes of questions commonl seen on standardized tests. A description of each tpe of question is shown in the table below. Tpe of Question Description See Pages Preparing for Standardized Tests multiple choice gridded response short response etended response Four or five possible answer choices are given from which ou choose the best answer. You solve the problem. Then ou enter the answer in a special grid and shade in the corresponding circles. You solve the problem, showing our work and/or eplaining our reasoning. You solve a multipart problem, showing our work and/or eplaining our reasoning PRACTICE After being introduced to each tpe of question, ou can practice that tpe of question. Each set of practice questions is divided into five sections that represent the concepts most commonl assessed on standardized tests. Number and perations Algebra Geometr Measurement Data Analsis and Probabilit USING A CALCULATR n some tests, ou are permitted to use a calculator. You should check with our teacher to determine if calculator use is permitted on the test ou will be taking, and if so, what tpe of calculator can be used. TEST-TAKING TIPS In addition to Test-Taking Tips like the one shown at the right, here are some additional thoughts that might help ou. Get a good night s rest before the test. Cramming the night before does not improve our results. Budget our time when taking a test. Don t dwell on problems that ou cannot solve. Just make sure to leave that question blank on our answer sheet. Watch for ke words like NT and EXCEPT. Also look for order words like LEAST, GREATEST, FIRST, and LAST. If ou are allowed to use a calculator, make sure ou are familiar with how it works so that ou won t waste time tring to figure out the calculator when taking the test. Preparing for Standardized Tests 9

69 Preparing for Standardized Tests Multiple-Choice Questions Multiple-choice questions are the most common tpe of questions on standardized tests. These questions are sometimes called selected-response questions. You are asked to choose the best answer from four or five possible answers. To record a multiple-choice answer, ou ma be asked to shade in a bubble that is a circle or an oval or to just write the letter of our choice. Alwas make sure that our shading is dark enough and completel covers the bubble. The answer to a multiple-choice question is usuall not immediatel obvious from the choices, but ou ma be able to eliminate some of the possibilities b using our knowledge of mathematics. Another answer choice might be that the correct answer is not given. EXAMPLE Incomplete shading A B C D Too light shading A B C D Correct shading A B C D White chocolate pieces sell for $. per pound while dark chocolate pieces sell for $.0 per pound. How man pounds of white chocolate are needed to produce a 0-pound miture of both kinds that sells for $.0 per pound? A lb B lb C lb D 0 lb STRATEGY Reasonableness Check to see that our answer is reasonable with the given information. The question asks ou to find the number of pounds of the white chocolate. Let w be the number of pounds of white chocolate and let d be the number of pounds of dark chocolate. Write a sstem of equations. w + d = 0 There is a total of 0 pounds of chocolate..w +.0d =.0(0) The price is $.0 0 for the mied chocolate. Use substitution to solve..w +.0d =.0(0) riginal equation.w +.0(0 - w) = Solve the first equation for d and substitute..w + -.w = Distributive Propert 0.7w = Simplif. w = Divide each side b 0.7. The answer is B. EXAMPLE Josh throws a baseball upward at a velocit of 0 feet per second, releasing the baseball when it is feet above the ground. The height of the baseball t seconds after being thrown is given b the formula h(t) = -t + 0t +. Find the time at which the baseball reaches its maimum height. Round to the nearest tenth of a second. F.0 s G. s H. s J 77. s STRATEGY Diagrams Drawing a diagram for a situation ma help ou to answer the question. Graph the equation. The graph is a parabola. Make sure to label the horizontal ais as t (time in seconds) and the vertical ais as h for height in feet. The ball is at its maimum height at the verte of the graph. The graph indicates that the maimum height is achieved between and seconds after launch. The answer is G. Height (ft) (s) h Time (s) t 9 Preparing for Standardized Tests

70 Multiple-Choice Practice Choose the best answer. Number and perations. In 00,. 0 people in the United States and Canada used the Internet, while. 0 people worldwide used the Internet. What percentage of users were from the United States and Canada? A % B % C 7% D 0%. Serena has plants to put in her garden. How man different was can she arrange the plants? F G 0 H 0 J 70 Algebra. The sum of Kevin s, Anna s, and Tia s ages is 0. Anna is ear more than twice as old as Tia. Kevin is ears older than Anna. How old is Anna? A 7 B C D. Rafael s Theatre Compan sells tickets for $0. At this price, the sell 00 tickets. Rafael estimates that the would sell 0 fewer tickets for each $ price increase. What charge would give the most income? F 0 G H J 0 Geometr. Hai stands 7 feet from the base of a building and sights the top at a angle. What is the height of the building to the nearest tenth of a foot? A 0.0 ft B.0 ft C. ft D. ft. Samone draws QRS on grid paper to use for a design in her art class. She needs to rotate the triangle 0 counterclockwise. What Q will be the -coordinate of the image of S? F - H - G - J 7 ft R S Measurement 7. Lakeisha is teaching a summer art class for children. For one project, she estimates that she will need _ ard of string for each students. How man ards will she need for students? A d C 0 _ d B _ d D d 9. Kari works at night so she needs to make her room as dark as possible during the da to sleep. How much black paper will she need to cover the window in her room, which is shaped as shown. Use. for π. Round to the nearest tenth of a square foot. F.0 ft H 0. ft G. ft J. ft Data Analsis and Probabilit 9. A card is drawn from a standard deck of cards. If one card is drawn, what is the probabilit that it is a heart or a? A _ B _ C _ D _ 0. The weight of cand in boes is normall distributed with a mean of ounces and a standard deviation of 0. ounce. About what percent of the time will ou get a bo that weighs over. ounces? F.% G % H 0% J % Question Man standardized tests include a reference sheet with common formulas that ou ma use during the test. If it is available before the test, familiarize ourself with the reference sheet for quick reference during the test. Preparing for Standardized Tests Preparing for Standardized Tests 9

71 Preparing for Standardized Tests Gridded-Response Questions Gridded-response questions are another tpe of question on standardized tests. These questions are sometimes called student-produced response griddable, or grid-in, because ou must create the answer ourself, not just choose from four or five possible answers. For gridded response, ou must mark our answer on a grid printed on an answer sheet. The grid contains a row of four or five boes at the top, two rows of ovals or circles with decimal and fraction smbols, and four or five columns of ovals, numbered 0 9. At the right is an eample of a grid from an answer sheet. EXAMPLE Find the -coordinate for the solution of the given sstem of equations. / / = + = - What value do ou need to find? You need to find onl the -coordinate of the point where the graphs of the two equations intersect. You could graph the sstem, but that takes time. The easiest method is probabl the substitution method since the second equation can be solved easil for. - + = - Second equation = - + Solve the second equation for. - = First equation - (- + ) = Substitute for. + - = = Distributive Propert Simplif. The answer to be filled in on the grid is. How do ou fill in the grid for the answer? Write our answer in the answer boes. Write onl one digit or smbol in each answer bo. Do not write an digits or smbols outside the answer boes. You ma write our answer with the first digit in the left answer bo, or with the last digit in the right answer bo. You ma leave blank an boes ou do not need on the right or the left side of our answer. Fill in onl one bubble for ever answer bo that ou have written in. Be sure not to fill in a bubble under a blank answer bo. / / / / Man gridded response questions result in an answer that is a fraction or a decimal. These values can also be filled in on the grid. 9 Preparing for Standardized Tests

72 EXAMPLE Zuri is solving a problem about the area of a room. The equation she needs to solve is + - = 0. Since the answer will be a length, she onl needs to find the positive root. What is the solution? Since ou can see the equation is not easil factorable, use the Quadratic Formula. -b ± = b - ac a - ± -()(-) = () - + = _ There are two roots, but ou onl need the positive one. = _ or _ How do ou grid the answer? You can either grid the fraction _, or rewrite it as 0. and grid the decimal. Be sure to write the decimal point or fraction bar in the answer bo. The following are acceptable answer responses that represent _ and 0.. Preparing for Standardized Tests / / / / / / / / / / Do not leave a blank answer bo in the middle of an answer. Some problems ma result in an answer that is a mied number. Before filling in the grid, change the mied number to an equivalent improper fraction or decimal. For eample, if the answer is _, do not enter /, as this will be interpreted as _. Instead, either enter / or.. EXAMPLE José is using this figure for a computer 7_ graphics design. He wants to dilate the figure b a scale factor of. What will be the -coordinate of the image of D? To find the -coordinate of the image of D, multipl the -coordinate b the scale factor of 7_. 7_ = 7_ Grid in 7/ or.. Do not grid /. C B D A 7 / / / / / Preparing for Standardized Tests 9

73 Preparing for Standardized Tests Gridded-Response Practice Solve each problem. Then cop and complete a grid. Number and perations. Rewrite as a power of. What is the value of the eponent for?. Wolf 9 is the fourth closest star to Earth. It is,,0 million miles from Earth. A light-ear, the distance light travels in a ear, is. 0 miles. What is the distance from Earth to Wolf 9 in light-ears? Round to the nearest tenth.. A store received a shipment of coats. The coats were marked up 0% to sell to the customers. At the end of the season, the coats were discounted 0%. Find the ratio of the discounted price of a coat to the original cost of the coat to the store.. Find the value of the determinant Kendra is displaing eight sweaters in a store window. There are four identical red sweaters, three identical brown sweaters, and one white sweater. How man different arrangements of the eight sweaters are possible?. An electronics store reduced the price of a DVD plaer b 0% because it was used as a displa model. If the reduced price was $07.0, what was the cost in dollars before it was reduced? Round to the nearest cent if necessar. Algebra 9. The graph shows the retail price per gallon of unleaded gasoline in the U.S. from 90 to 000. What is the slope if a line is drawn through the points for and 0 ears since 90? Cost per Gallon (dollars) Retail Price of Unleaded Gasoline (0,.) 0. Solve = -. Geometr (,.0) (0,.) 0 0 Years Since 90 Source: U.S. Dept. of Energ. Polgon DABC is rotated 90 counterclockwise and then reflected over the line =. What is the -coordinate of the final image of A? D (0,.) (,.) 7. The bo shown can be purchased to ship merchandise at the Pack n Ship Store. The volume of the bo is 9 cubic inches. What is the measure of the greatest dimension of the bo in inches? C B A 9 in.. A garden is shaped as shown below. What is the measure of A to the nearest degree? ( ) in. ( ) in. A m. If ƒ()= - + 0, find f( ). Question Fractions do not have to be written in lowest terms. An equivalent fraction that fits the grid is correct.. A circle of radius r is circumscribed about a square. What is the ratio of the area of the circle to the area of the square? Epress the ratio as a decimal rounded to the nearest hundredth. 9 Preparing for Standardized Tests

74 . Find the value of 0. Each angle of a regular polgon measures 0. How man sides does the polgon have? Measurement 7. The Pascal (P) is a measure of pressure that is equivalent to Newton per square meter. The tpical pressure in an automobile tire is 0 P while tpical blood pressure is. 0 P. How man times greater is the pressure in a tire than tpical blood pressure?. A circular ride at an amusement park rotated 7π_ radians while loading riders. What is the degree measure of the rotation? 9. Find the value of in the triangle. Round to the nearest tenth of a foot. 0. Four equal-sized clindrical juice cans are packed tightl in the bo shown. What is the volume of space in the bo that is not occupied b the cans in cubic inches? Use. for π and round to the nearest cubic inch.. Caroline is making a quilt. The diagram shows a piece of cloth she will cut for a portion of the pattern. Find the area of the entire heagonal piece to the nearest tenth of a square inch. ft. in. 0 ft in. Data Analsis and Probabilit. ften girls on a team, three have blue ees. If two girls are chosen at random, what is the probabilit that neither has blue ees?. In order to win a game, Miguel needs to advance his game piece spaces. What is the probabilit that the sum of the numbers on the two dice he rolls will be?. The table shows the number of televisions owned per 000 people in each countr. What is the absolute value of the difference between the mean and the median of the data? Countr Televisions United States Latvia 7 Japan 79 Canada 7 Australia 70 United Kingdom Norwa Finland France Source: International Telecommunication Union. The table shows the amount of breakfast cereal eaten per person each ear b the ten countries that eat the most. Find the standard deviation of the data set. Round to the nearest tenth of a pound. Countr Cereal (lb) Sweden Canada 7 Australia United Kingdom Nauru New Zealand Ireland United States Finland 0 Denmark 7 Source: Euromonitor. Two number cubes are rolled. If the two numbers appearing on the faces of the number cubes are different, find the probabilit that the sum is. Round to the nearest hundredth. Preparing for Standardized Tests Preparing for Standardized Tests 97

75 Preparing for Standardized Tests Short-Response Questions Short-response questions require ou to provide a solution to the problem, as well as an method, eplanation, and/or justification ou used to arrive at the solution. These are-sometimes called constructed-response, open-response, open-ended, freeresponse, or student-produced questions. The following is a sample rubric, or scoring guide, for scoring short-response questions. Criteria Full credit: The answer is correct and a full eplanation is provided that shows each step in arriving at the fi nal answer. Partial credit: There are two different was to receive partial credit. The answer is correct, but the eplanation provided is incomplete or incorrect. The answer is incorrect, but the eplanation and method of solving the problem is correct. No credit: Either an answer is not provided or the answer does not make sense. Score 0 n some standardized tests, no credit is given for a correct answer if our work is not shown. EXAMPLE Mr. Youngblood has a fish pond in his backard. It is circular with a diameter of 0 feet. He wants to build a walkwa of equal width around the pond. He wants the total area of the pond and walkwa to be about 0 square feet. To the nearest foot, what should be the width of the walkwa? Full Credit Solution STRATEGY Diagrams Draw a diagram of the pond and the walkwa. Label important information. Since length must be positive, eliminate the negative solution. First draw a diagram to represent the situation. Since the diameter of the pond is 0 feet, the radius is ft. Let the width of the walkwa be feet. 0 ft A = πr 0 = π( + ) r = +, A = 0 0 = π( ) Multipl. _ 0 π = π( ) π Divide b π, using. for π. = or = 0 Use the Quadratic Formula. = b ± b ac a ( 0) ()( 9) = 0 ± a =, b = 0, c = 9 () -0 + = or The width of the walkwa should be feet. ft ft The steps, calculations, and reasoning are clearl stated. Before taking a standardized test, memorize common formulas, like the Quadratic Formula, to save time. 9 Preparing for Standardized Tests

76 There is no eplanation of how the quadratic equation was found. Partial Credit Solution In this sample solution, the equation that can be used to solve the problem is correct. However, there is no justification for an of the calculations = = _ = - or The walkwa should be feet wide. Partial Credit Solution In this sample solution, the answer is incorrect because the wrong root was chosen. Preparing for Standardized Tests Since the diameter of the pond is 0 feet, the radius is ft. Let the width of the walkwa be feet. Use the formula for the area of a circle. A = πr 0 = π( + ) 0 = π( ) _ 0 π = π( ) π = a 0 a or a 0-9 = 0 Use the Quadratic Formula. -b ± b = - ac a = - or The walkwa should be feet wide. The negative root was chosen as the solution. No Credit Solution Use the formula for the area of a circle. A = πr 0 = π() 0 =.() 0 = 7. =. Build the walkwa feet wide. The width of the walkwa is used incorrectl in the area formula for a circle. However, when the student rounds the value for the width of the walkwa, the answer is correct. No credit is given for an answer achieved using fault reasoning. Preparing for Standardized Tests 99

77 Preparing for Standardized Tests Short-Response Practice Solve each problem. Show all our work. Number and perations. An earthquake that measures a value of on the Richter scale releases the same amount of energ as 70 grams of TNT, while one that measures on the scale releases the energ of metric tons of TNT. ne metric ton is 000 kilograms and 000 grams is kilogram. How man times more energ is released b an earthquake measuring than one measuring?. In 000, Cook Count, Illinois was the second largest count in the U.S. with a population of about,77,000. This was about.% of the population of Illinois. What was the approimate population of Illinois in 000?. Show wh [ 0 0 ] is the identit matri for multiplication for matrices.. The total volume of the oceans on Earth is. 0 cubic miles. The total surface area of the water of the oceans is 9. million square miles. What is the average depth of the oceans? 0. Write an equation that fits the data in the table. Geometr A sledding hill at the local park has an angle of elevation of. Its vertical drop is 00 feet. What is the length of the sledding path? sledding path 00 ft. Polgon BDFH is transformed using the matri [ 0 0 ]. Graph B D F H and identif the tpe of transformation. B D. At the Blaine Count Fair, there are finalists in the technolog project competition. How man was can st, nd, rd, and th place be awarded? H Algebra. Factor a + b. Eplain each step. - a 7. Solve and graph 7 - a < _.. Solve the sstem of equations. + 9 = - = - 9. The table shows what Miranda Richards charges for landscaping services for various numbers of hours. Write an equation to find the charge for an amount of time, where is the total charge in dollars and is the amount of time in hours. Eplain the meaning of the slope and -intercept of the graph of the equation. Hours Charge (dollars) Hours 90 Preparing for Standardized Tests Charge (dollars) The map shows the trails that connect three hiking destinations. If Amparo hikes from Deer Ridge to Egg Mountain to Lookout Point and back to Deer Ridge, what is the distance she will have traveled? Lookout Point Deer Ridge mi. F Egg Mountain. Mr Washington is making a cement table for his backard. The tabletop will be circular with a diameter of feet and a depth of inches. How much cement will Mr. Washington need to make the top of the table? Use. for π and round to the nearest cubic foot.

78 . A triangular garden is plotted on grid paper, where each unit is meter. Its sides are segments that are parts of the lines with equations = - _ +, - =, and = -. Graph the triangle and find its area. Measurement. Dlan is fling a kite. He wants to know how high above the ground it is. He knows that he has let out 7 feet of string and that it is fling directl over a nearb fence post. If he is 0 feet from the fence post, how high is the kite? Round to the nearest tenth of a foot. Data Analsis and Probabilit. The table shows the 000 populations of the si largest cities in Tennessee. Which measure, mean or median, do ou think best represents the data? Eplain our answer. Cit Population Chattanooga,0 Clarksville 0,9 Jackson 0, Knoville 7, Memphis, Nashville-Davidson,9 Preparing for Standardized Tests 7. The temperature of the Sun can reach 7,000,000 F. The relationship between Fahrenheit F and Celsius C temperatures is given b the equation F =.C +. Find the temperature of the Sun in degrees Celsius.. In 00, Monaco was the most densel populated countr in the world. There were about,0 people occuping the countr at the rate of,77 people per square kilometer. What is the area of Monaco? 9. A bo containing laundr soap is a clinder with a diameter of 0. inches and a height of inches. What is the surface area of the bo? 0. Light travels at,9 miles per second or 99,79 kilometers per second. What is the relationship between miles and kilometers?. Home Place Hardware sells storage buildings for our backard. The front of the building is a trapezoid as shown. The store manager wants to advertise the total volume of the building. Find the volume in cubic feet. 0 ft ft ft Questions,, and Be sure to read the instructions of each problem carefull. Some questions ask for more than one solution, specif how to round answers, or require an eplanation. Source: International Communication Union. The scatter plot shows the number of hours worked per week for U.S. production workers from 970 through 000. Let be the hours worked per week and be the ears since 970. Write an equation that ou think best models the data. Hours 7 0 Average Hours Worked per Week for Production Workers (0, 7.) (,.) (0,.) (0,.) (,.9) Years Since 970 Source: Bureau of Labor Statistics (,.) (0,.). A da camp has 0 participants. Children can sign up for various activities. Suppose children take swimming, 0 take soccer, and 7 take both swimming and soccer. What is the probabilit that a child selected at random takes swimming or soccer?. In how man different was can seven members of a student government committee sit around a circular table?. Illinois residents can choose to bu an environmental license plate to support Illinois parks. Each environmental license plate displas or letters followed b a number thru 99. How man different environmental license plates can be issued? Preparing for Standardized Tests 9

79 Preparing for Standardized Tests Etended-Response Questions Etended-response questions are often called open-ended or constructed-response questions. Most etended-response questions have multiple parts. You must answer all parts to receive full credit. Etended-response questions are similar to short-response questions in that ou must show all of our work in solving the problem and a rubric is used to determine whether ou receive full, partial, or no credit. The following is a sample rubric for scoring etendedresponse questions. Criteria Full credit: The answer is correct and a full eplanation is provided that shows each step in arriving at the fi nal answer. Partial credit: There are two different was to receive partial credit. The answer is correct, but the eplanation provided is incomplete or incorrect. The answer is incorrect, but the eplanation and method of solving the problem is correct. No credit: Either an answer is not provided or the answer does not make sense. Credit 0 n some standardized tests, no credit is given for a correct answer if our work is not shown. Make sure that when the problem sas to Show our work, ou show ever aspect of our solution including figures, sketches of graphing calculator screens, or reasoning behind computations. EXAMPLE Libb throws a ball into the air with a velocit of feet per second. She releases the ball feet above the ground. The height of the ball above the ground t seconds after release is modeled b an equation of the form h(t) = -t + v o t + h o where v o is the initial velocit in feet per second and h o is the height at which the ball is released. a. Write an equation for the flight of the ball. Sketch the graph of the equation. b. Find the maimum height that the ball reaches and the time that this height is reached. c. Change onl the speed of the release of the ball such that the ball will reach a maimum height greater than 00 feet. Write an equation for the flight of the ball. Full Credit Solution Part a A complete graph includes appropriate scales and labels for the aes, and points that are correctl graphed. A complete graph also shows the basic characteristics of the graph. The student should realize that the graph of this equation is a parabola opening downward with a maimum point reached at the verte. The student should choose appropriate points to show the important characteristics of the graph. Students should realize that t and and h(t) and are interchangeable on a graph on the coordinate plane. 9 Preparing for Standardized Tests

80 To write the equation for the ball, I substituted v o = and h o = into the equation h(t) = -t + v o t + h o, so the equation is h(t) = -t + t +. To graph the equation, I found the equation of the ais of smmetr and the verte. = - b_ a = - _ (-) or The equation of the ais of smmetr is =, so the -coordinate of the verte is. You let t = and then h(t) = -t + t + = -() + () + or 9. The verte is (, 9). I found some other points and sketched the graph. I graphed points (t, h(t)) as (, ) h(t) (, ) (0, ) (, 9) (, ) (, ) t Preparing for Standardized Tests Part b The maimum height of the ball is reached at the verte of the parabola. So, the maimum height is 9 feet and the time it takes to reach the maimum height is seconds. In part c, an equation whose graph has a verte with -coordinate greater than 00 would be a correct answer earning full credit. Part c Since I have a graphing calculator, I changed the value of v o until I found a graph in which the or h(t) coordinate was greater than 00. The equation I used was h(t) = -t + 0t +. Partial Credit Solution Part a This sample answer includes no labels for the graph or the aes and one of the points is not graphed correctl. h(t) = -t + t + ; (, 9) h(t) 0 (, 9) 0 t Preparing for Standardized Tests 9

81 Part b Full credit is given because the verte is correct and is interpreted correctl. Preparing for Standardized Tests The verte shows the maimum height of the ball. The time it takes to reach the maimum height of 9 feet is seconds. Part c Partial credit is given for part c since no eplanation is given for using this equation. The student did not mention that the verte would have a -coordinate greater than 00. I will write the equation h(t) = -t + 00t +. This sample answer might have received a score of or, depending on the judgment of the scorer. Had the student sketched a more accurate graph and given more complete eplanations for Parts a and c, the score would probabl have been a. No Credit Solution Part a No credit is given because the equation is incorrect with no eplanation and the sketch of the graph has no labels, making it impossible to determine whether the student understands the relationship between the equation for a parabola and the graph. h(t) = -t + t + t Part b It reaches about 0 feet. Part c A good equation for the ball is h(t) = t + t In this sample answer, the student does not understand how to substitute the given information into the equation, graph a parabola, or interpret the verte of a parabola. 9 Preparing for Standardized Tests

82 Etended Response Practice Solve each problem. Show our work. Number and perations. Mrs. Ebbrect is assigning identification (ID) numbers to freshman students. She plans to use onl the digits,,,, 7, and 9. The ID numbers will consist of three digits with no repetitions. a. How man -digit ID numbers can be formed? b. How man more ID numbers can Mrs. Ebbrect make if she allows repetitions? c. What tpe of sstem could Mrs. Ebbrect use to choose the numbers if there are at least 00 students who need ID numbers?. Use these four matrices. A = [ - 0 -] B = [ - 0 -] C = [ -7 - ] D = [- ] a. Find A + C. b. Compare the dimensions of AB and DB. c. Compare the matrices BC and CB. b. Write an equation in slope-intercept form for the line passing through the point for 90 and the point for 000. Compare the slope of this line to the slope of the line in part a. c. Which equation, if an, do ou think Roger should use to model the data? Eplain. d. Suggest an equation that is not linear for Roger to use.. Brad is coaching the bantam age division ( ears old and ounger) swim team. n the first da of practice, he has the team swim laps of the -meter pool. For each of the net practices, he increases the laps b. In other words, the children swim laps the first da, 7 laps the second da, 0 laps the third da, and so on. a. Write a formula for the nth term of the sequence of the number of laps each da. Eplain how ou found the formula. b. How man laps will the children swim on the 0th da? c. Brad s goal is to have the children swim at least one mile during practice on the 0th da. If one mile is approimatel. kilometers, will Brad reach his goal? Preparing for Standardized Tests Algebra. Roger is using the graph showing the gross cash income for all farms in the U.S. from 90 through 000 to make some predictions for the future. Farm Income Geometr. Alejandra is planning to use a star shape in a gala-themed mural on her wall. The pentagon in the center is regular, and the triangles forming the points are isosceles. Income (millions of dollars) 0,000 00,000 0,000 00,000 0, Year 970 Source: U.S. Department of Agriculture a. Write an equation in slope-intercept form for the line passing through the point for 90 and the point for ft ft. ft a. Find the measures of,, and. Eplain our method. b. The approimate dimensions of the design are given. The segment of length. feet is the apothem of the pentagon. Find the approimate area of the design. c. If Alejandra circumscribes a circle about the star, what is the area of the circle? Preparing for Standardized Tests 9

83 Preparing for Standardized Tests. Kareem is using polgon ABCDE, shown on a coordinate plane, as a basis for a computer graphics design. He plans to perform various transformations on the polgon to produce a variet of interesting designs. A E B D C a. First, Kareem creates polgon A B C D E b rotating ABCDE counterclockwise about the origin 70. Graph polgon A B C D E and describe the relationship between the coordinates of ABCDE and A B C D E. b. Net, Kareem reflects polgon A B C D E in the line = to produce polgon A B C D E. Graph A B C D E and describe the relationship between the coordinates of A B C D E and A B C D E. c. Describe how Kareem could transform polgon ABCDE to polgon A B C D E with onl one transformation. Measurement. A clindrical cooler has a diameter of 9 inches and a height of inches. Scott plans to use it for soda cans that have a diameter of. inches and a height of.7 inches. in. 9 in..7 in.. in. a. Scott plans to place two laers consisting of 9 cans each into the cooler. What is the volume of the space that will not be filled with cans? b. Find the ratio of the volume of the cooler to the volume of the cans in part a. Data Analsis and Probabilit 9. The table shows the total world population from 90 through 000. Year Population Year Population 90,,000,0 90,,,7 90,09,,0 990,7,9,79 970,70,, 000,0,9,9 7. The speed of a satellite orbiting Earth can be found using the equation v = _ GmE r_ me. G is the gravitational constant for Earth, me is the mass of Earth, and r is the radius of the orbit which includes the radius of Earth and the height of the satellite. a. The radius of Earth is. 0 meters. The distance of a particular satellite above Earth is 0 kilometers. What is the value of r? (Hint: The center of the orbit is the center of Earth.) b. The gravitational constant for Earth is.7 0 N m /kg. The mass of Earth is.97 0 kg. Find the speed of the satellite in part a. c. As a satellite increases in distance from Earth, what is the effect on the speed of the orbit? Eplain our reasoning. a. Between which two decades was the percent increase in population the greatest? b. Make a scatter plot of the data. c. Find a function that models the data. d. Predict the world population for Each ear, a universit sponsors a conference for women. The Venn diagram shows the number of participants in three activities for the 0 women that attended. Suppose women who attended are selected at randomfor a surve. Sculpting Hiking 9 7 Quilting Question When questions require graphing, make sure our graph is accurate to receive full credit for our correct solution. 9 Preparing for Standardized Tests a. What is the probabilit that a woman selected participated in hiking or sculpting? b. Describe a set of women such that the probabilit of their being selected is about 0.9.

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85 Glossar/Glosario A mathematics multilingual glossar is available at The glossar includes the following languages. Arabic Haitian Creole Portuguese Tagalog Bengali Hmong Russian Urdu Cantonese Korean Spanish Vietnamese English English absolute value (p. 7) A number s distance from zero on the number line, represented b. absolute value function (p. 9) A function written as f() =, where f() 0 for all values of. algebraic epression (p. ) An epression that contains at least one variable. amplitude (p. ) For functions in the form = a sin b or = a cos b, the amplitude is a. angle of depression (p. 7) The angle between a horizontal line and the line of sight from the observer to an object at a lower level. A Cómo usar el glosario en español:. Busca el término en inglés que desees encontrar.. El término en español, junto con la definición, se encuentran en la columna de la derecha. Español valor absoluto Distancia entre un número cero en una recta numérica; se denota con. función del valor absoluto Una función que se escribe f() =, donde f() 0, para todos los valores de. epresión algebraica Epresión que contiene al menos una variable. amplitud Para funciones de la forma = a sen b o = a cos b, la amplitud es a. ángulo de depresión Ángulo entre una recta horizontal la línea visual de un observador a una figura en un nivel inferior. Glossar/Glosario angle of elevation (p. 7) The angle between a horizontal line and the line of sight from the observer to an object at a higher level. arccosine (p. 07) The inverse of = cos, written as = arccos. arcsine (p. 07) The inverse of sin, written as arcsin. arctangent (p. 07) The inverse of tan written as arctan. ángulo de elevación Ángulo entre una recta horizontal la línea visual de un observador a una figura en un nivel superior. arcocoseno La inversa de = cos, que se escribe como = arccos. arcoseno La inversa de sen, que se escribe como arcsen. arcotangente La inversa de tan que se escribe como arctan. area diagram (p. 70) A model of the probabilit of two events occurring. arithmetic mean (p. ) The terms between an two nonconsecutive terms of an arithmetic sequence. arithmetic sequence (p. ) A sequence in which each term after the first is found b adding a constant, the common difference d, to the previous term. diagrama de área Modelo de la probabilidad de que ocurran dos eventos. media aritmética Cualquier término entre dos términos no consecutivos de una sucesión aritmética. sucesión aritmética Sucesión en que cualquier término después del primero puede hallarse sumando una constante, la diferencia común d, al término anterior. R Glossar

86 arithmetic series (p. 9) The indicated sum of the terms of an arithmetic sequence. asmptote (p. 7, 9) A line that a graph approaches but never crosses. augmented matri (p. ) A coefficient matri with an etra column containing the constant terms. ais of smmetr (p. 7) A line about which a figure is smmetric. serie aritmética Suma específica de los términos de una sucesión aritmética. asíntota Recta a la que se aproima una gráfica, sin jamás cruzarla. matriz ampliada Matriz coeficiente con una columna etra que contiene los términos constantes. eje de simetría Recta respecto a la cual una figura es simétrica. f() ais of smmetr f() eje de simetría b _ n (p. ) For an real number b and for an positive integer n, b _ n = n b, ecept when b < 0 and n is even. binomial (p. 7) A polnomial that has two unlike terms. B b _ n Para cualquier número real b para cualquier entero positivo n, b _ n = n b, ecepto cuando b < 0 n es par. binomio Polinomio con dos términos diferentes. binomial eperiment (p. 70) An eperiment in which there are eactl two possible outcomes for each trial, a fied number of independent trials, and the probabilities for each trial are the same. Binomial Theorem (p. ) If n is a nonnegative integer, then (a + b ) n = a n b 0 + n a n- b + n(n + ) a n- b + + a 0 b n. bivariate data (p. ) Data with two variables. eperimento binomial Eperimento con eactamente dos resultados posibles para cada prueba, un número fijo de pruebas independientes en el cual cada prueba tiene igual probabilidad. teorema del binomio Si n es un entero no negativo, entonces (a + b ) n = a n b 0 + n a n- b n(n + ) + a n- b + + a 0 b n. datos bivariados Datos con dos variables. Glossar/Glosario boundar (p. 0) A line or curve that separates the coordinate plane into two regions. bounded (p. ) A region is bounded when the graph of a sstem of constraints is a polgonal region. frontera Recta o curva que divide un plano de coordenadas en dos regiones. acotada Una región está acotada cuando la gráfica de un sistema de restricciones es una región poligonal. Glossar R

87 C Cartesian coordinate plane (p. ) A plane divided into four quadrants b the intersection of the -ais and the -ais at the origin. Quadrant II -ais Quadrant I -coordinate (, ) origin -coordinate -ais plano de coordenadas cartesiano Plano dividido en cuatro cuadrantes mediante la intersección en el origen de los ejes. Cuadrante II eje Cuadrante I coordenada (, ) origen coordenada eje Quadrant III Quadrant IV Cuadrante III Cuadrante IV center of a circle (p. 7) The point from which all points on a circle are equidistant. center of a hperbola (p. 9) The midpoint of the segment whose endpoints are the foci. center of an ellipse (p. ) The point at which the major ais and minor ais of an ellipse intersect. Change of Base Formula (p. 0) For all positive numbers a, b, and n, where a and b, lo g a n = _ lo g b n lo g b a. circle (p. 7) The set of all points in a plane that are equidistant from a given point in the plane, called the center. centro de un círculo El punto desde el cual todos los puntos de un círculo están equidistantes. centro de una hipérbola Punto medio del segmento cuos etremos son los focos. centro de una elipse Punto de intersección de los ejes maor menor de una elipse. fórmula del cambio de base Para todo número positivo a, b n, donde a b, lo g a n = _ lo g b n lo g b a. círculo Conjunto de todos los puntos en un plano que equidistan de un punto dado del plano llamado centro. Glossar/Glosario radius (, ) r (h, k) center radio (, ) r (h, k) centro circular functions (p. 00) Functions defined using a unit circle. coefficient (p. 7) The numerical factor of a monomial. column matri (p. ) A matri that has onl one column. combination (p. 9) An arrangement of objects in which order is not important. funciones circulares Funciones definidas en un círculo unitario. coeficiente Factor numérico de u monomio. matriz columna Matriz que sólo tiene una columna. combinación Arreglo de elementos en que el orden no es importante. R Glossar

88 common difference (p. ) The difference between the successive terms of an arithmetic sequence. common logarithms (p. ) Logarithms that use 0 as the base. common ratio (p. ) The ratio of successive terms of a geometric sequence. completing the square (p. 9) A process used to make a quadratic epression into a perfect square trinomial. comple conjugates (p. ) Two comple numbers of the form a + bi and a - bi. comple fraction (p. ) A rational epression whose numerator and/or denominator contains a rational epression. comple number (p. ) An number that can be written in the form a + bi, where a and b are real numbers and i is the imaginar unit. composition of functions (p. ) A function is performed, and then a second function is performed on the result of the first function. The composition of f and g is denoted b f g, and [ f g]() = f [ g ()]. compound event (p. 70) Two or more simple events. compound inequalit (p. ) Two inequalities joined b the word and or or. diferencia común Diferencia entre términos consecutivos de una sucesión aritmética. logaritmos comunes El logaritmo de base 0. razón común Razón entre términos consecutivos de una sucesión geométrica. completar el cuadrado Proceso mediante el cual una epresión cuadrática se transforma en un trinomio cuadrado perfecto. conjugados complejos Dos números complejos de la forma a + bi a - bi. fracción compleja Epresión racional cuo numerador o denominador contiene una epresión racional. número complejo Cualquier número que puede escribirse de la forma a + bi, donde a b son números reales e i es la unidad imaginaria. composición de funciones Se evalúa una función luego se evalúa una segunda función en el resultado de la primera función. La composición de f g se define con f g, [ f g]() = f [ g ()]. evento compuesto Dos o más eventos simples. desigualdad compuesta Dos desigualdades unidas por las palabras u o. conic section (p. 7) An figure that can be obtained b slicing a double cone. conjugate ais (p. 9) The segment of length b units that is perpendicular to the transverse ais at the center. conjugates (p. ) Binomials of the form a b + c d and a b - c d, where a, b, c, and d are rational numbers. sección cónica Cualquier figura obtenida mediante el corte de un cono doble. eje conjugado El segmento de b unidades de longitud que es perpendicular al eje transversal en el centro. conjugados Binomios de la forma a b + c d a b - c d, donde a, b, c, d son números racionales. Glossar/Glosario consistent (p. ) A sstem of equations that has at least one solution. constant (p. 7) Monomials that contain no variables. constant function (p. 9) A linear function of the form f() = b. consistente Sistema de ecuaciones que posee por lo menos una solución. constante Monomios que carecen de variables. función constante Función lineal de la forma f() = b. Glossar R

89 constant of variation (p. ) The constant k used with direct or inverse variation. constant term (p. ) In f() = a + b + c, c is the constant term. constraints (p. ) Conditions given to variables, often epressed as linear inequalities. continuit (p. 7) A graph of a function that can be traced with a pencil that never leaves the paper. continuous probabilit distribution (p. 7) The outcome can be an value in an interval of real numbers, represented b curves. continuous relation (p. 9) A relation that can be graphed with a line or smooth curve. cosecant (p. 79) For an angle, with measure, a point P(, ) on its terminal side, r = +, csc r. cosine (p. 79) For an angle, with measure, a point P(, ) on its terminal side, r = +, cos r. cotangent (p. 79) For an angle, with measure, a point P(, ) on its terminal side, r = +, cot. constante de variación La constante k que se usa en variación directa o inversa. término constante En f() = a + b + c, c es el término constante. restricciones Condiciones a que están sujetas las variables, a menudo escritas como desigualdades lineales. continuidad La gráfica de una función que se puede calcar sin levantar nunca el lápiz del papel. distribución de probabilidad continua El resultado puede ser cualquier valor de un intervalo de números reales, representados por curvas. relación continua Relación cua gráfica puede ser una recta o una curva suave. cosecante Para cualquier ángulo de medida, un punto P(, ) en su lado terminal, r = +, csc r. coseno Para cualquier ángulo de medida, un punto P(, ) en su lado terminal, r = +, cos r. cotangente Para cualquier ángulo de medida, un punto P(, ) en su lado terminal, r = +, cot. Glossar/Glosario coterminal angles (p. 77) Two angles in standard position that have the same terminal side. convergent series (p. ) An infinite series with a sum. countereample (p. 7) A specific case that shows that a statement is false. Cramer s Rule (p. 0) A method that uses determinants to solve a sstem of linear equations. ángulos coterminales Dos ángulos en posición estándar que tienen el mismo lado terminal. serie convergente Serie infinita con una suma. contraejemplo Caso específico que demuestra la falsedad de un enunciado. regla de Crámer Método que usa determinantes para resolver un sistema de ecuaciones lineales. D degree (p. 7) The sum of the eponents of the variables of a monomial. degree of a polnomial (p. 0) The greatest degree of an term in the polnomial. grado Suma de los eponentes de las variables de un monomio. grado de un polinomio Grado máimo de cualquier término del polinomio. R Glossar

90 dependent events (p. ) The outcome of one event does affect the outcome of another event. dependent sstem (p. ) A consistent sstem of equations that has an infinite number of solutions. dependent variable (p. ) The other variable in a function, usuall, whose values depend on. depressed polnomial (p. 7) The quotient when a polnomial is divided b one of its binomial factors. determinant (p. 9) A square arra of numbers or variables enclosed between two parallel lines. dilation (p. 7) A transformation in which a geometric figure is enlarged or reduced. dimensional analsis (p. ) Performing operations with units. dimensions of a matri (p. ) The number of rows, m, and the number of columns, n, of the matri written as m n. directri (p. 7) See parabola. direct variation (p. ) varies directl as if there is some nonzero constant k such that = k. k is called the constant of variation. discrete probabilit distributions (p. 7) Probabilities that have a finite number of possible values. eventos dependientes El resultado de un evento afecta el resultado de otro evento. sistema dependiente Sistema de ecuaciones que posee un número infinito de soluciones. variable dependiente La otra variable de una función, por lo general, cuo valor depende de. polinomio reducido El cociente cuando se divide un polinomio entre uno de sus factores binomiales. determinante Arreglo cuadrado de números o variábles encerrados entre dos rectas paralelas homotecia Transformación en que se amplía o se reduce un figura geométrica. anállisis dimensional Realizar operaciones con unidades. tamaño de una matriz El número de filas, m, columnas, n, de una matriz, lo que se escribe m n. directriz Véase parábola. variación directa varía directamente con si ha una constante no nula k tal que = k. k se llama la constante de variación. distribución de probabilidad discreta Probabilidades que tienen un número finito de valores posibles. discrete relation (p. 9) A relation in which the domain is a set of individual points. discriminant (p. 79) In the Quadratic Formula, the epression b - ac. dispersion (p. 7) Measures of variation of data. Distance Formula (p. ) The distance between two points with coordinates (, ) and (, ) is given b d = ( - ) + ( - ). relación discreta Relación en la cual el dominio es un conjunto de puntos individuales. discriminante En la fórmula cuadrática, la epresión b - ac. dispersión Medidas de variación de los datos. fórmula de la distancia La distancia entre dos puntos (, ) and (, ) viene dada por d = ( - ) + ( - ). Glossar/Glosario domain (p. ) The set of all -coordinates of the ordered pairs of a relation. dominio El conjunto de todas las coordenadas de los pares ordenados de una relación. E e (p. ) The irrational number.7. e is the base of the natural logarithms. e El número irracional.7. e es la base de los logaritmos naturales. Glossar R7

91 element (p. ) Each value in a matri. elimination method (p. ) Eliminate one of the variables in a sstem of equations b adding or subtracting the equations. ellipse (p. ) The set of all points in a plane such that the sum of the distances from two given points in the plane, called foci, is constant. elemento Cada valor de una matriz. método de eliminación Eliminar una de las variables de un sistema de ecuaciones sumando o restando las ecuaciones. elipse Conjunto de todos los puntos de un plano en los que la suma de sus distancias a dos puntos dados del plano, llamados focos, es constante. Major ais eje maor (a, 0) a a (a, 0) (a, 0) a a (a, 0) b F (c, 0) c F (c, 0) b F (c, 0) c F (c, 0) Center Minor ais centro eje menor empt set (p. ) The solution set for an equation that has no solution, smbolized b { } or ø. end behavior (p. ) The behavior of the graph as approaches positive infinit (+ ) or negative infinit (- ). equal matrices (p. ) Two matrices that have the same dimensions and each element of one matri is equal to the corresponding element of the other matri. conjunto vacío Conjunto solución de una ecuación que no tiene solución, denotado por { } o ø. comportamiento final El comportamiento de una gráfica a medida que tiende a más infinito (+ ) o menos infinito (- ). matrices iguales Dos matrices que tienen las mismas dimensiones en las que cada elemento de una de ellas es igual al elemento correspondiente en la otra matriz. Glossar/Glosario equation (p. ) A mathematical sentence stating that two mathematical epressions are equal. event (p. ) ne or more outcomes of a trial. epansion b minors (p. 9) A method of evaluating a third or high order determinant b using determinants of lower order. ecuación Enunciado matemático que afirma la igualdad de dos epresiones matemáticas. evento Uno o más resultados de una prueba. epansión por determinantes menores Un método de calcular el determinante de tercer orden o maor mediante el uso de determinantes de orden más bajo. eponential deca (p. 00) Eponential deca occurs when a quantit decreases eponentiall over time. f() desintegración eponencial curre cuando una cantidad disminue eponencialmente con el tiempo. f() Eponential Deca desintegración eponencial R Glossar

92 eponential equation (p. 0) An equation in which the variables occur as eponents. eponential function (p. 99) A function of the form = ab, where a 0, b > 0, and b. ecuación eponencial Ecuación en que las variables aparecen en los eponentes. función eponencial Una función de la forma = ab, donde a 0, b > 0, b. eponential growth (p. 00) Eponential growth occurs when a quantit increases eponentiall over time. f() Eponential Growth crecimiento eponencial El que ocurre cuando una cantidad aumenta eponencialmente con el tiempo. f() Eponential Growth eponential inequalit (p. 0) An inequalit involving eponential functions. etraneous solution (p. ) A number that does not satisf the original equation. etrapolation (p. 7) Predicting for an -value greater than an in the data set. desigualdad eponencial Desigualdad que contiene funciones eponenciales. solución etraña Número que no satisface la ecuación original. etrapolación Predicción para un valor de maor que cualquiera de los de un conjunto de datos. F factorial (p. ) If n is a positive integer, then n! = n(n - )(n - ).... failure (p. 97) An outcome other than the desired outcome. famil of graphs (p. 7) A group of graphs that displas one or more similar characteristics. factorial Si n es un entero positivo, entonces n! = n(n - )(n - ).... fracaso Cualquier resultado distinto del deseado. familia de gráficas Grupo de gráficas que presentan una o más características similares. feasible region (p. ) The intersection of the graphs in a sstem of constraints. Fibonacci sequence (p. ) A sequence in which the first two terms are and each of the additional terms is the sum of the two previous terms. focus (pp. 7,, 90) See parabola, ellipse, hperbola. región viable Intersección de las gráficas de un sistema de restricciones. sucesión de Fibonacci Sucesión en que los dos primeros términos son iguales a cada término que sigue es igual a la suma de los dos anteriores. foco Véase parábola, elipse, hipérbola. Glossar/Glosario FIL method (p. ) The product of two binomials is the sum of the products of F the first terms, the outer terms, I the inner terms, and L the last terms. método FIL El producto de dos binomios es la suma de los productos de los primeros (First) términos, los términos eteriores (uter), los términos interiores (Inner) los últimos (Last) términos. formula (p. 7) A mathematical sentence that epresses the relationship between certain quantities. fórmula Enunciado matemático que describe la relación entre ciertas cantidades. Glossar R9

93 function (p. 9) A relation in which each element of the domain is paired with eactl one element in the range. function notation (p. ) An equation of in terms of can be rewritten so that = f(). For eample, = + can be written as f() = +. Fundamental Counting Principle (p. ) If event M can occur in m was and is followed b event N that can occur in n was, then event M followed b event N can occur in m n was. función Relación en que a cada elemento del dominio le corresponde un solo elemento del rango. notación funcional Una ecuación de en términos de puede escribirse en la forma = f(). Por ejemplo, = + puede escribirse como f() = +. principio fundamental de conteo Si el evento M puede ocurrir de m maneras es seguido por el evento N que puede ocurrir de n maneras, entonces el evento M seguido por el evento N pueden ocurrir de m n maneras. G geometric mean (p. ) The terms between an two nonsuccessive terms of a geometric sequence. media geométrica Cualquier término entre dos términos no consecutivos de una sucesión geométrica. geometric sequence (p. ) A sequence in which each term after the first is found b multipling the previous term b a constant r, called the common ratio. sucesión geométrica Sucesión en que cualquier término después del primero puede hallarse multiplicando el término anterior por una constante r, llamada razón común. geometric series (p. ) The sum of the terms of a geometric sequence. serie geométrica La suma de los términos de una sucesión geométrica. greatest integer function (p. 9) A step function, written as f() =, where f() is the greatest integer less than or equal to. función del máimo entero Una función etapa que se escribe f() =, donde f() es el meaimo entero que es menor que o igual a. Glossar/Glosario hperbola (p. 90) The set of all points in the plane such that the absolute value of the difference of the distances from two given points in the plane, called foci, is constant. H hipérbola Conjunto de todos los puntos de un plano en los que el valor absoluto de la diferencia de sus distancias a dos puntos dados del plano, llamados focos, es constante. asmptote asmptote asíntota asíntota transverse ais center verte verte F F a b c eje transversal centro vértice vértice F F a b c conjugate ais eje conjugado R0 Glossar

94 I identit function (p. 9, 9) The function I() =. identit matri (p. 0) A square matri that, when multiplied b another matri, equals that same matri. If A is an n n matri and I is the n n identit matri, then A I = A and I A = A. image (p. ) The graph of an object after a transformation. imaginar unit (p. 0) i, or the principal square root of -. inclusive (p. 7) Two events whose outcomes ma be the same. inconsistent (p. ) A sstem of equations that has no solutions. independent events (p. ) Events that do not affect each other. independent sstem (p. ) A sstem of equations that has eactl one solution. independent variable (p. ) In a function, the variable, usuall, whose values make up the domain. unción identidad La función I() =. matriz identidad Matriz cuadrada que al multiplicarse por otra matriz, es igual a la misma matriz. Si A es una matriz de n n e I es la matriz identidad de n n, entonces A I = A I A = A. imagen Gráfica de una figura después de una transformación. unidad imaginaria i, o la raíz cuadrada principal de -. inclusivo Dos eventos que pueden tener los mismos resultados. inconsistente Sistema de ecuaciones que no tiene solución alguna. eventos independientes Eventos que no se afectan mutuamente. sistema independiente Sistema de ecuaciones que sólo tiene una solución. variable independiente En una función, la variable, por lo general, cuos valores forman el dominio. inde of summation (p. ) The variable used with the summation smbol. In the epression below, the inde of summation is n. n n= inductive hpothesis (p. 70) The assumption that a statement is true for some positive integer k, where k n. infinite geometric series (p. 0) A geometric series with an infinite number of terms. initial side of an angle (p. 7) The fied ra of an angle. índice de suma Variable que se usa con el símbolo de suma. En la siguiente epresión, el índice de suma es n. n n= hipótesis inductiva El suponer que un enunciado es verdadero para algún entero positivo k, donde k n. serie geométrica infinita Serie geométrica con un número infinito de términos. lado inicial de un ángulo El rao fijo de un ángulo. Glossar/Glosario terminal side 0 initial side lado terminal 0 lado inicial verte vértice Glossar R

95 intercept form (p. ) A quadratic equation in the form = a( - p)( - q) where p and q represent the -intercept of the graph. forma intercepción Ecuación cuadrática de la forma = a( - p)( - q) donde p q representan la intersección de la gráfica. interpolation (p. 7) Predicting for an -value between the least and greatest values of the set. interpolación Predecir un valor de entre los valores máimo mínimo del conjunto de datos. intersection (p. ) The graph of a compound inequalit containing and. intersección Gráfica de una desigualdad compuesta que contiene la palabra. inverse (p. 09) Two n n matrices are inverses of each other if their product is the identit matri. inversa Dos matrices de n n son inversas mutuas si su producto es la matriz identidad. inverse function (p. 9) Two functions f and g are inverse functions if and onl if both of their compositions are the identit function. función inversa Dos funciones f g son inversas mutuas si sólo si las composiciones de ambas son la función identidad. inverse of a trigonometric function (p. 0) The arccosine, arcsine, and arctangent relations. inversa de una función trigonométrica Las relaciones arcocoseno, arcoseno arcotangente. inverse relations (p. 9) Two relations are inverse relations if and onl if whenever one relation contains the element (a, b) the other relation contains the element (b, a). relaciones inversas Dos relaciones son relaciones inversas mutuas si sólo si cada vez que una de las relaciones contiene el elemento (a, b), la otra contiene el elemento (b, a). inverse variation (p. 7) varies inversel as if there is some nonzero constant k such that = k or = _ k, where 0 and 0. irrational number (p. ) A real number that is not rational. The decimal form neither terminates nor repeats. variación inversa varía inversamente con si ha una constante no nula k tal que = k o = _ k, donde 0 0. número irracional Número que no es racional. Su epansión decimal no es ni terminal ni periódica. iteration (p. 0) The process of composing a function with itself repeatedl. iteración Proceso de componer una función consigo misma repetidamente. Glossar/Glosario joint variation (p. ) varies jointl as and z if there is some nonzero constant k such that = kz. latus rectum (p. 9) The line segment through the focus of a parabola and perpendicular to the ais of smmetr. J L variación conjunta varía conjuntamente con z si ha una constante no nula k tal que = kz. latus rectum El segmento de recta que pasa por el foco de una parábola que es perpendicular a su eje de simetría. Law of Cosines (pp ) Let ABC be an triangle with a, b, and c representing the measures of sides, and opposite angles with measures A, B, and C, respectivel. Then the following equations are true. a = b + c - bc cos A b = a + c - ac cos B c = a + b - ab cos C Le de los cosenos Sea ABC un triángulo cualquiera, con a, b c las longitudes de los lados con ángulos opuestos de medidas A, B C, respectivamente. Entonces se cumplen las siguientes ecuaciones. a = b + c - bc cos A b = a + c - ac cos B c = a + b - ab cos C R Glossar

96 Law of Sines (p. 7) Let ABC be an triangle with a, b, and c representing the measures of sides opposite angles with measurements A, B, and C, respectivel. Then sin a A = sin B = sin C b c. leading coefficient (p. ) The coefficient of the term with the highest degree. like radical epressions (p. ) Two radical epressions in which both the radicands and indices are alike. like terms (p. 7) Monomials that can be combined. limit (p. ) The value that the terms of a sequence approach. linear correlation coefficient (p. 9) A value that shows how close data points are to a line. linear equation (p. ) An equation that has no operations other than addition, subtraction, and multiplication of a variable b a constant. linear function (p. ) A function whose ordered pairs satisf a linear equation. linear permutation (p. 90) The arrangement of objects or people in a line. linear programming (p. 0) The process of finding the maimum or minimum values of a function for a region defined b inequalities. Le de los senos Sea ABC cualquier triángulo con a, b c las longitudes de los lados con ángulos opuestos de medidas A, B C, respectivamente. Entonces sin a A = sin B = sin C b c. coeficiente líder Coeficiente del término de maor grado. epresiones radicales semejantes Dos epresiones radicales en que tanto los radicandos como los índices son semejantes. términos semejantes Monomios que pueden combinarse. límite El valor al que tienden los términos de una sucesión. coeficiente de correlación lineal Valor que muestra la cercanía de los datos a una recta. ecuación lineal Ecuación sin otras operaciones que las de adición, sustracción multiplicación de una variable por una constante. función lineal Función cuos pares ordenados satisfacen una ecuación lineal. permutación lineal Arreglo de personas o figuras en una línea. programación lineal Proceso de hallar los valores máimo o mínimo de una función lineal en una región definida por las desigualdades. linear term (p. ) In the equation f() = a + b + c, b is the linear term. line of best fit (p. 9) A line that best matches a set of data. line of fit (p. ) A line that closel approimates a set of data. Location Principle (p. 0) Suppose = f( ) represents a polnomial function and a and b are two numbers such that f(a) < 0 and f(b) > 0. Then the function has at least one real zero between a and b. término lineal En la ecuación f() = a + b + c, el término lineal es b. recta de óptimo ajuste Recta que mejor encaja un conjunto de datos. recta de ajuste Recta que se aproima estrechamente a un conjunto de datos. principio de ubicación Sea = f( ) una función polinómica con a b dos números tales que f(a) < 0 f(b) > 0. Entonces la función tiene por lo menos un resultado real entre a b. Glossar/Glosario logarithm (p. 0) In the function = b, is called the logarithm, base b, of. Usuall written as = lo g and is read equals log b base b of. logarithmic equation (p. ) An equation that contains one or more logarithms. logaritmo En la función = b, es el logaritmo en base b, de. Generalmente escrito como = lo g se lee es igual al logaritmo en b base b de. ecuación logarítmica Ecuación que contiene uno o más logaritmos. Glossar R

97 logarithmic function (p. ) The function = lo g, where b > 0 and b, which is the b inverse of the eponential function = b. logarithmic inequalit (p. ) An inequalit that contains one or more logarithms. función logarítmica La función = lo g b, donde b > 0 b, inversa de la función eponencial = b. desigualdad logarítmica Desigualdad que contiene uno o más logaritmos. M major ais (p. ) The longer of the two line segments that form the aes of smmetr of an ellipse. mapping (p. ) How each member of the domain is paired with each member of the range. margin of sampling error (ME) (p. 7) The limit on the difference between how a sample responds and how the total population would respond. mathematical induction (p. 70) A method of proof used to prove statements about positive integers. eje maor El más largo de dos segmentos de recta que forman los ejes de simetría de una elipse. transformaciones La correspondencia entre cada miembro del dominio con cada miembro del rango. margen de error muestral (EM) Límite en la diferencia entre las respuestas obtenidas con una muestra cómo pudiera responder la población entera. inducción matemática Método de demostrar enunciados sobre los enteros positivos. matri (p. ) An rectangular arra of variables or constants in horizontal rows and vertical columns. matri equation (p. ) A matri form used to represent a sstem of equations. matriz Arreglo rectangular de variables o constantes en filas horizontales columnas verticales. ecuación matriz Forma de matriz que se usa para representar un sistema de ecuaciones. Glossar/Glosario maimum value (p. ) The -coordinate of the verte of the quadratic function f() = a + b + c, where a < 0. measure of central tendenc (p. 77) A number that represents the center or middle of a set of data. measure of variation (p. 7) A representation of how spread out or scattered a set of data is. valor máimo La coordenada del vértice de la función cuadrática f() = a + b + c, where a < 0. medida de tendencia central Número que representa el centro o medio de un conjunto de datos. medida de variación Número que representa la dispersión de un conjunto de datos. midline (p. ) A horizontal ais used as the reference line about which the graph of a periodic function oscillates. minimum value (p. ) The -coordinate of the verte of the quadratic function f() = a + b + c, where a > 0. minor (p. 9) The determinant formed when the row and column containing that element are deleted. R Glossar recta central Eje horizontal que se usa como recta de referencia alrededor de la cual oscila la gráfica de una función periódica. valor mínimo La coordenada del vértice de la función cuadrática f() = a + b + c, donde a > 0. determinante menor El que se forma cuando se descartan la fila columna que contienen dicho elemento.

98 minor ais (p. ) The shorter of the two line segments that form the aes of smmetr of an ellipse. monomial (p. ) An epression that is a number, a variable, or the product of a number and one or more variables. mutuall eclusive (p. 70) Two events that cannot occur at the same time. eje menor El más corto de los dos segmentos de recta de los ejes de simetría de una elipse. monomio Epresión que es un número, una variable o el producto de un número por una o más variables. mutuamente eclusivos Dos eventos que no pueden ocurrir simultáneamente. N nth root (p. 0) For an real numbers a and b, and an positive integer n, if a n = b, then a is an nth root of b. natural base, e (p. ) An irrational number approimatel equal to.7. natural base eponential function (p. ) An eponential function with base e, = e. natural logarithm (p. 7) Logarithms with base e, written ln. raíz enésima Para cualquier número real a b cualquier entero positivo n, si a n = b, entonces a se llama una raíz enésima de b. base natural, e Número irracional aproimadamente igual a.7 función eponencial natural La función eponencial de base e, = e. logaritmo natural Logaritmo de base e, el que se escribe ln. natural logarithmic function (p. 7) = ln, the inverse of the natural base eponential function = e. negative eponent (p. ) For an real number a 0 and an integer n, a -n = _ a n and _ a -n = a n. nonrectangular hperbola (p. 9) A hperbola with asmptotes that are not perpendicular. normal distribution (p. 7) A frequenc distribution that often occurs when there is a large number of values in a set of data: about % of the values are within one standard deviation of the mean, 9% of the values are within two standard deviations from the mean, and 99% of the values are within three standard deviations. función logarítmica natural = ln, la inversa de la función eponencial natural = e. eponente negativo Para cualquier número real a 0 cualquier entero positivo n, a -n = _ a _ n a -n = a n. hipérbola no rectangular Hipérbola con asíntotas que no son perpendiculares. distribución normal Distribución de frecuencia que aparece a menudo cuando ha un número grande de datos: cerca del % de los datos están dentro de una desviación estándar de la media, 9% están dentro de dos desviaciones estándar de la media 99% están dentro de tres desviaciones estándar de la media. Glossar/Glosario Normal Distribution Distribución normal Glossar R

99 one-to-one function (p. 9). A function where each element of the range is paired with eactl one element of the domain. A function whose inverse is a function. función biunívoca. Función en la que a cada elemento del rango le corresponde sólo un elemento del dominio.. Función cua inversa es una función. open sentence (p. ) A mathematical sentence containing one or more variables. enunciado abierto Enunciado matemático que contiene una o más variables. ordered pair (p. ) A pair of coordinates, written in the form (, ), used to locate an point on a coordinate plane. par ordenado Un par de números, escrito en la forma (, ), que se usa para ubicar cualquier punto en un plano de coordenadas. ordered triple (p. ). The coordinates of a point in space. The solution of a sstem of equations in three variables,, and z. triple ordenado. Las coordenadas de un punto en el espacio. Solución de un sistema de ecuaciones en tres variables, z. rder of perations (p. ) Step Evaluate epressions inside grouping smbols. Step Evaluate all powers. Step Do all multiplications and/or divisions from left to right. Step Do all additions and subtractions from left to right. orden de las operaciones Paso Evalúa las epresiones dentro de símbolos de agrupamiento. Paso Evalúa todas las potencias. Paso Ejecuta todas las multiplicaciones divisiones de izquierda a derecha. Paso Ejecuta todas las adiciones sustracciones de izquierda a derecha. outcomes (p. ) The results of a probabilit eperiment or an event. resultados Lo que produce un eperimento o evento probabilístico. outlier (p. 7) A data point that does not appear to belong to the rest of the set. valor atípico Dato que no parece pertenecer al resto el conjunto. P Glossar/Glosario parabola (p., 7) The set of all points in a plane that are the same distance from a given point, called the focus, and a given line, called the directri. h parábola Conjunto de todos los puntos de un plano que están a la misma distancia de un punto dado, llamado foco, de una recta dada, llamada directriz. h verte ais of smmetr (h, k) vértice eje de simetría (h, k) parallel lines (p. 7) Nonvertical coplanar lines with the same slope. parent graph (p. 7) The simplest of graphs in a famil. rectas paralelas Rectas coplanares no verticales con la misma pendiente. gráfica madre La gráfica más sencilla en una familia de gráficas. R Glossar

100 partial sum (p. 0) The sum of the first n terms of a series. Pascal s triangle (p. ) A triangular arra of numbers such that the (n + ) th row is the coefficient of the terms of the epansion ( + ) n for n = 0,,... period (p. 0) The least possible value of a for which f() = f( + a). periodic function (p. 0) A function is called periodic if there is a number a such that f() = f( + a) for all in the domain of the function. permutation (p. 90) An arrangement of objects in which order is important. perpendicular lines (p. 7) In a plane, an two oblique lines the product of whose slopes is. phase shift (p. 9) A horizontal translation of a trigonometric function. piecewise function (p. 97) A function that is written using two or more epressions. point discontinuit (p. 7) If the original function is undefined for = a but the related rational epression of the function in simplest form is defined for = a, then there is a hole in the graph at = a. suma parcial La suma de los primeros n términos de una serie. triángulo de Pascal Arreglo triangular de números en el que la fila (n + ) n proporciona los coeficientes de los términos de la epansión de ( + ) n para n = 0,,... período El menor valor positivo posible para a, para el cual f() = f( + a). función periódica Función para la cual ha un número a tal que f() = f( + a) para todo en el dominio de la función. permutación Arreglo de elementos en que el orden es importante. rectas perpendiculares En un plano, dos rectas oblicuas cualesquiera cuas pendientes tienen un producto igual a. desvío de fase Traslación horizontal de una función trigonométrica. función a intervalos Función que se escribe usando dos o más epresiones. discontinuidad evitable Si la función original no está definida en = a pero la epresión racional reducida correspondiente de la función está definida en = a, entonces la gráfica tiene una ruptura o corte en = a. point discontinuit f() discontinuidad evitable f() Glossar/Glosario point-slope form (p. 0) An equation in the form - = m( - ) where (, ) are the coordinates of a point on the line and m is the slope of the line. polnomial (p. 7) A monomial or a sum of monomials. polnomial function (p. ) A function that is represented b a polnomial equation. forma punto-pendiente Ecuación de la forma - = m( - ) donde (, ) es un punto en la recta m es la pendiente de la recta. polinomio Monomio o suma de monomios. función polinomial Función representada por una ecuación polinomial. Glossar R7

101 polnomial in one variable (p. ) a n n + a n- n a + a + a 0, where the coefficients a n, a n-,..., a 0 represent real numbers, and a n is not zero and n is a nonnegative integer. power (p. 7) An epression of the form n. power function (p. 7) An equation in the form f() = a b, where a and b are real numbers. prediction equation (p. ) An equation suggested b the points of a scatter plot that is used to predict other points. preimage (p. ) The graph of an object before a transformation. principal root (p. 0) The nonnegative root. principal values (p. 0) The values in the restricted domains of trigonometric functions. probabilit (p. 97) A ratio that measures the chances of an event occurring. probabilit distribution (p. 99) A function that maps the sample space to the probabilities of the outcomes in the sample space for a particular random variable. pure imaginar number (p. 0) The square roots of negative real numbers. For an positive (real number b, - b = b -, or bi. polinomio de una variable a n n + a n- n a + a + a 0, donde los coeficientes a n, a n-,..., a 0 son números reales, a n no es nulo n es un entero no negativo. potencia Epresión de la forma n. función potencia Ecuación de la forma f() = a b, donde a b son números reales. ecuación de predicción Ecuación sugerida por los puntos de una gráfica de dispersión que se usa para predecir otros puntos. preimagen Gráfica de una figura antes de una transformación. raíz principal La raíz no negativa. valores principales Valores en los dominios restringidos de las funciones trigonométricas. probabilidad Razón que mide la posibilidad de que ocurra un evento. distribución de probabilidad Función que aplica el espacio muestral a las probabilidades de los resultados en el espacio muestral obtenidos para una variable aleatoria particular. número imaginario puro Raíz cuadrada de un número real negativo. Para cualquier número (real positivo b, - b = b -, ó bi. Q Glossar/Glosario quadrantal angle (p. 77) An angle in standard position whose terminal side coincides with one of the aes. quadrants (p. ) The four areas of a Cartesian coordinate plane. quadratic equation (p. ) A quadratic function set equal to a value, in the form a + b + c, where a 0. ángulo de cuadrante Ángulo en posición estándar cuo lado terminal coincide con uno de los ejes. cuadrantes Las cuatro regiones de un plano de coordenadas Cartesiano. ecuación cuadrática Función cuadrática igual a un valor, de la forma a + b + c, donde a 0. quadratic form (p. ) For an numbers a, b, and c, ecept for a = 0, an equation that can be written in the form a[f( ) ] + b[f()] + c = 0, where f() is some epression in. Quadratic Formula (p. 7) The solutions of a quadratic equation of the form a + b + c, where a 0, are given b the Quadratic Formula, which is = -b ± b - ac. a R Glossar forma de ecuación cuadrática Para cualquier número a, b, c, ecepto a = 0, una ecuación que puede escribirse de la forma [f( ) ] + b[f()] + c = 0, donde f() es una epresión en. fórmula cuadrática Las soluciones de una ecuación cuadrática de la forma a + b + c, donde a 0, se dan por la fórmula cuadrática, que es = -b ± b - ac. a

102 quadratic function (p. ) A function described b the equation f() = a + b + c, where a 0. quadratic inequalit (p. 9) A quadratic equation in the form > a + b + c, a + b + c, < a + b + c, or a + b + c. quadratic term (p. ) In the equation f() = a + b + c, a is the quadratic term. función cuadrática Función descrita por la ecuación f() = a + b + c, donde a 0. desigualdad cuadrática Ecuación cuadrática de la forma > a + b + c, a + b + c, < a + b + c, a + b + c. término cuadrático En la ecuación f() = a + b + c, el término cuadrático es a. R radian (p. 770) The measure of an angle θ in standard position whose ras intercept an arc of length unit on the unit circle. radical equation (p. ) An equation with radicals that have variables in the radicands. radical inequalit (p. ) An inequalit that has a variable in the radicand. random (p. 97) All outcomes have an equall likel chance of happening. random variable (p. 99) The outcome of a random process that has a numerical value. range (p. ) The set of all -coordinates of a relation. rate of change (p. 7) How much a quantit changes on average, relative to the change in another quantit, often time. radián Medida de un ángulo en posición normal cuos raos interse can un arco de unidad de longitud en el círculo unitario. ecuación radical Ecuación con radicales que tienen variables en el radicando. desigualdad radical Desigualdad que tiene una variable en el radicando. aleatorio Todos los resultados son equiprobables. variable aleatoria El resultado de un proceso aleatorio que tiene un valor numérico. rango Conjunto de todas las coordenadas de una relación. tasa de cambio Lo que cambia una cantidad en promedio, respecto al cambio en otra cantidad, por lo general el tiempo. rate of deca (p. ) The percent decrease r in the equation = a( - r ) t. rate of growth (p. ) The percent increase r in the equation = a( + r ) t. rational equation (p. 79) An equation that contains one or more rational epressions. tasa de desintegración Disminución porcentual r en la ecuación = a( - r ) t. tasa de crecimiento Aumento porcentual r en la ecuación = a( + r ) t. ecuación racional Cualquier ecuación que contiene una o más epresiones racionales. Glossar/Glosario rational eponent (p. ) For an nonzero real number b, and an integers m and n, with n >, b m n = n b m = ( n b ) m, ecept when b < 0 and n is even. rational epression (p. 7) A ratio of two polnomial epressions. rational function (p. 7) An equation of the form f() = _ p(), where p() and q() q() are polnomial functions, and q() 0. eponent racional Para cualquier número real no nulo b cualquier entero m n, con n >, b m n = n b m = ( n b ) m, ecepto cuando b < 0 n es par. epresión racional Razón de dos epresiones polinomiales. función racional Ecuación de la forma f() = _ p(), donde p() q() son q() funciones polinomiales q() 0. Glossar R9

103 rational inequalit (p. ) An inequalit that contains one or more rational epressions. rationalizing the denominator (p. 09) To eliminate radicals from a denominator or fractions from a radicand. rational number (p. ) An number _ m n, where m and n are integers and n is not zero. The decimal form is either a terminating or repeating decimal. real numbers (p. ) All numbers used in everda life; the set of all rational and irrational numbers. rectangular hperbola (p. 9) A hperbola with perpendicular asmptotes. recursive formula (p. ) Each term is formulated from one or more previous terms. reference angle (p. 77) The acute angle formed b the terminal side of an angle in standard position and the -ais. reflection (p. ) A transformation in which ever point of a figure is mapped to a corresponding image across a line of smmetr. reflection matri (p. ) A matri used to reflect an object over a line or plane. regression line (p. 9) A line of best fit. relation (p. ) A set of ordered pairs. desigualdad racional Cualquier desigualdad que contiene una o más epresiones racionales. racionalizar el denominador La eliminación de radicales de un denominador o de fracciones de un radicando. número racional Cualquier número _ m n, donde m n son enteros n no es cero. Su epansión decimal es o terminal o periódica. números reales Todos los números que se usan en la vida cotidiana; el conjunto de los todos los números racionales e irracionales. hipérbola rectangular Hipérbola con asíntotas perpendiculares. fórmula recursiva Cada término proviene de uno o más términos anteriores. ángulo de referencia El ángulo agudo formado por el lado terminal de un ángulo en posición estándar el eje. refleión Transformación en que cada punto de una figura se aplica a través de una recta de simetría a su imagen correspondiente. matriz de refleión Matriz que se usa para reflejar una figura sobre una recta o plano. reca de regresión Una recta de óptimo ajuste. relación Conjunto de pares ordenados. Glossar/Glosario relative frequenc histogram (p. 99) A table of probabilities or a graph to help visualize a probabilit distribution. relative maimum (p. 0) A point on the graph of a function where no other nearb points have a greater -coordinate. f() relative maimum histograma de frecuencia relativa Tabla de probabilidades o gráfica para asistir en la visualización de una distribución de probabilidad. máimo relativo Punto en la gráfica de una función en donde ningún otro punto cercano tiene una coordenada maor. f() máimo relativo relative minimum mínimo relativo relative minimum (p. 0) A point on the graph of a function where no other nearb points have a lesser -coordinate. mínimo relativo Punto en la gráfica de una función en donde ningún otro punto cercano tiene una coordenada menor. R0 Glossar

104 root (p. ) The solutions of a quadratic equation. rotation (p. ) A transformation in which an object is moved around a center point, usuall the origin. rotation matri (p. ) A matri used to rotate an object. row matri (p. ) A matri that has onl one row. raíz Las soluciones de una ecuación cuadrática. rotación Transformación en que una figura se hace girar alrededor de un punto central, generalmente el origen. matriz de rotación Matriz que se usa para hacer girar un objeto. matriz fila Matriz que sólo tiene una fila. S sample space (p. ) The set of all possible outcomes of an eperiment. scalar (p. 7) A constant. scalar multiplication (p. 7) Multipling an matri b a constant called a scalar; the product of a scalar k and an m n matri. scatter plot (p. ) A set of data graphed as ordered pairs in a coordinate plane. scientific notation (p. ) The epression of a number in the form a 0 n, where a < 0 and n is an integer. secant (p. 79) For an angle, with measure, a point P(, ) on its terminal side, r = +, sec = r. espacio muestral Conjunto de todos los resultados posibles de un eperimento probabilístico. escalar Una constante. multiplicación por escalares Multiplicación de una matriz por una constante llamada escalar; producto de un escalar k una matriz de m n. gráfica de dispersión Conjuntos de datos graficados como pares ordenados en un plano de coordenadas. notación científica Escritura de un número en la forma a 0 n, donde a < 0 n es un entero. secante Para cualquier ángulo de medida, un punto P(, ) en su lado terminal, r = +, sec α = r. second-order determinant (p. 9) The determinant of a matri. sequence (p. ) A list of numbers in a particular order. series (p. 9) The sum of the terms of a sequence. set-builder notation (p. ) The epression of the solution set of an inequalit, for eample { > 9}. determinante de segundo orden El determinante de una matriz de. sucesión Lista de números en un orden particular. serie Suma específica de los términos de una sucesión. notación de construcción de conjuntos Escritura del conjunto solucion de una desigualdad, por ejemplo, { > 9}. Glossar/Glosario sigma notation (p. ) For an sequence a, a, a,..., the sum of the first k terms k ma be written a n, which is read the n= n= summation from n = to k of a n. Thus, k a n = a + a + a + + a k, where k is an integer value. notación de suma Para cualquier sucesión a, a, a,..., la suma de los k primeros k términos puede escribirse a n, lo que se n= lee la suma de n = a k de los a n. k Así, n= un valor entero. a n = a + a + a a k, donde k es Glossar R

105 simple event (p. 70) ne event. simplif (p. ) To rewrite an epression without parentheses or negative eponents. simulation (p. 7) The use of a probabilit eperiment to mimic a real-life situation. sine (p. 79) For an angle, with measure, a point P(, ) on its terminal side, r = +, sin = r. skewed distribution (p. 7) A curve or histogram that is not smmetric. evento simple Un solo evento. reducir Escribir una epresión sin paréntesis o eponentes negativos. simulación Uso de un eperimento probabilístico para imitar una situación de la vida real. seno Para cualquier ángulo de medida, un punto P(, ) en su lado terminal, r = +, sin = r. distribución asimétrica Curva o histograma que no es simétrico. Positivel Skewed Negativel Skewed Positivamente Alabeada Negativamente Alabeada slope (p. 7) The ratio of the change in -coordinates to the change in -coordinates. slope-intercept form (p. 79) The equation of a line in the form = m + b, where m is the slope and b is the -intercept. solution (p. 9) A replacement for the variable in an open sentence that results in a true sentence. pendiente La razón del cambio en coordenadas al cambio en coordenadas. forma pendiente-intersección Ecuación de una recta de la forma = m + b, donde m es la pendiente b la intersección. solución Sustitución de la variable de un enunciado abierto que resulta en un enunciado verdadero. Glossar/Glosario solving a right triangle (p. 7) The process of finding the measures of all of the sides and angles of a right triangle. square matri (p. ) A matri with the same number of rows and columns. square root (p. 9) For an real numbers a and b, if a = b, then a is a square root of b. resolver un triángulo rectángulo Proceso de hallar las medidas de todos los lados ángulos de un triángulo rectángulo. matriz cuadrada Matriz con el mismo número de filas columnas. raíz cuadrada Para cualquier número real a b, si a = b, entonces a es una raíz cuadrada de b. square root function (p. 97) A function that contains a square root of a variable. square root inequalit (p. 99) An inequalit involving square roots. Square Root Propert (p. 0) For an real number n, if = n, then = ± n. standard deviation (p. 7) The square root of the variance, represented b a. función radical Función que contiene la raíz cuadrada de una variable. desigualdad radical Desigualdad que presenta raíces cuadradas. Propiedad de la raíz cuadrada Para cualquier número real n, si = n, entonces = ± n. desviación estándar La raíz cuadrada de la varianza, la que se escribe a. R Glossar

106 standard form (p. 7, ). A linear equation written in the form A + B = C, where A, B, and C are integers whose greatest common factor is, A 0, and A and B are not both zero.. A quadratic equation written in the form a + b + c = 0, where a, b, and c are integers, and a 0. forma estándar. Ecuación lineal escrita de la forma A + B = C, donde A, B, C son enteros cuo máimo común divisores, A 0, A B no son cero simultáneamente.. Una ecuación cuadrática escrita en la forma a + b + c = 0, donde a, b, and c are integers, and a 0. standard notation (p. ) Tpical form for written numbers. notación estándar Forma típica de escribir números. standard position (p. 77) An angle positioned so that its verte is at the origin and its initial side is along the positive -ais. posición estándar Ángulo en posición tal que su vértice está en el origen su lado inicial está a lo largo del eje positivo. step function (p. 9) A function whose graph is a series of line segments. fución etapa Función cua gráfica es una serie de segmentos de recta. substitution method (p. ) A method of solving a sstem of equations in which one equation is solved for one variable in terms of the other. método de sustitución Método para resolver un sistema de ecuaciones en que una de las ecuaciones se resuelve en una de las variables en términos de la otra. success (p. 97) The desired outcome of an event. éito El resultado deseado de un evento. snthetic division (p. 7) A method used to divide a polnomial b a binomial. división sintética Método que se usa para dividir un polinomio entre un binomio. snthetic substitution (p. ) The use of snthetic division to evaluate a function. sustitución sintética Uso de la división sintética para evaluar una función polinomial. sstem of equations (p. ) A set of equations with the same variables. sistema de ecuaciones Conjunto de ecuaciones con las mismas variables. sstem of inequalities (p. 0) A set of inequalities with the same variables. sistema de desigualdades Conjunto de desigualdades con las mismas variables. tangent (pp. 7, 79). A line that intersects a circle at eactl one point.. For an angle, with measure, a point P(, ) on its terminal side, r = +, tan =. term (p. 7, ). The monomials that make up a polnomial.. Each number in a sequence or series. T tangente. Recta que interseca un círculo en un solo punto.. Para cualquier ángulo, de medida, un punto P(, ) en su lado terminal, r = +, tan =. término. Los monomios que constituen un polinomio.. Cada número de una sucesión o serie. Glossar/Glosario terminal side of an angle (p. 77) A ra of an angle that rotates about the center. terminal side 0 90 initial side lado terminal de un ángulo Rao de un ángulo que gira alrededor de un centro. lado terminal 0 90 lado inicial verte vértice determinante de tercer orden Determinante de Glossar R

107 third-order determinant (p. 9) Determinant of a matri. transformation (p. ) Functions that map points of a pre-image onto its image. translation (p. ) A figure is moved from one location to another on the coordinate plane without changing its size, shape, or orientation. translation matri (p. ) A matri that represents a translated figure. transverse ais (p. 9) The segment of length a whose endpoints are the vertices of a hperbola. trigonometric equation (p. ) An equation containing at least one trigonometric function that is true for some but not all values of the variable. trigonometric functions (pp. 79, 77) For an angle, with measure, a point P(, ) on its terminal side, r = +, the trigonometric functions of a are as follows. una matriz de. transformación Funciones que aplican puntos de una preimagen en su imagen. traslación Se mueve una figura de un lugar a otro en un plano de coordenadas sin cambiar su tamaño, forma u orientación. matriz de traslación Matriz que representa una figura trasladada. eje transversal El segmento de longitud a cuos etremos son los vértices de una hipérbola. ecuación trigonométrica Ecuación que contiene por lo menos una función trigonométrica que sólo se cumple para algunos valores de la variable. funciones trigonométricas Para cualquier ángulo, de medida, un punto P(, ) en su lado terminal, r = +, las funciones trigonométricas de a son las siguientes. sen = r cos = r tan = sin = r cos = r tan = csc = r sec = r cot = csc = r sec = r cot = trigonometric identit (p. 7) An equation involving a trigonometric function that is true for all values of the variable. identidad trigonométrica Ecuación que involucra una o más funciones trigonométricas que se cumple para todos los valores de la variable. Glossar/Glosario trigonometr (p. 79) The stud of the relationships between the angles and sides of a right triangle. trinomial (p. 7) A polnomial with three unlike terms. unbiased sample (p. 7) A sample in which ever possible sample has an equal chance of being selected. unbounded (p. 9) A sstem of inequalities that forms a region that is open. uniform distribution (p. 99) A distribution where all of the probabilities are the same. union (p. ) The graph of a compound inequalit containing or. U trigonometría Estudio de las relaciones entre los lados ángulos de un triángulo rectángulo. trinomio Polinomio con tres términos diferentes. muestra no sesgada Muestra en que cualquier muestra posible tiene la misma posibilidad de seleccionarse. no acotado Sistema de desigualdades que forma una región abierta. distribución uniforme Distribución donde todas las probabilidades son equiprobables. unión Gráfica de una desigualdad compuesta que contiene la palabra o. R Glossar

108 unit circle (p. 7) A circle of radius unit whose center is at the origin of a coordinate sstem. círculo unitario Círculo de radio cuo centro es el origen de un sistema de coordenadas. (0, ) measures radian. (0, ) mide radián. (, 0) unit (, 0) (, 0) unidad (, 0) (0, ) (0, ) univariate date (p. 77) Data with one variable. datos univariados Datos con una variable. V variable (p. ) Smbols, usuall letters, used to represent unknown quantities. variance (p. 7) The mean of the squares of the deviations from the arithmetic mean. verte (p., 7, 9). An of the points of intersection of the graphs of the constraints that determine a feasible region.. The point at which the ais of smmetr intersects a parabola.. The point on each branch nearest the center of a hperbola. variables Símbolos, por lo general letras, que se usan para representar cantidades desconocidas. varianza Media de los cuadrados de las desviaciones de la media aritmética. vértice. Cualqeiera de los puntos de intersección de las gráficas que los contienen que determinan una región viable.. Punto en el que el eje de simetría interseca una parábola.. El punto en cada rama más cercano al centro de una hipérbola. verte form (p. ) A quadratic function in the form = a( - h ) + k, where (h, k) is the verte of the parabola and = h is its ais of smmetr. verte matri (p. ) A matri used to represent the coordinates of the vertices of a polgon. vertical asmptote (p. 7) If the related rational epression of a function is written in simplest form and is undefined for = a, then = a is a vertical asmptote. forma de vértice Función cuadrática de la forma = a( - h ) + k, donde (h, k) es el vértice de la parábola = h es su eje de simetría. matriz de vértice Matriz que se usa para escribir las coordenadas de los vértices de un polígono. asíntota vertical Si la epresión racional que corresponde a una función racional se reduce está no definida en = a, entonces = a es una asíntota vertical. Glossar/Glosario vertical line test (p. 9) If no vertical line intersects a graph in more than one point, then the graph represents a function. prudba de la recta vertical Si ninguna recta vertical interseca una gráfica en más de un punto, entonces la gráfica representa una función. X -intercept (p. ) The -coordinate of the point at which a graph crosses the -ais. intersección La coordenada del punto o puntos en que una gráfica interseca o cruza el eje. Glossar R

109 Y -intercept (p. ) The -coordinate of the point at which a graph crosses the -ais. intersección La coordenada del punto o puntos en que una gráfica interseca o cruza el eje. Z zeros (p. ) The -intercepts of the graph of a quadratic equation; the points for which f() = 0. zero matri (p. ) A matri in which ever element is zero. ceros Las intersecciones de la gráfica de una ecuación cuadrática; los puntos para los que f() = 0. matriz nula matriz cuos elementos son todos igual a cero. Glossar/Glosario R Glossar

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111 Selected Answers Selected Answers Chapter Equations and Inequalities Page Chapter Get Read _. - _ _. _. $ _. or. true 7. true 9. false. false Pages 0 Lesson $ _.. drops per min. π (_ + ) $, Sample answer: - + = ; + = ; ( + + ) = ; ( - ) + = ; ( + ) = ; ( + ) + = ; - = 7; ( + ) ( ) = ; + + = 9; ( - ) = 0 9. A table of IV flow rates is limited to those situations listed, while a formula can be used to find an IV flow rate. If a formula used in a nursing setting is applied incorrectl, a patient could die.. H _ 7 Pages 7 Lesson -. Z, Q, R. Q, R. Assoc. (+) 7., - _. $ a -. Q, R 7. I, R 9. -., _ 9. N, W, Z, Q, R. Z, Q, R. Add. Iden.. Comm. (+) 7. Distributive 9. -.; 0.. _ ; - _. _ ; - _. _ ( + _ ) ( ) = ( + _ + ) ( + _ ) Def. of a mied number = () + ( _ ) + () + ( _ ) Distributive Prop. = + _ + + _ Multipl. = + + _ + _ Commutative Propert = + _ + _ Add. = + ( _ + _ Associative Propert ) = + or 9 Add m + 0a. c - d..p -.9q..; $ m; Add. Inv. 9.. units. W, Z, Q, R. I, R 7. Sample answer: - 9. true. false;. Yes; _ + = _ + _ = 7; dividing b a number is the same as multipling b its reciprocal.. B in 7. 7_ 7. 0 Pages Lesson -. + n. 9 times a number decreased b is.. Refleive (=) = _ 9 + n. D 7. + n 9. n -. (9 + n). Sample answer: less than a number is.. Sample answer: A number squared is equal to times the number. 7. Substitution (=) 9. Trans. (=) d_ = r 9. V_ t πr = h. _. s = length of a side; s = ;. in.. (n - 7) 7. πr(h + r) 9. Sample answer: 7 minus half a number is equal to divided b the square of the number.. _ = _ 9. n = number of students that can attend 7 each meeting; n + = ; 0 students. c = cost per student; 0(0 - c) + 0_ () = 00; $. h = height of can A; π(. )h = π( ); _ units. Central: 90 mi; Union: 0 mi 7. $9 9. Sample answer: - = The Smmetric Propert of Equalit allows the two sides of an equation to be switched; the order is changed. The Commutative Propert of Addition allows the order of terms in an epression on one side of an equation to be changed; the order of terms is changed, but not necessaril on both sides of an equation. 7. D z cm. - _. - + Pages 9 Lesson least: F; greatest: F 7. {-, } 9. {-, 9}.. {} {, }. {-, } 7. {-, } 9. { _ } = ; maimum: 0 F; minimum: 9 F. {, 9_ } 7. {-, } 9. {- _, - }. {} = ; maimum: km, minimum: km 9. Sometimes; it is true onl if a 0 and b 0 or if a 0 and b 0.. Alwas; since the opposite of 0 is still 0, this equation has onl one case, a + b = 0. The solution is - b_ a.. B. _ Distributive. ft.. _ Pages 7 9 Lesson -. {a a <.} 0. { _ }. {w w < -7} R Selected Answers

112 7. {n n -} 0 9. at least 9. {b b } {d d > -}. {p p -} 7. { < } 9. {b b _ } {r r } 0. {k k < -} 7 0. at least h 7. n > ; n > 9. n + > ; n > -. _ n - 7 ; n. {n n.7} { < -79} {d d -} 0 9. {g g < } 0. { < _ }. 0., (0,00n) 0, (n + ) n + ; n - 9. (7m) 7; m 7_ ; at least child-care staff members. s 9; Flavio must score at least 9 on his net test to have an A test average.. -. Sample answer: + < + 7a. It holds onl for or ; <. 7b. < but 7c. For all real numbers a, b, and c, if a < b and b < c then a < c. 9. Let n equal the number of minutes used. Write an epression representing the cost of Plan and for Plan for n minutes. The cost for Plan would include a monthl access fee of $ plus 0 for each minute over 00 minutes or + 0.(n - 00). The cost for Plan for 0 minutes or less would be $. To find where Plan would cost less than Plan, solve < + 0.(n - 00) for n. The solution set is {n n > 0}, which means that for more than 0 minutes of calls, Plan is cheaper.. J. _ {-, _ }. b = billions of dollars spent online each ear; b +. = 9.; about $0. billion each ear 7. Q, R 9..(. + );.(.) +.() 7. {, -} 7. {, } 7. {-, 0} Pages Lesson -. {d - < d < }. { > or < -}. {a a or a -} 7. {h - < h < } 9. {k - < k < 7} 0.. c. between $. and $.0. { - < < } 0. {c c < - or c } {b b > 0 or b < -} 0. {r - < r < }. s. all real numbers {n -9 n- 0}. {n - < n < } n >. n. 7. n + > 9. b - 9. ; {b b > 0. or b < 90.}. in. < L 0 in.. red:..9; blue:.7.7; green:.9.9. a - b < c < a + b 7. < < 9. abs( - ) > 0; { < - or > }. Sabrina; an absolute value inequalit of the form a > b should be rewritten as an or compound inequalit, a > b or a < -b.. Compound inequalities can be used to describe the acceptable time frame for the fasting state before a glucose tolerance test is administered to a patient suspected of having diabetes. 0 h ; hours would be an acceptable fasting time for this test since it is part of the solution set of 0 h, as indicated on the graph.. G { < } = ; highest: 9 kes, lowest: kes. {-, }. Addition (=). Transitive (=) m - 7n Selected Answers Selected Answers R9

113 Selected Answers Pages 9 Chapter Stud Guide and Review. empt set. rational numbers. absolute value 7. coefficient 9. equation mi. Q, R. -m + n $ = _ C - B 7. p = A_ 9. about. in. A + rt. {, -}. {}. _ {-, - } 7. {w w < -} 9. {n n }. {z z }. (9 +.) 7,. ; or fewer toppings. {a - < a < } 0 7. { > or < - _ } 0 9. { -9 }. {b b > _-0 or b < -} 7. D = {7}, R = {-,,, }; no; discrete (7, ) (7, ) (7, ) (7, ) 9. D = all reals, R = all reals; es; continuous. 0. D = {0, 0, 0}, R = {,, }; es. D = {0., }, R = {-, 0., }; no 7. D = all reals, R = all reals; no 9. discrete. discrete. D = {-,, }, R = {0,, }; es; discrete (, ) Chapter Linear Relations and Functions Page 7 Chapter Get Read. (-, ). (-, -). (0, - ) 7. (, ) 9 (, 9) (, ) 7 (, 7) (, ) (0 + ) mi (, ) (, 0). D = {-, }, R = {, 7, }; no; discrete (, ) (, 7) (, ) 7. D = {-., 0,., }, R = {-, -.,, }; es; discrete (., ) Pages Lesson -. D = {-,, }, R = {, }; es. D = {-,, }, R = {,,, }; no. {(97, ), (7, 7), (, 09), (9, 9)} (0,.) (., ) (, ) R0 Selected Answers

114 9. D = all reals, R = all reals; es; continuous. D = all reals, R = all reals; es; continuous. Representatives Years of Service Year. Yes; each domain value is paired with onl one range value so the relation is a function.. Sample answer: {(-, ), (-, ), (, ), (-, )}. For = -, there are two different -values. 7. Sample answer: f() = - 9. C. { - < < }. { <.} Selected Answers. D = all reals, R = { 0}; es; continuous Pages 70 Lesson -. No; the variables have an eponent other than.. $ = ;, -, 7. - = -;, -, - 9., _ 9 9. a es. No; has eponents other than.. No; appears in a denominator. 7. No; is inside a square root. 9. Sound travels onl 7 m in seconds in air, so it travels faster in water..,000 ft. - = 0;, -, = ;, -7, 7. - = -;, -, - 9., -. Yes; each domain value is paired with onl one range value so the relation is a function Stock Price 0 Price ($) , Year 9. Yes; each domain value is paired with onl one range value. 0 0 Selected Answers R

115 Selected Answers. _, -. + = ;,, 7. = ;, 0, 9. + = 9;,, 9. none, - 9. T(h) h c b.c b Yes; the graph passes the vertical line test.., none. Sample answer: + =. The lines are parallel but have different -intercepts.., none 0 7. Regardless of whether 0 is substituted in for or, the value of the other variable is also 0. So the onl intercept is (0, 0). 9. B. D = {-,,, }, R = {-,, }; es (, ) (, ) (, ) 7., g() g() 0. (, ). { - < < }. $ R Selected Answers

116 Pages 7 77 Lesson -. - _... about million per ear 7. mph 9. speed or velocit. Selected Answers 7.. /h _ _ Yes; slopes show that adjacent sides are perpendicular. 9. The graphs have the same -intercept. As the slopes become more negative, the lines get steeper.. -. Sometimes; the slope of a vertical line is undefined.. D Selected Answers R

117 Selected Answers 7. -0, , 0 0 b. Sample answer using (000,.0) and (000, 9.): = c. Sample answer:. C a. strong positive correlation Lives Saved b Minimum Drinking Age Year Lives (thousands) 7.. a -. {z z 7} 7. 7a - b 9. = 9-7. = = _ + _ Pages Lesson -. = = -. = - _ + 7. = B. = - _ + _. = -. = - _ + 7_ 7. = - _ + 7_ 9. = _ + _ 0. = -. = d = 0c F. = = +. = - _ - _ 7. Sample answer: = + 9. = +. A {r r }.... Pages 9 Lesson - a. strong negative correlation b. Sample answer using (999, 9.) and (00,.): = c. Sample answer:,900 a. strong positive correlation Bottled Water Consumption Gallons Year b. Sample answer using (99, ) and (00, ): = c. Sample answer:. gal 7. Sample answer using (000, 09.9) and (00, 7.9): = -, The value predicted b the equation is significantl lower than the one given in the graph.. No. Past performance is no guarantee of the future performance of a stock. ther factors that should be considered include the companies earnings data and how much debt the have.. Sample answer using (., -) and (7., -7): = Sample answer: The predicted value differs from the actual value b onl F, less than %. 7. Sample answer using (90,.) and (99,.7): 0% 9. Sample answer using (,.) and (, 7.): = D. = +. = _ 9. undefined Pages 99 0 Lesson -. D = all reals, R = all integers f() f() R Selected Answers

118 . D = all reals, R = {} f() 9. D = all reals, R = all integers f() f() Selected Answers. D = all reals, R = { -} h(). D = all reals, R = all nonnegative reals h() h() 7. D = all reals, R = { } g(). D = all reals, R = { -} g() g() 9. A. step function. $. D = all reals, R = all integers g() g(). D = all reals, R = all nonnegative reals f() f() 7. D = all reals, R = {a a is an integer} h() 9 h() 9 7. D = { < - or > }, R = {-, } h() Selected Answers R

119 Selected Answers 9. A. S. P. D = all reals, R = all nonnegative reals f() f() 7. D = all reals, R = { 0 or = } f() 9.. B. B. Sample answer using (0, 9.7) and (7, 7.): = = { } 0. es. no. no Pages 0 0 Lesson D = all reals, R = all whole numbers f(). f() Minutes. f() = -. f() Cost ($). 7. 0c + d 0 9. No; (, ) is not in the shaded region.. 7. Sample answer: f() = - R Selected Answers

120 . 7. < Selected Answers [0, 0] scl: b [0, 0] scl: 7.. es. b 000.a.b a [0, 0] scl: b [0, 0] scl: 9. Substitute the coordinates of a point not on the boundar into the inequalit. If the inequalit is satisfied, shade the region containing the point. If the inequalit is not satisfied, shade the region that does not contain the point. Selected Answers R7

121 Selected Answers. Linear inequalities can be used to track the performance of plaers in fantas football leagues. Let be the number of passing ards and let be the number of touchdowns. The number of points Dana gets from passing ards is and the number of points he gets from touchdowns is 00. His total number of points is He wants at least 000 points, so the inequalit represents the situation f() D = all reals, R = all reals; function; continuous D = all reals, { 0} R = {.0} function; continuous. J. g() D = all reals, g() R = { -} 7. No; this function is not linear because the is under a square root = -;,, -., 7. There is a strong positive correlation between salar and eperience.. _. 9. Sample answer: $,000. Pages 0 0 Chapter Stud Guide and Review. identit. slope-intercept. vertical line test 7. D = {-,, }, R = {, }; function; (, ) (, ) discrete (, ) 7. R Selected Answers

122 9. _. People (millions). = _ + 7_ = - _ + 7_ Year 7. There is a strong negative correlation. 0 There is a strong positive correlation Selected Answers f() f() D = all reals, R = all integers.. g() D = all reals, R = { } g() Chapter Sstems of Equations and Inequalities Page Chapter Get Read. f() D = all reals, R = { 0 or = }. Selected Answers R9

123 .. 9. inconsistent Selected Answers. (0, -) 7..7b +.c = 9. Yes; the graph passes the vertical line test (, ) (, ). 7. s (7, ) (7, ) a Pages 0 Lesson -. (-, ) (., ) (., ) -. (, -) 9 (, ) 9. inconsistent. = , = You should use Ez nline photos if ou are printing more than 7 digital photos and the local pharmac if ou are printing fewer than 7 digital photos. R0 Selected Answers

124 .. 9 consistent and independent inconsistent 7. inconsistent 9. (.0, -.). (,.). Two lines cannot intersect in eactl two points.. You can use a sstem of equations to track sales and make predictions about future growth based on past performance and trends in the graphs. The coordinates (,.) represent that ears after 999, both the instore sales and online sales will be $,00. It would not be ver reasonable. The unpredictabilit of the market, companies, and consumers makes models such as this one accurate for onl a short period of time. 7. H 9. A. P Selected Answers. (-, ) 7. Suppl, 00,000; demand, 00,000; prices will tend to rise. 9. 0,000; $ Population (in thousands) (9, ) 0 9, , Years After 00 (-9, ) Pages 7 9 Lesson -. (, ). (9, 7). C 7. (, -0) 9. (, ). infinitel man solutions. (, 7). (-, ) 7. (, ) 9. (, -7). (, -). no solution. members rented skis and 0 members rented snowboards. 7. printers, monitors 9. (, ). (7, -). (-, ). ( _, ) 7. (, ) 9. (, -). 0 true/false, 0 multiple-choice. a + s = 0, a + s =. one equation should have a variable with a coefficient of. 7. Jamal; Juanita subtracted the two equations incorrectl; - - = -, not You can use a sstem of equations to find the monthl fee and rate per minute charged during the months of Januar and Februar. The coordinates of the point of intersection are (0.0,.). Currentl, Yolanda is paing a monthl fee of $.0 and an additional per minute.. J. consistent and dependent. (, -) (, ) Selected Answers R

125 . 7. (-, -), (, ), (, -) 9. Selected Answers = 0;, -, 0. - = -;,-,-. + = ;,,. es 7. no. Pages Lesson -.. (0, ) no solution. 7. (0, ) no solution. (0, ) R Selected Answers

126 9. Cost Hours. (-, -), (, -), (, ). (-, -9), (, 7), (0, -). units 7. categor ; ft 9. Sample answer: pumpkin, soda; pumpkin, soda; pumpkin, soda Pages Lesson -. (, ) (, ). (, ) vertices: (, ), (, ), (, ); ma: f(, ) = ; min: f(, ) = -0 vertices: (-, -), (, -), (, ); ma: f(, -) = 9; min: f(, ) = - Selected Answers.. (, ) (7,.) vertices: (, 0), (, ), (7,.), (7, -); ma: f(7,.) =.; min: f(, 0) = (, 0). (7, ) 7. (, ) (, ) vertices: (-, ), ( _, ) ; no maimum; min: f(-, ) = Sample answer: > +, < - 9. units. B. (-, ). (, -) 7. infinitel man 9 9. c 0, l 0, c + l, c + l 0. (0, 0), (, 0), (0, ), (0, _ ). Make 0 canvas tote bags and leather tote bags. Selected Answers R

127 Selected Answers. 7. (0, ) (, ) (, ) (, ) vertices: (0, ), (, ), (, ); ma f(, ) = 9; min; f(0, ) = vertices: (, ), (, ), (, ), (, ); ma f(, ) = ; min; f(, ) = -. (, ) (0, ) (, ) (0, 0) (, 0) 9. g Pro Boards 0 0 (0,.7) 0 0 (0, 0) (0, 0) vertices: (0, 0), (0, ), (, ), (, ), (, 0); ma f(, 0) = 9; min; f(0, ) = - (, 0) c (, ) Specialt 9.. (0, ) (, ) (, ) (, ) (, ) (, ) (, ) (, ) vertices: (, ), (, ), (, ), (, -); ma f(, ) = 0; min; f(, -) = - vertices: (0, ), (, 0), (, ); ma f(, 0) = ; min; f(0, ) = -. f(c, g) = c + 0g. $00. s (0, 000) (0, 0) (00, 000) (00, 0) c (0, 0), (0, 000), (00, 000), (00, 0) acres corn, 0 acres sobeans; $0,00 9. Sample answer: -, -, 0. (-,); the other coordinates are solutions of the sstem of inequalities.. There are man variables in scheduling tasks. Linear programming can help make sure that all the requirements are met. Let = the number of buo replacements and let = the number of buo repairs. Then, 0, 0, and. +. The captain would want to maimize the number of buos that a crew could repair and replace so f(, ) = +.. J 7. no solution (, 0). (, ) vertices: (, ), (, 0); no maimum; no minimum (, 0) 9. (, ). = Pages 9 Lesson -. (,, -). infinitel man. no solution 7. c + s + r =, c + s + r = _, r = s R Selected Answers

128 9. (,, 7). (, -, ). no solution. (,, -) 7. infinitel man 9.,,. -point goals, -point goals, -point free throws. $7.0. ( _, - _, _ 7. (-, 9, ) ) 9. You can use elimination or substitution to eliminate one of the variables. Then ou can solve two equations in two variables.. a = _, b = _, c = ; = _ + _ +. A. 79 gallons of skim and of whole milk Time (min) (,, ). (, -, ) Units Selected Answers 9. Sample answer using (0, ) and (, 9): = feet; the -intercept.. 0 Pages Chapter Stud Guide and Review. constraints. feasible region. consistent sstem 7. elimination method 9. sstem of equations. (, 0). (-, -). hr 7. (-, -) 9. (., -.). (-, ).. Chapter Matrices Page Chapter Get Read. -; _. -; _. -.; _ ; - _ 9.. (, ). (9, ) Pages -7 Lesson -. Fri Sat Sun Mon Tue High 90 Low.. (, ) 7. 0,00,700 9,7,900,9,00 7,,00,7,000,,0,00, (, - _ ) 7. (, ) 9. (, -).. Evening Matinee Twilight Adult Child Senior Weekda Weekend Single 0 79 Double 70 9 Suite Selected Answers R

129 Selected Answers. Matrices are used to organize information so it can be read and compared more easil. For eample, Sabrina can see that the hbrid SUV has the best price and fuel econom; the standard SUV has the most horsepower, eterior length, and cargo space; the midsize SUV has a lower price than the standard but high horsepower and cargo space; and the compact SUV has the a low price and good fuel econom.. J. (7,, -9) 7. 0 dresses, 0 skirts 9. - = Pages 7-7 Lesson -. impossible Males 7,9,,9 0,9 7, 7,0 0,0,09 7, Females, 9, , 7 7,9,, 09,0, 7. No; man schools offer the same sport for males and females, so those schools would be counted twice impossible [ -9 -] _ m and 00m Sample answer: [-, ], [, -] 7. You can use matrices to track dietar requirements and add them to find the total each da or each week. Breakfast Lunch Dinner add the three matrices: J (,, 7) 9. (, ). (, -). No, it would cost $.0.. Assoc. (+) 7. Comm. ( ) Pages - Lesson $7,. es; A(BC) = - ( ) = = -0 - (AB)C = ( ) - = - - = , ,70 9. c(ab) = ( - - = = A(cB) = - ( - ) ) = = The equation is true.. AC + BC = = = -0 (A + B)C = ( = ) - = -0 - The equation is true = 99.0 ; juniors 7 - R Selected Answers

130 7. $, $0. Never; the inner dimensions will never be equal.. a =, b = 0, c = 0, d = ; the original matri. C =, = -9. $.0; $.0., -. - M M' - - ; M (-, 0), N (, ), (-, -); N N' Selected Answers ' D, E (, -), F (, -9) -7 D' E F E' 9. F' 7. -, X (-, ), Y (. ), Z (, -); ; 0 ; A (-, -), B (, -), 0 - D (,), C (-,); A B Pages 9-9 Lesson A A' C C' D D' C C' B B' A' B' A (0, ), B ( _, ), C ( _, 0 ), D (0, 0) 9. A (0, ), B (-, ), C (-, 0), D (0, 0). A (, 0), B (, -), C (0, -), D (0, 0) Selected Answers R7

131 Selected Answers. - - (-, ); ' M - ; N N'. S' R' T Q' - 0 M' S 0 ; M (, ), N (-, -), - Q T' R. J(-, ), K(7, ), L(, -) 7. P(, ), Q(-, ), R(, -), S(, -) The figures in Eercise and Eercise 9 have the same coordinates, but the figure in Eercise 0 has different coordinates.. (.,.). (-.7, -.) 7. The object is reflected over the -ais, then translated units to the right. 9. No; since the translation does not change the -coordinate, it does not matter whether or not ou do the translation or the reflection first. However, if the translation did change the -coordinate, the order would be important Sample answer: Sometimes; the image of a dilation is congruent to its preimage if and onl if the scale factor is or A D = {all real numbers}; R = {all real numbers}; es _ mi.. 9_. _ Pages 9-00 Lesson units ft 9.. units. _, -. or Sample answer: 9. Sample answer:,. If ou know the coordinates of the vertices of a triangle, ou can use a determinant to find the area. This is convenient since ou don t need to know an additional information such as the measure of the angles. You could place a coordinate grid over a map of the Bermuda Triangle with one verte at the origin. B using the scale of the map, ou could determine coordinates to represent the other two vertices and use a determinant to estimate the area. The determinant method is advantageous because ou don t need to phsicall measure the lengths of each side or the measure of the angles at the vertices.. H. A (-,.), B (., ), C (, -7.); B' A' B A C C' 7. undefined 9., ft. = - _. = _ +. (, 9) Pages 0-07 Lesson -. (, ). s + d = 000, 0.0s + 0.0d = 7.0. no solution 7. (, -) 9. (, ). (-, -.7). (-., ). g + r = 9; 7g + r = 7. $.99, $.9 9. (, -, ). ( _ 9, -_ 0 9,_ 9 ). _ (-,_ 70,_ 7. (-., -9.0) 0) 7. ( _, _ 9. p + r + c =, r - c = 0,.p +.r ) + c =.; peanuts, lb; raisins, lb; pretzels, lb. + = -, - = 0. Cramer s Rule is a formula for the variables and where (, ) is a solution for a sstem of equations. Cramer s Rule uses determinants composed of the coefficients and constant terms in a sstem of linear equations to solve the sstem. Cramer s rule is convenient when coefficients are large or involve fractions or decimals. Finding the value of the determinant is sometimes easier than tring to find a greatest common factor if R Selected Answers

132 ou are solving b using elimination or substituting complicated numbers.. J (-, -) (, ) dilation b a scale factor of (, ) (, ) Selected Answers (, ). no solution. [- ] 7. 0 Pages - Lesson -7. no. es _ - 9. es no. _ 0. No inverse eists. 7. _ _ 7. No inverse eists. -. AT_SIX_THIRTY 7. true 9. false. es. - _ a. no b. es _ B'' C'' A A' A'' C C' B B' (0, 0) _ 0. B - 0 = _ ; the graph of the inverse transformation is the original figure.. No inverse eists.. Echange the values for a and d in the first diagonal in the matri. Multipl the values for b and c b - in the second diagonal in the matri. Find the determinant of the original matri. Multipl the negative reciprocal of the determinant b the matri with the above mentioned changes. 7. a = ±, d = ±, b = c = 0 9. B. (, -). (-,, ) [-] 9. [ -]. (, ) _ tons/in Pages 9- Lesson -. - = -. h =, c =, o =. (,.7) 7. no solution = m n = -. 7 h of flight instruction -0 and h in the simulator. no solution 7. (, -) 9. no solution. (,.). ( _, _. carbon = ) ; hdrogen = (-,, ). (0, -, ). Sample answer: + = and + =. The solution set is the empt set or infinitel man solutions. 7. C 9. D (, -). (-, -) Pages - Chapter Stud Guide and Review. identit matri. rotation. matri equation 7. matri 9. inverses. dilation. (-, -) 7 0. (-, 0) 7. 9 row, column 7 9. [ ] [-] Selected Answers R9

133 Selected Answers. No product eists. 7. A (, 0), B (, -), C (, -7) 9. A (, ), B (-, ), C (, -). A (, ), B (, ), C (, ), D (, ) ( _, ). (, -). (,, -). ($., $.7) 7. _ 7-9. No inverse eists.. (, ) -9. (-, ). 70 ml of the 0% solution and 70 ml of the 7% solution Chapter Quadratic Functions and Inequalities Page Chapter Get Read f() = 9. ( + )( + ). ( - )( + 7). prime 7. ( - ) 9. ( + 7) feet a. 0; = 0; 0 b. c. f() f() (0, 0) a. -9; = 0; 0 b. c. f() f() f() 0 9 Pages Lesson - a. 0; = 0; 0 b. c. f () ( 0, 0) f () f() 0 0 (0, 9) f() 9 7a. ; = 0; 0 7b. 7c. f() f() (0, ) f() 0 a. -; = ; b. c. f () (, ) f () f() 0 9a. 9; =.;. 9b. 9c. f() f() 9 9 f() (, ) a. ; = ; b. c. f () f () (, ) f() a. ; = -; - b. c. f() f() (, 0) f() ma.; 7; D = all reals; R = { 7} 9. min.; 0; D = all reals; R = { 0}. $.7. ma.; -9; D = all reals, R = { -9}. min.; -; D = all reals, R = { -} 7. ma.; ; D = all reals, R = { } 9. min.; -; D = all reals, R = { -}. ma.; -0; D = all reals, R = { -0}. 0 m. 00 ft,. s R0 Selected Answers

134 7a. -; = -; - 7b. 7c. f() f() (, ) 9a. 0; = - _ ; - _ 9c. (, ) f() f() 9b. a. -; = 0; 0 b. c. f() f() 0. (0, ) f() 0 f() f() _ 0 _ a. _ 9 ; = -; - b. f() c. f() 0. 0 (, 0) 0. f() 9. min.; _ 9 ; D = all reals, R = { _ 9 7. ma.; ; D = all reals, R = { } 9. ma.; ; D = all reals, R = { } ft b 0 ft. in. b in. 7. $ c; the - coordinate of the verte of = a + c is - 0_ or 0, so a the -coordinate of the verte, the minimum of the function, is a (0) + c or c; C 9. (, ) } 7. [0 - ] 79. $0, $. (, -). (, ) _ 9 9. {-, } 9. in ( -, ); consistent and independent Pages 9 Lesson. -,. -. -, no real solutions. between - and 0; between and. s no real solutions. 0,.,. 7. no real solutions 9. between - and 0; between and. about s. - _, _. - _, 7. between 0 and ; between and 9. between - and -; between and. Let be the first number. Then, 7 - is the other number. (7 - ) = ; = 0; Since the graph 7 of the related function does not intersect the -ais, this equation has no real solutions. Therefore no such numbers eist.. -,. about s 7. The -intercepts of the related function are the solutions to the equation. You can estimate the solutions b stating the consecutive integers between which the -intercepts are located. 9. h(t) 0 h(t) t t Locate the positive - intercept at about.. This represents the time when the height of the ride is 0. Thus, if the ride were allowed to fall to the ground, it would take about. seconds.. F Selected Answers Selected Answers R

135 Selected Answers. -; = ; ; f() (, ) f(). (, ) $00. ( - 0)( + 0). ( - 9). ( + )( - ) numbers. a and c must have the same sign. The solutions are ±i. 79. H. + + = 0. -, - _ C' B' A' Pages Lesson. - - = = 0. ( + )( - ) 7. {0, } 9. - _,. {} = = 0 7. ( - ) ( - ) 9. ( + 7)( - ). {-, }. {-, }. {-, } 7. {, } 9. {}., or -, -. 0, _. -, _ 7. - _, - _ 9. - _, - _. 0, -, = = 0 7. _ s 9. ; The logs must have a diameter greater than in. for the rule to produce positive board feet values.. Sample answer: Roots and -; = 0; the sign of the linear term changes, but the others sta the same.. To use the Zero Product Propert, the equation must be written as a product of factors equal to zero. Move all the terms to one side and factor (if possible). Then set each factor equal to zero and solve for the variable. To use the Zero Product Propert, one side of the equation must equal zero, so the equation cannot be solved b setting each factor on the left side equal to.. G 7. - _ 9. min.; -9. = - -. Comm. (+). Assoc. (+) Pages Lesson -.. _. i i. ±i., j amps 7. + i i. 7_ 7 - _ 7 i. 7. _ 7. 9i 9. 0 a b i. -7i i. _ _ i. ±i 7. ±i 7., - 9. _,. + j amps. ( - i) + (- + i) i. i i. _ + _ i. 0 + i. - _ - _ i 7. ±i 0 9. ± _ i 7. _ 7, _ 9 7. Sample answer: + i and - i 7. (i)(i)(i); The other three epressions represent real numbers, but (i)(i)(i) = -i, which is an imaginar number. 77. Some polnomial equations have comple solutions and cannot be solved using onl the real 9. $0. < <$ es 9. no 9. no Pages 7 7 Lesson -. {-0, -}. {- ± 7 }. Jupiter 7. Yes; the acceleration due to gravit is significantl greater on Jupiter, so the time to reach the ground should be much less. 9. _ 9 ; ( - _ ). { ± }. {- ± 0 }. { ± i } 7. {-, } 9. - _, - _. { ± }. _ ±. ; ( - 9) 7. _ 9 ; ( + 7_ ) 9. {-, 0}. { ± }. _,. ± _ 7. {- ± i} 9. {- ± i }. _ in. b _ in.. {-., 0.}. - ± _ 7..; ( -.) 9. _ ; ( + _ ). {0.7, }. _ ±. 7 ± i 7 _ 7. _, _ - 9. Sample answers: The golden ratio is found in much of ancient Greek architecture, such as the Parthenon, as well as in modern architecture, such as in the windows of the United Nations building. Man songs have their clima at a point occurring.% of the wa through the piece, with 0. being about the reciprocal of the golden ratio. The reciprocal of the golden ratio is also used in the design of some violins.. Sample answer: - _ + _ 9 = _ ; _, - _. Never; the value of c that makes a + b + c a perfect square trinomial is the square of b_ and the square of a number can never be negative.. To find the distance traveled b the accelerating racecar in the given situation, ou must solve the equation t + t + = or t + t - = 0. Since the epression t + t - is prime, the solutions of t + t + = cannot be obtained b factoring. Rewrite t + t + as (t + ). Solve (t + ) = b appling the Square Root Propert. Using a calculator, the two solutions are about.7 or -.7. Since time cannot be negative, the driver takes about.7 seconds to reach the finish line. 7. J i 7. -, 0 R Selected Answers

136 7. _, 7. _ (, - _ 77. greatest: - C; least: -9 C 7) Pages Lesson -. _, - _. - _. _ ± 7. - _ ± i 9. at about 0.7 s and again at about. s a. b. rational; es, there were rational roots a. b. irrational; es, there were irrational roots a. b. rational c. - _, _ 7a. 0 7b. rational 7c. _ 9a. 9b. irrational 9c. _- ± a. 0 b. irrational c. - ± a. - b. imaginar c. ± i. -, 7. ± i 9. ±. D: 0 t (current ear - 97), R: 7.7 A(t). (current ear - 97) -.(current ear - 97) No; the fastest the car could have been traveling is about 7. mph, which is less than the Teas speed limit. a. - b. comple c. 9 _ ± i 7a. _ 7b. irrational 7c. _ ± ± i 9a b. comple 9c _ ±. 0, - _. -, 7. This means that 0 the cables do not touch the floor of the bridge, since the graph does not intersect the -ais and the roots are imaginar..-, _. The diver s height above the pool at an time t can be determined b substituting the value of t in the equation and evaluating. When the diver hits the water, her height above the pool is 0. Substitute 0 for h and use the quadratic formula to find the positive value of t which is a solution to the equation. This is the number of seconds that it will take for the diver to hit the water.. G 7. ± 7 9. _ + _ i. _ + _ i.. = - _ + 7. no 9. es; ( + ) 7. no Pages 9 9 Lesson -7. Selected Answers 9a. ( ) 9b.. 9c.. (-, -); = -; up 7. = - ( + ) + ; (-, ); = -; down 9. = - ( + ) +. h(d) = - d + d + The graph opens downward and is narrower than the parent, and the verte is at (, ).. ( ) Selected Answers R

137 Selected Answers. ( ) 7.. = a + b + c = a ( + b_ a ) + c = a + b_ a + ( a) b_ + c - a ( a) b_ = a ( + a) b_ ac - b + _ a The ais of smmetr is = h or - a. 7. The equation of a parabola can be written in the form = a + b + c with a 0. For each of the three points, substitute the value of the -coordinate for in the equation and substitute the value of the -coordinate for in the equation. This will produce three equation in the three variables a, b, and c. Solve the sstem of equations to find the values of a, b, and c. These values determine the quadratic equation. 9. D. ; irrational. -; comple. { ± i} 7. es 9. es b_ 9. The graph is congruent to the original graph, and the verte moves 7 units down the -ais.. (-, 0); = -; down. = -( + ) + ; (-, ); = -; down. (0, -); = 0; up 7. = 9 ( - ) + 9. = - _ ( - ). = _ +. Angle A; the graph of the equation for angle A is higher than the other two since.7 is greater than.9 or... Angle C, Angle A Pages 9 0 Lesson < or > 7. { < - or > } 9. { - }.. = ( + ) - ; (-, -); = -; up. = -( - ) + ; (, ); = ; down. = ( - _ ) - 0; (_, -0 ); = _ ; up 7. = _ ( + ) - 9. Sample answer: The graphs have the same shape, but the graph of = ( - ) - is unit to the left and units above the graph of = ( - ) +.. about. s. about.0 s R Selected Answers

138 t + t +.7 > 0; ne method of solving this inequalit is to graph the related quadratic function h(t) = - t + t The interval in which the graph is above the t-ais represents the times when the trampolinist is above 0 feet. A second method of solving this inequalit would be find the roots of the related quadratic equation - t + t = 0 and then test points in the three intervals determined b these roots to see if the satisf the inequalit. The interval in which the inequalit is satisfied represent the times when the trampolinist is above 0 feet.. H. = -( - ) ; (, 0), = ; down. -, - 7. _ - ± 9. (-, -). (, ). [- ]. C 7a. Sample answer using (000,,90) and (00, 7,9): = 0, - 0,,0 7b. Sample answer: 7,00 Selected Answers < - or >. { < - or > }. { - }. { - } 7. 0 to 0 ft or to ft Pages 0 0 Chapter Stud Guide and Review. parabola. ais of smmetr. roots 7. discriminant 9. completing the square a. 0; = -; - b. f() c. f() f() 0 (, ) a. -9; = ; b. f() c. f() (, 9) f() 9.. { = _ } all reals. { - < < or > }. P(n) = n[ +.(0 - n)] - = -. n + 0n -. $.0; passengers 7. Sample answer: -, 0, and. {-, } 7. between - and -, between - and s = 0. {-, }. {-, } 7. _, - _ 9. base = cm; height = cm. n m. 0-0i _ - _ i 9. 9; ( + 7). - _,. ft b ft a. 0 b. irrational c. ± _ 7. about 0. ft 9. = - _ ( - ) + ; (, ); = ; down; ( ) Selected Answers R

139 Selected Answers. = ( + ) + ; (-, ); = -; up; (,, -) 9. A. S. Sample answer using (0,.) and (,.): = Pages Lesson -. es,. no p q - p q + p q m - mn + 9n es, 7. no 9. es, r - r +. b c - bdz 7. a b - 0a b + a b 9. p + p -. b b - 7b c + 9bc - c $ a - a b + a b _ 9. m - 7m -. + c + c. Sample answer: + +. ; Sample answer: ( + ) ( + ) = D 9. -d. _ z. < - _ or > _ 7. _ _ s 7.9 mph Chapter Polnomial Functions Page Chapter Get Read. + (-7). + (-). + (-z) 7. $ + (-$0.0) _ - z. $ _, - _ 7 9., _.. Pages Lesson ab. -_. _ w z. _. _ a0 b. an n.. ab. _ cd ; π 0 - m 9.. _ a b. _. _ a 7. _ 9. 7 b. about 0,000 times. Alejandra; when Kle used the Power of a Product propert in his first step, he forgot to use the eponent - for both - and a = (0 ) 0 or 0 0, and 0 00 > 0 0, so 0 00 > D 9. { < < }. Ø ma.; = _ - _ Pages 0 Lesson w+ + _ 000 w. a - 9a + 7a b + b - + _. + b -. ab - b. c - d + d b + 0b ( ) t + t + t + t + 0. c + c + + _ c - _ _ t + - t _. ; Let be the number. + R Selected Answers

140 Multipling b results in. The sum of the number,, and the result of the multiplication is + + or +. + Dividing b the sum of the number and gives _ + or. The end result is alwas. 7. about, subscriptions 9. - s. Sample answer: ( + + ) ( + ). Jorge; Shell is subtracting in the columns instead of adding.. Division of polnomials can be used to solve for unknown quantities in geometric formulas that appl to manufacturing situations. 0 in. b + f in. The area of a rectangle is equal to the length times the width. That is, A = lw. Substitute for A, 0 for l, and + f for w. Solving for f involves dividing b 0. A = lw = 0( + f ) _ = + f 0 + = + f = f = f The flaps are each inches wide. 7. H 9. z - z + z. a - ab + b. 0. a - 0a +. f() f () 7. C 9. t - t +. +.,0( + p);,0( + p). 7_ {-, _ 7. > } 9. + < 7. Distributive Selected Answers Pages Lesson -. ;. -;. 09 lumens 7. 00a a. f() - as +, f() + as - ; b. odd; c.. a. f() + as +, f() - as - ; b. odd; c.. ;. No, this is not a polnomial because the term _ c cannot be written in the form c n, where n is a nonnegative integer. 7. ; - 9. ;. 00; -. a - a + 0. a - a a. f() + as +, f() + as - ; 9b. even; 9c. a. f() + as +, f() - as - ; b. odd; c. a. f() - as +, f() - as - ; b. even; c.. 0,. joules 7. ; 9. 7; odd. Sample answer: Decrease; the graph appears to be turning at = 9, indicating a maimum at that point. So attendance will decrease after regions; Pages Lesson -. f() f() f() 0. between - and 0 f() 9. = 0 ; =. Sometimes; a polnomial function with real roots ma be a sith-degree polnomial function with imaginar roots. A polnomial function that has real roots is at least a fourth-degree polnomial.. -, 0, f() Selected Answers R7

141 Selected Answers. f() f() Sample answer: rel. ma. at -, rel. min. at 0.; domain: all real numbers, range: all real numbers 7. c () 000 Cable TV Sstems c().t t 790 c. Sample answer: rel. ma. at 0, rel. min. at a. f() f() f() 0 b. between 0 and, at =, and at = c. Sample answer: rel. ma. at, rel. min. at 7a. f() f () f() 7 Years Since 9 9. The domain is all real numbers. The range is all real numbers less than or equal to approimatel,. a. f() f () f () t b. at = - and = 0 c. Sample answer: rel. ma. at 0, rel. min. at - a. f() f () f() b. at =, between - and 0, and between and 7b. between - and -, and between and 7c. Sample answer: no rel. ma., rel. min. at = 0 9. highest: 9; lowest: s and about. s. about. s 7a. f() f () f() -7 7b. between - and -, between - and 0, between 0 and, and between and 7c. Sample answer: rel. ma. at -. and at., rel. min. at 0 9a. f() f () f () 0 R Selected Answers

142 9b. between - and -, and between and 9c. Sample answer: rel. ma. at 0., rel. min. at -0. and at. a. f() f() f() 7 9 b. between - and -, between - and 0, between 0 and, between and, and between and c. Sample answer: rel. ma. at - and at, rel. min. at 0 and at.. The growth rate for both bos and girls increases steadil until age and then begins to level off, with bos averaging a height of 7 in. and girls a height of 0 in...; ; -0.9,. 9. Sample answer:. ft. ab (a + b) 7. prime 9. (a + ) ( - ). (b - )(b + 7). (t - )(t + t + ). not possible 7. b[7(b ) - (b ) + )] 9. ( ) - ( ) -. -,, -i, i. -, + i, - i. _,_ - + i,_ - - i 7. in. in. 9. w = cm, l = cm, h = cm. ( + )( + ). ( + z)( - z). ( + ) ( - ) 7. (a + b)(a + )(a - ) 9. The height increased b, the width increased b, and the length increased b.. es. no; ( + )( - ). Sample answer: - = 0; [( ) - ] = 0 7. Sample answer: If a = and b =, then a + b = but (a + b) =. 9. Solve the cubic equation + (- ) + 00 = 00 in order to determine the dimensions of the cut square if the desired volume is 00 in -. Solutions are 0 and _ 0 in. There can be more than one square cut to produce the same volume because the height of the bo is not specified and 00 has man factors.. G. Sample answer: rel. ma. at 0., rel. min. at. 0 0 Selected Answers. Sample answer: f(). 7; 7 7. _ 7 ; 9. es The turning points of a polnomial function that models a set of data can indicate fluctuations that ma repeat. Polnomial functions best model data that contain turning points. To determine when the percentage of foreign-born citizens was at its highest, look for the rel. ma. of the graph which is at about t. The lowest percentage is found at t 7, the rel. min. of the graph.. H 7. 0c - c _ (-, -) 9. (, ). 9.. Pages Lesson -. -( + ). ( + 7)( - ). (z - )(z + ) 7. (w + )(w - ) 9. not possible. -7, -,, 7 Pages 9 Lesson -7. 7, -9. $. billion. Sample answer: Direct substitution, because it can be done quickl with a calculator. 7. -, , , -9., 7. 7, 0 7., , +. -, -. -, +. -, , +, , +, +. f() =.9 ft/s. This means the boat is traveling at.9 ft/s when it passes the second buo.. Yes; -ft lengths; the binomial - is a factor of the polnomial since f() = $.70. No, he will still owe $.0.. dividend: + + ; divisor: + ; quotient: - + 0; remainder:. Using the Remainder Theorem ou can evaluate a polnomial for a value of a b dividing the polnomial b - a using snthetic division. It is easier to use the Remainder Theorem when ou have polnomials of degree and lower or when ou have access to a calculator. The estimated number of international travelers to the U.S. in 00 is.9 million. 7. G Selected Answers R9

143 Selected Answers 9. (a + )(b - ). (c - )(c + c + ). f() f () f () 0 _. -7 ± 7 _ 7. - ± i 7 Pages Lesson -. i, -i; imaginar. or 0; ; or 0. -, + i, - i 7. i, -i, 9. f() = _ ; real. 0, i, -i; real, imaginar., -, i, and -i; real, imaginar 7. or 0; ; or 0 9. or ; 0; or 0.,, or 0; ;,, or 0. -, - + i, - - i. - i, + i, _, + i, - i 9. i, -i, i_, _-i. - i, + i, -,. f() = f() = f() = or 0; ; or 0. The compan needs to produce no fewer than and no more than computers per da.. radius = m, height = m. ft 7. ne root is a double root. Sample graph: f() 9. g. Sample answer: f() = - +. The polnomial equation that represents the volume of the compartment is V = h + h - 0h. Measures of the width of the compartment are, in inches,,,,,, 7, 9,,,,,,,,,,,,,, 77, and. The solution shows that h = in., l = in., and w = 9 in.. G 7. -, + i, - i 9. -7, + i, - i. -, + Pages 7 7 Chapter Stud Guide and Review. relative minimum. quadratic form. scientific notation 7. depressed polnomial 9. end behavior. _.. 0. times f 9. a + a _ ; - - h + 7. ; + h + h ; + h + h + h - a. f() f () 0 b. at = c. Sample answer: rel.ma. at -., rel. min. at. a. p () 9. Sample answer: f() = and g() = ; each has zeros at =, = -, and =.. C. -7,. ab (a - c ) 7. ( + ) 9. ± _, ±, ± _, ±. ± _ 9, ± _, ±, ± Pages 7 7 Lesson -9. ±, ±, ±, ±0. -,, 7., -,, cm cm cm 9., -, i, -i. ±, ±, ±, ±. ±, ±, ±, ±, ±9, ±. ±, ± _, ± _ 9, ±, ±9, ±7 7. -, -, 9. 0,, -. -, -. _, 0, _ ± i. -7,, 7. - _, _, _, _ 9., _, - _, _ - ±. No; the dimensions of the space are l = in., w = in., h = in., so the package is too tall to fit.., - ± i ;. V = _ l - l 7. l = 0 in., w = 0 in., h = in. p () b. between - and - c. Sample answer: rel. ma. at -., rel. min. at 0. a. r() 0 b. between - and -, between 0 and, and between and c. Sample answer: rel. ma. at -, rel. min. at : rel. ma. and rel. R0 Selected Answers

144 min. 9. (w + )(w - ). prime. -, 0,., - ± i 7., , or ; ; or 0. or ; ; 0 or 7. ( - )( - )( - ) = _,,.,,, -. _, Chapter 7 Radical Equations and Inequalities Page Chapter 7 Get Read. between 0 and, between and _ t + Pages 90 Lesson 7- _. + 9; - ; ; + +, -. {(-, 7), (, 9)}; {(, )}. - ; _ - ; price of CD when % discount is taken and then the coupon is subtracted. Discount first, then coupon; c[p(9.99)] gives a sale price of $.9, but p[c(9.99)] gives $ ; - - ; + - 7; _ - + 9, - 9_ ; + + ; ; _ +, , -; , -; - + 9, -; + + +, -,. (C - W)() = {(, ), (, )}; {(, ), (, ), (, )}. {(, ), (, ), (, ), (, )}; does not eist 7. {(, ), (, )}; {(-, ), (, ), (-9, -)} 9. - ; +. - ; ; ,0, s[p()]; The 0% would be taken off first, and then the sales ta would be calculated on this price.. $700, $.0, $.7, $.7, $.0. Danette is correct because [g f]() = g[f()] which means ou evaluate the f function first and then the g function. Marquan evaluated the functions in the wrong order.. Using the revenue and cost functions, a new function that represents the profit is p() = r(c()). The benefit of combining two functions into one function is that there are fewer steps to compute and it is less confusing to the general population of people reading the formulas. 7. G 9. ±, ± _, ± _, ±, ±, ± _, ± _, ±. or 0; or 0;,, or 0. about 0 times. = _ t = I_ pr Fr 9. m = _ GM Pages 9 9 Lesson 7-. {(, ), (, -), (, )}. f - () = - f (). = - 0 f() f () m/s 9. no. {(, ), (-, ), (-, )}. {(-, -), (-, -), (-, -), (, 0)}. {(, ), (, -), (, ), (-, )} 7. g - () = - _ g() g () 9. g - () = -. = - _ - _ g() g() g () g() Selected Answers Selected Answers R

145 Selected Answers. f - () = _ f () f () f () f - () = _ + _ 0 f () f () 0 7 f() Pages 99 0 Lesson 7-. D: 0, R: f - () = _ 7 + _ 7 f () f () 7 7 f () 7. D: ; R: cm. no. es. es 7. = F - () = _ 9 ( - ); F[F- ()] = F - [F()] =.. n is an odd whole number.. Sample answer: f() = and f - () = or f() = - and f - () = -.. A ± _, ± _, ±, ± _, ±, ± _, ±, ±, ±0, ± consistent and independent ,. { > } Yes; sample answer: the advertised pump will reach a maimum height of 7.9 ft D: 0, R: R Selected Answers

146 . D: 0, R: D: -, R: Selected Answers. D: -0., R: 0 7. D: -, R: - 9. D:, R: 7 7. h > ft.. lb If a is negative, the graph is reflected over the -ais. The larger the value of a, the less steep the graph. If h is positive, the graph is translated to the right, and if h is negative, the graph is translated to the left. When k is positive, the graph is translated up, and when k is negative, the graph is translated down.. Square root functions are used in bridge design because the engineers must determine what diameter of steel cable needs to be used to support a bridge based on its weight. Sample answer: when the weight to be supported is less than tons;,0 tons. G 7. no 9. (f + g)() = + ; (f - g)() = ; (f g)() = + - ; (f g)() = _ + -. (f + g)() = ; + (f - g)() = ; + (f g)() = - ; (f g)() = rational. rational 7. irrational Pages 0 0 Lesson a b not a real number _. 0.. z. 7 m 7. r 9. g... ab about 0 0 m. Sample answer:. = 0 and 0, or = 0 and 0. The radius and volume of a sphere can be related b an epression containing a cube root. As the value of V increases, the value of r increases. 7. G 9. V m D = { 0}, R = { -} Selected Answers R

147 Selected Answers. no. 9 - i. (, -) 7. (-, ) 9. f () 7. 7 f () a + ab + b 77. w - 7wz - z Pages Lesson _. a ab b 7. s = l _ a b 0a 7. mn mn 9. _ wz. _. _ r Rt wz t feet _ - 9. _ _ 0. 0 ft/s 7. about. m 9. Sample answer: ; Simplif the term 7 to 9. Then combine and 9. The simplified epression is The ratio of the lengths of the sides of the rectangle around the face is _. You can - simplif this epression b multipling the numerator and denominator b the conjugate of the denominator. The new epression is _ +.. G. ab _ _ _ 0 R Selected Answers 7. does not eist 7. _ 7. _ Pages 9- Lesson $ _ c or ( c - ). _. z. 7. _ 9.. _. about. in. _. 7. b 9. w _ w. a _ a 7. z _ z r s. +. about 7. In radical form, the epression would be -, which is not a real number because the inde is even and the radicand is negative. 9. Alwas; in eponential form n b m equals (b m ) _ n. B the Power of a Power Propert, (b m ) _ n = b m_ n. But, b m_ n is also equal to ( _ b n ) m b the Power of a Power Propert. This last epression is equal to ( n b ) m. Thus, n b m = ( n b ) m.. B [K C](F) = _ (F - ) s Pages 7 Lesson no solution b <.. no solution no solution 9. no solution _ 9. about. ft. > b 9. ft. _ ( ) - = _ ( ) / - = _ - = = ()(-) -, Never.. Sample answer: + + =. If a compan s cost and number of units manufactured are related b an equation involving radicals or rational eponents, then the production level associated with given cost can be found b solving a radical equation. C = 0 n + 00 _ 0,000 = 0n + 00 C = 0,000 _ 00 = 0n Subtract 00 from each side. _ 0 = n Divide each side b 0. _ 0 = n Raise each side to the _ power.,7. n Use a calculator. Round down so that the cost does not eceed $0,000. The compan can make at most,7 chips. 7. G

148 9. 7. ( 00 + ). _. I(m) = m; $00 7. (f + g)() = + - ; (f - g)() = - - ; (f g)() = ; (f g)() = - ; - 9. ; If is our number, ou can write the epression _ + +, which equals after dividing + the numerator and denominator b the GCF, +.. p - p - 0. Sample answer: = Pages 0 Chapter 7 Stud Guide and Review. radical equation. like radical epressions. inverse functions 7. one-to-one 9. inverse relations. - ; ; ; + 7. f - () = _ + f () f - (). D: -, R: 0 7. D:, R: Selected Answers 9. g - () = -. - () = ±. I(m) = m; $000 f () g () g() g () ± m 9. 0 meters per second _ 7. _ 0-9. _. 9_. z _ 7 9 z.. amps > _ d > - _ 7. m Chapter Rational Epressions and Equations Page Chapter Get Read. _. _. 7. _ _ 9. $ $0 Pages 9 Lesson -. 9m_. +. D 7. - b - ab - a 9. _ n a + b. _. _ + 9. _ ( - ) 7. - n_ 9 + ( + ) 7m t +. -_. -_ bc. -p 7. _ 9. _ p - 7 t + 7a p p. _ +. d = -, -, or - 9. _ Selected Answers R

149 Selected Answers 7. _ ( + - ) m 9. s_. _ + -. _ +. -_ b - 7. _ b 9. _ z ( + ) b + a (r + ). _. a = -b or b. _ + m r +, + a 7. _ ; Sample answer: the second airplane travels a 7 bit further than the first airplane ; The epression defines the function g().. The tables are the same ecept for f() the value f(0) is undefined.. Sample answer: _ -, _ -. _ + does + not belong with the other three. The other three epressions are rational epressions. Since the denominator of _ + is not a polnomial, _ + is + + not a rational epression. 7. A rational epression can be used to epress the fraction of a nut miture + that is peanuts. The epression _ could be + + used to represent the fraction that is peanuts if pounds of peanuts and pounds of cashews were added to the original miture. 9. F 7. V D = { 0}, R = { -} could be used to determine the distance between the lens and the film if the focal length of the lens is 0 mm and the distance between the lens and the a(a + ) object is 000 mm.. F. _ 7. ±i, ± a ft 7. ( + )( + ) 7. ( + )( - ) 7. ( - )( + ) Pages 0 Lesson -. asmptote: =.. f() f() ( ) f() f() m 7. f() 0 7. no 7. odd; 77. about.99 0 s or about min 9 s 79. _ {-, _.. - _. _ 7. - } _ 9 Pages Lesson -.. ( - )( + ). _ _ m d + 9. _ _. _ (d + ) ( + )( - ) z. ( - )( + ). _. _ - 7ab 7. _ a + 9. ( - 9) v a b a - ( + )( - ) -d p q (d - )(d + )(d - ) 9. (n - )(n - )(n + ). + _. _ 0w - 90w _ a + 7 ( + ) ( + ) ( - )( - ) a + -. _. _ ( - ) ( - ) h. _ ( - ) h 7. Sample answer: d - d, d + 9. Sample answer: _ +, _ -. Subtraction of rational epressions can be used to determine the distance between the lens and the film if the focal length of the lens and the distance between the lens and the object are known. _ q = _ 0 - _ 000 f() 9. l f() R f(). 0. amperes. asmptotes: =, =. asmptote: = -; hole: = - R Selected Answers

150 9.. f() f() f(). m = -, V f = 0; -.; 0. P() P() 0 Selected Answers. It represents her original free-throw percentage of 0%. 7. hole: = 9. f() f(). f() f() ( ) f() ( )( ). f(). f() f() f(). f() 7. f() f() ( ) f() 9. V f 0. f() f() m Selected Answers R7

151 Selected Answers 7. f() f() - 9. Since _ + = - _ (, the graph of + ) - f() = _ is the reflection image of the graph of + f() = _ over the -ais.. Each of the graphs + is a straight line passing through (-, 0) and (0, ). ( - )( + ) However, the graph of f() = has a hole - at (, ), and the graph of g() = + does not have a + hole.. Sample answers: f() = ( + )( - ), ( + ) f() = ( + )( - ), f() = ( + ). A ( + )( - ) 7. _ m + 9. _ (w - ). - _,,. {- ± i} m + n (w + ). {_ -7 ± } equation to represent the amount s students will spend for lunch in d das. How much will 0 students spend in a week? a =.0sd; $7. C. asmptote: t = ; hole: = -. hole: = t - (t + )(t - ) ; 7. C. S 7. A Pages 7 7 Lesson -. greatest integer. constant. b 7. direct variation 9. absolute value Pages 7 Lesson psi 7. Depth (ft) Pressure (psi) P. square root. direct variation. constant 7. direct variation P 0.d d about 9. mi 7. direct; 9. joint; _. inverse;.. direct; _ 9... V = _ k. l = md 7. joint P 9. 0 mph. I I d 9. inverse variation or rational. greatest integer d. about 0 0 Newtons Newtons 9. Sample answer: If the average student spends $.0 for lunch in the school cafeteria, write an R Selected Answers

152 . quadratic. e 7. a 9. direct variation. parabola. The graph is similar to the graph of the greatest integer function because both graphs look like a series of steps. In the graph of the postage rates, the solid dots are on the right and the circles are on the left. However, in the greatest integer function, the circles are on the right and the solid dots are on the left. a. absolute value b. quadratic c. greatest integer d. square root 7. There are several tpes of functions. Each tpe of function has features which distinguish it from other tpes. Knowing which features are characteristic of each tpe of graph can help ou determine which tpe of function best describes the relationship between two quantities. 9. G. f () f (). or. 7_ 7. _ ± 9. p < 0 or p > _.. cm/g. km/h; With the wind, Alfonso s speed would be km/h, and his -km trip would take hours. Against the wind, his speed would be km/h, and his -km trip would take hours. The answer makes sense.. { < - or > } 7. _ 0 9. Jeff; when Dustin multiplied b a, he forgot to multipl the b a.. If something has a general fee and cost per unit, rational equations can be used to determine how man units a person must bu in order for the actual unit price to be a given number. Since the cost is $.00 per download plus $.00 per month, the actual cost per download could never be $.00 or less.. J. square root { 0 } beats per min Selected Answers. f () Pages 9 9 Chapter Stud Guide and Review. false; point discontinuit. false; rational bc. true 7. true 9. -_. _ +. ( + )( - ) a -. ( + ) m 7. 7_ 9. _ ( + ) -. (m - m + 7).. (m + )(m - ) f (). f() f( ). -7, _ 7. 0 m 9.. ( - )( + ). (t - )(t + )(t + ) Pages Lesson -.. _. 7. _ h; The answer is reasonable. 9 The time to complete the job when working together must be less than the time it would take either person working alone. 9. v < 0 or v > _. - _. -, < m <. 0 < b < 7. f() f() Selected Answers R9

153 Selected Answers _ f(). _ _ < b < 0 f() ( )( ) square root 9. _ 9 Chapter 9 Eponential and Logarithmic Relations Page 97 Chapter 9 Get Read.. -_ 7 z..9 0 kg/m 7. f - () = _ + f () f () 9. f - () = + f () f () 9. D = all real numbers, R = { > 0} (). D = all real numbers, R = { > 0} ( ). growth. growth 7. deca 9. = (). = -( _ ). = - 0.(). about,00,90 7. A(t) = 000 (.0) t 9. _. - _. _. n > 7. n < 9. D = all real numbers. R = { > 0} f () ( ). $7.77 f () Pages 0 0 Lesson 9-. c. b. D = all real numbers, R = { > 0}. s. =.9 (.)..7 million;. million; No, the growth rate has slowed considerabl. The population in 000 was much smaller than the equation predicts it would be. 7. ( ) [, ] scl: b [, 9] scl: 7. growth 9. = -(). about $,7,70; Yes, the mone is continuing to grow at a faster rate each ear. In the first 0 ears it grew b $7,000, and in the net ten ears it grew about $900, a - The graphs have the same shape. The graph of = + is the graph of = translated one unit to the left. The asmptote for the graphs = and for = + is the line = 0. The graphs have the same domain, all real numbers, and range, > 0. The - intercept of the graph of = is and of the graph of = + is. R70 Selected Answers

154 9.. [, ] scl: b [, 7] scl: The graphs have the same shape. The graph of = ( _ ) - is the graph of = ( _ ) translated one unit down. The asmptote for the graph of = ( _ ) is the line = 0 and for the graph of = ( _ ) - is the line = -. The graphs have the same domain, all real numbers, but the range of = ( _ ) is > 0 and of = ( _ ) - is > -. The -intercept of the graph of = ( _ ) is and for the graph of = ( _ ) - is 0.. Sample answer: 0.. Sometimes; true when b >, but false when b <.. A 7., 9. - _, 7. greatest integer _ g[h()] = - ; - h[g()] = g[h()] = - - ; h[g()] = - + Pages 7 Lesson 9- _. log =. log =. = or about, times 7. { _ < } 9. _,. >. =. - = 7. = 9. log =. log _ = -. log 00 0 = _. 7. _ ± <. 7. ± 9. a >. log log riginal equation log log = and = _ () Inverse Propert of Eponents and Logarithms = log ( ) The graphs are reflections of each other over the line =.. 0 or about 000 times as great or about 0 times 9. D = { > 0}, D = { > 0}, D = { > }, D = { > -}, respectivel; R = {all reals} 7. log = ; all other choices are equal to 7. All powers of are, so the inverse of = is not a function. 7. B ± 7_. $000, CD; $000, savings. a b 7. Pages Lesson Mt. Everest:,. pascals; Mt. Trisuli:,9. pascals; Mt. Bonete:,0. pascals; Mt. McKinle: 9,. pascals; Mt. Logan:,. pascals _ About.. _ 9 decibels; L = 0 log 0 R, where L is the loudness of the sound in decibels and R is the relative intensit of the sound. Since the crowd increased b a factor, we assume that the intensit also increases b a factor of. Thus, we need to find the loudness of R. L = 0 log 0 R; L = 0 ( log 0 + log 0 R); L = 0 log log 0 R; L 0(0.77) + 90; L or about m p = m p Refleive propert ( b log b m ) p = b log b ( m p ) m = b log b m and b log b mp = b log b ( m p ) log b mp = log b ( m p ) p log b m = log b ( m p ) m p = b log b ( m p ). Use Propert of Powers on the left hand side of the equation. Power of a Power: a mn = (a m ) n Eponents must be equal b the Propert of Equalit for Eponential Functions. Reverse the order of multiplication on the left hand side. Selected Answers Selected Answers R7

155 Selected Answers 7. log ( a a ) = _ log a log a = log a - log a = log ( a ) - log ( a ) = log ( a ) - log ( a ) _ ( = log a ) _ = _ log ( a ) 9. False; log ( + ) = log, log + log = +, or, and log, since.. Let b = m and b = n. Then log b m = and log b n =. _ b b = m_ n b - = m_ n log b b - = log b m_ n - = log b m_ n Quotient Propert Propert of Equalit for Logarithmic Equations Inverse Propert of Eponents and Logarithms log b m - log b n = log b m_ n Replace with log b m and with log b n.. A s.. - _ < < Pages Lesson ±. 9. n > _ log ; 0.7. _ log 9 log 7 log ; {a a <.90}. {n n < -.07}. { 0.7} log 0. _. 7. _ log log log.9 0. log 9. _ ±. log cents. about.9 ears 7. log a = log a riginal equation _ log a = log log a a a Change of Base Formula _ log a = log a (a) = log a Quotient Propert of Logarithms log a ( _ a ) = log a = _ a _ = a a Quotient Propert of Logarithms Propert of Equalit for Logarithmic Functions Rationalize the denominator 9a. log = and log = _ 9b. log 9 7 = _ and log 7 9 = _ 9c. Conjecture: log a b = _ log b a ; Proof: log a b _ riginal statement log b a log b b _ log b a _ Change of Base Formula log b a _ log b a = _ Inverse Propert of log b a Eponents and Logarithms. C z 0 < z _ = 7. = Pages 0 Lesson = ln h = -,00 ln P_. { >.0} = ln 7. e = e 9. + = ln 9. e = 7_ about 7.9 billion. about 9. r. 00 ln < about 0 people ,. Sample answer: e =. Alwas; _ log log _ ln riginal statement ln _ log _ log log _ log e Change of Base Formula log _ log e _ log log _ log log e _ log e log _ log log = _ log log. B 7. log _ log Multipl _ log b the reciprical log e of _ log log e. Simplif _ log log 0 7. joint, 7. free throws and 7 field goals Pages 0 Lesson 9-. about h. about. watts. C 7. about, people 9. about.7 hr. more than,000 ears ago. $,9 billion. about after the ear 9. t = _ 0 n 0.. Take the common logarithm of each side, use the Power Propert to write log ( + r) t as t log( + r), and then divide each side b the quantit log( + r).. Never; theoreticall, the amount left will alwas be half of the amount that eisted 0 ears before.. D 7. ln = 9. = e. p >.9. _ 0.(0.0p) _ 0.(0.0p). _ 0.(0.0p) R7 Selected Answers

156 Pages Chapter 9 Stud Guide and Review. true. false, common logarithm. true 7. false, logarithmic function 9. false; Propert of Inequalit for Logarithms. growth. = 7 ( _ ) or 9. log 7 =. =. 9. _ , decibels. ± log 7. _; ln = log r 9..0 das. about.%. 0 ( 7) 0 Selected Answers. Chapter 0 Conic Selections Page Chapter 0 Get Read. {-, -}. (_, - ). 9 in. b in. 7a. - 7c b Pages Lesson 0. (-, _ ). (.,.). 0 units 7.. units 9.. units. (-, -). ( 7_, 7_ ). around th St. and 0th Ave. 7. units 9. 7 units. 70. units. 0 units. _ ( 0, - _ ; unit 7. _ ) (0, );_ units 9. 0 π units, 90π units. Sample answer: Draw several line segments across the U.S. ne should go from the northeast corner to the southwest corner; another should go from the southeast corner to the northwest corner; another should go across the middle of the U.S. from east to west, and so on. Find the midpoints of these segments. Locate a point to represent all of these midpoints.. about mi. in. 7. all of the points on the perpendicular bisector of the segment 9. Most maps have a superimposed grid. Think of the grid as a coordinate sstem and assign approimate coordinates to the two cities. Then use the Distance Formula to find the distance between the points with those coordinates.. G = ( + ) Pages 7 7 Lesson 0. = ( - ) - ; verte = (, -); ais of smmetr: = ; opens upward 7. = ( - ) + ; verte = (, ); ais of smmetr: = ; opens upward 9. = _ ( + ) - 0; verte = (-, -0); ais of smmetr: = -; opens upward... ( ) ( ) ( ) Selected Answers R7

157 Selected Answers ( _, - _ ), ( _, -7) = _, = - 7_ downward, _ unit (,), _ ( 0, ), =, = _ 79, right, _ 0 unit. 0.7 cm. = - _ 00 ( - 0) +. = - _ 7. The graph s verte is shifted to the left _ unit and down _ unit. 9. = - _ (-) +. = _ ( - ) ( ) 7 ( ) 7. = _ ( - ) + ( ) (, -), ( _, -), = -, = _, left, units. Rewrite it as = ( - h), where h > 0.. When she added 9 to complete the square, she forgot to also subtract 9. The standard form is = ( + ) or = ( + ) -.. A parabolic reflector can be used to make a car headlight more effective. Answers should include the following. Reflected ras are focused at that point. The light from an unreflected bulb would shine in all directions. With a parabolic reflector, most of the light can be directed forward toward the road. 7. J 9. 0 units. about. das Pages Lesson 0. ( - ) + ( + ) = 9. Earth Satellite,00 km 00 km,00 km R7 Selected Answers

158 . + ( + ) = 7. (, ), units ( ) ( ) 9. (, -7), units 7. (0, ), units ( ) ( 7) Selected Answers 9. (, 0), _ unit ( ). (-, ), units ( ). ( + ) + ( - ) =. + = 7. ( + ) + ( - 7) = _ 9. ( + ) + ( + _ ) = _ 9. (0, 0), units 0 9. (9, 9), 09 units. (_, - ),_ 7 0 units 0 0. (-, -7), 9 units ( ) ( 7) 0 0. ( + ) + ( - ) = 777. ( - ) + ( - ) = 7. ( + ) + ( - ) = 9. about 09 mi. = - ( + ), = - -( + ). = - ± - ; The equations = ; and = represent the right and left halves of the circle, respectivel.. ( + ) + ( - ) = ; left units, up unit 7. ( + ) + ( + ) = Selected Answers R7

159 Selected Answers 9. D. (, 0), ( _, 0 ), = 0, = _, left, _ unit _. (-, -), (-, - _, = -, = - ) 7, upward unit (±, 0); 0; ;. (, -); (, - ± ); ; ; 0 0 ( ) ( ) 9. (0, 0); (0, ± ); ; ;. (-, -) 7. -, -, 9. in. b in... Pages Lesson 0 _. _ + = =. (0, 0); (0, ±); ;. (-, ); (, ), (-, ); 0; ; _ + _ ( - ) + _ 7. _ + ( - ) =. _ + ( - ) =. _ + 00 _ = 9. (0, 0); 9 ( - ) _ 9 _( - ) 9 (0, 0); (±, 0); ; =. = _( + ) ( - ) + 79,. + ( - ) 7. _. 0 9 = = _ =. Let the equation of a 9,00 circle be ( - h) + ( - k) = r. Divide each side b _( - ) ( + k) _ r to get + =. This is the equation of r r an ellipse with a and b both equal to r. In other words, a circle is an ellipse whose major and minor are both diameters.. _ + _ 9 = 7. C 9. ( - ) + ( + ) =. = _ ( - ) + R7 Selected Answers

160 ( ). Sample answer using (0, 0.) and (0,.): = ( ) 0 ( ) (, - ± ); (, - ± ); + = ± _ ( - ) ( ±, -); ( ±, -); + = ± _ ( - ) 0 Selected Answers ( - ) 9. _ -_ ( + ) =. _( - ) -. _ - _ 9 = ( - ). _ - = ± ( + ) _ = 9 _( + ) = 7. (0, ±); (0, ± 0 ); ( ) Pages 9 97 Lesson 0 _. _ - =. (0, ±); (0, ±); = ± _ ; (±, 0); (±, 0) ; = ± _ 9. (, -), (, ); (, ± ) ; - = ± _ ( - ) 0 ( ) ( ) 0 Selected Answers R77

161 . (±, 0); (±, 0) ; = ±. F. _( + ) ( - ) + _ = 7. (, -), units 9 Selected Answers. (0, ± ); (0, ± ); = ± _ 9. -7, _. -,.,, -., 0, 0 Pages 99 0 Lesson 0. parabola = ( + _ ) - _ 7. (-, -), (0, -); (- ±, -); + = ± _ ( + ) 0 ( ) ( ) 9 0. circle ( - _ ) + = _ 9 9. (-, 0), (, 0); ( ± 9, 0); = ± _ ( - ) 9 0. _ - _ =. about 7. ft. (, ), (-, - ) 7.The graph of = - can be obtained b reflecting the graph of = over the -ais or over the -ais. The graph of = - can also be obtained b rotationg the graph of = b As k increases, the branches of the hperbola become wider.. Hperbolas and parabolas have different graphs and different reflective properties. Answers should include the following. Hperbolas have two branches, two foci and two vertices. Parabolas have onl one branch, one focus, and one verte. Hperbolas have asmptotes, but parabolas do not. Hperbolas reflect ras directed at one focus toward the other focus. Parabolas reflect parallel incoming ras toward the onl focus.. parabola 7. hperbola 9. circle + = 7. parabola = _ R7 Selected Answers

162 . hperbola _( - ) ( - ) -_ =. parabola = _ 9 ( - ) + 7. ellipse 9. hperbola _( + ) + _( - ) = _( - ) -_ ( + ) = Selected Answers 7. circle; + ( + ) =. ellipse. parabola. Sample answer: + - = 0 7. intersecting lines 9. 0 < e <, e > ( - ). C. _ -_ ( - ) =. (, -); ( ±, -), ; ; 9. circle. parabola. b. c 7. about ft 9. hperbola. hperbola. ellipse _( - ) 9 + _ = 9_ 7. m n 9. 9 beats per min. = -_. (, ) - _. hperbola ( - ) _ - _ 9 = Pages 0 0 Lesson 0 7. (±, ). no solution. (0, 0) (_, _ 9, (-, ). no solution. no solution ). (0, ), _ (±, - _ ) 7. (0, ±) Selected Answers R79

163 9. (, ±), (-, ±).. ( + ) + ( + ) =, circle, Selected Answers.. (0, ± ), (0, ± ), = ± _. Pages 09 Chapter 0 Stud Guide and Review. true. False; a parabola is the set of all points that are the same distance from a given point called the focus and a given line called the directri.. False; the conjugate ais of a hperbola is a line segment perpendicular to the transverse ais. 7. true 9. ( -, _. (, ). 90 units. 7. (, - _ 9. (, -); (, - _ ; = ; = - _ ; upward; _ ) unit ) ) ( ) 7. (9., ±.) 9. _ (-, - 7_, (, ). 0. s ). = ±900 -_ (00) ; = ±90 -_ (00). Sample answer: The orbit of the satellite modeled b the second equation is closer to a circle than the other orbit. The distance on the -ais is twice as great for one satellite than the other. 7. Sample answer: + ( + ) =, _ - _ = 9. Sample answer: + =, _ + _ =. impossible. Sample 00 answer: + = 0, = +. none 7. none 9. + = 0, _ + _ = This sstem has four solutions whereas the other three onl have two solutions.. C. (0, 0); ( _, 0); = 0; = - _ ; right; _ unit. = - _ ( + ) + = _ 9 7. ( + ) + ( - ) = 9. (-, ), 7 units R0 Selected Answers

164 ( ) ( ) 9 (, ). (-, ), units (, ) 9 0 ( + ). _ + _ ( - ) =. (-, ); (- ± 7, ); ; ( ) ( ) 9. parabola, = ( + ) 0 7. ellipse _ 9 + _ = 9. hperbola. circle. (, -), (, -). 9 Selected Answers 7. _. + _. = 9. (0, ± ); (0 ± ); = ± _ 9 7. (0, 0) and (0, 0). (, -), (, -); ( ± 0, -); + = ± ( ) Chapter Sequences and Series Page Chapter Get Read ( ) ( ) 9 0. (_ 0 -,_ - ) Selected Answers R

165 Selected Answers _ Pages Lesson -.,,,.,,,, 7. _, _,, _, _ a n = n - 7.,, , 7,, 9., 0,,.,,,,.,, -, -, ft. 0th 7. a n = 9n - 9. a n = -n -. 70,, 00. -, -,,. 7_,, _, _ 7..,.,.7,. 9. _,, _, _, 0. 9.,,. No; there is no whole number n for which n + = _ a n = 7n a n = -n +. Sample answer: Maa has $0 in her savings account. She withdraws $ each week to pa for music downloads. 7. z = - 9. B 7. (-, ±), (, ±) 7. = _ ( + ) + ; parabola ( ) _, _, 7_. = + 7.,,,. -, -, -, -, -0 Pages Lesson h , 0, das , -, -.,, , _.,. $, True; for an series, a + a + a + + a n = ( a + a + a + + a n ).. Arithmetic series can be used to find the seating capacit of an amphitheater. The sequence represents the numbers of seats in the rows. The sum of the first n terms of the series is the seating capacit of the first n rows. ne method is to write out the terms and add them: = 0. Another method is to use the formula S n = n_ [ a + (n - )d]: S 0 = _ 0 [() + (0 - )] or 0.. G ( ) 7. log 7 = 7. _ 7 das _ _ ± a = -, b =. c = 9, d = 7. - Pages 9 Lesson -. 7., 0.. A. 7. _ 7 9. a n = ( _ ) n -. -.,. 9, 7., 9.,,,,. 9. $, a n = ( _ ) n -. a n = (-) n -. ±,, ±0 7.,,, 9. _, _. -.7,.7. 7, -,, -7,. das Sample answer:, _, _ 9, _,. The sequence 9,,, does not belong 7 with the other three. The other three sequences are geometric sequences, but 9,,, is not. 7. False; the sequence,,,,, for eample, is arithmetic (d = 0) and geometric (r = ). 9. C... 9,. + 0 units 7. _ Pages 9 Lesson -.,9. _ 0. 9 in. or 7 ft 9 in. 7. _ ,. _ 9. 9, ,, $0,77,.. 0, _ , _ 9.,,7. _ 7.. -,0, Sample answer: _. If the first term and common ratio of a geometric series are integers, then all the terms of the series are integers. Therefore, the sum of the series is an integer.. If the number of people that each person sends the joke to is constant, then the total number of people who have seen the joke is the sum of a geometric series. Increase the number of das that the joke circulates so that it is inconvenient to find and add all the terms of the series. R Selected Answers

166 . J 7. -, -_ 9, - 7_, - _ even; 7. (7p + )(q - ) Sample answer: _. 0. Pages Lesson does not eist. 9 cm _. _ does not eist... does not eist 7. does not eist 9. _ 9. _ cm _ 7. 7, 0, 9. -, - _, - 7_, - _. _ 90. ft can be written as the infinite geometric series _ _ _ The first term of this series is _ 9 0 common ratio is _, so the sum is 0 9_ 0_ - _ or. 0. S = a + a r + a r + a r + (-) rs = a r + a r + a r + a r + S - rs = a S( - r) = a a S = _ - r. D %.- _. and the -a + b. _ a b + 7 ( + )( + ) = 0 9. about -,07 visitors per ear Pages 0 Lesson -., 9,,, 0. 0, -,, -, 0. b n =.0 b n ,, 9 9.,,.,,,,., 0,,,.,,, 0, , 7,. -, -9, -9. a n = a n - + a n -.,,, 0, 7. 0,00 9. $ , -, -. _, _ 0, _ 7. Sometimes; if f() = and =, then = or, so. But, if =, then =, so =. 7. Under certain conditions, the Fibonacci sequence can be used to model the number of shoots on a plant. The th term of the sequence is, so there are shoots on the plant during the th month. 9. F. _ units 7. Pages 7 9 Lesson -7. p + p q + 0 p q + 0 p q + pq + q ,0 7. 7,0 9. a b. a - a b + ab - b. r + r 7 s + r s + r s + 70 r s + r s + r s 7 + rs + s , b - b + b - b _ a + _ a + a + 0 a + 0a +. 9.,0,0 a b 7. _ Sample answer: ( + ). The coefficients in a binomial epansion give the numbers of sequences of births resulting in given numbers of bos and girls. (b + g) = b + b g + 0 b g + 0 b g + bg + g ; There is one sequence of births with all five bos, five sequences with four bos and one girl, ten sequences with three bos and two girls, ten sequences with two bos and three girls, five sequences with one bo and four girls, and one sequence with all five girls.. H 7.,, 9, 7, 9. hperbola. _ log ;.9. _ log log log ;.90. asmptotes: = -, = 7. true 9. true. true Pages 7 7 Lesson -. Step : When n =, the left side of the given ( + ) equation is. The right side is _ or, so the equation is true for n =. Step : Assume k(k + ) + k = _ for some positive integer k. Step : k(k + ) k + (k + ) = _ + (k + ) = k(k + ) + (k + ) (k = + )(k + ) The last epression is the right side of the equation to be proved, where n = k +. Thus, the equation is true n(n + ) for n = k +. Therefore, n = _ for all positive integers n.. Step : After the first guest has arrived, no handshakes have taken place. _ (-) = 0, so the formula is correct for n =. Step : Assume that after k guests have arrived, a total of _ k(k - ) handshakes have taken place, for some positive integer k. Step : When the (k + )st guest arrives, he or she shakes hands with the k guests alread there, so the total number of handshakes that k(k - ) have then taken place is _ + k. _ k(k - ) k(k + k = - ) + k k[(k - ) + ] = k(k + ) = _ or _(k + )k The last epression is the right side of the equation to be proved, where n = k +. Thus, the formula is true for n = k +. n(n - ) Therefore, the total number of handshakes is _ for all positive integers n.. Step : + =, which is divisible b. The statement is true for n =. Selected Answers Selected Answers R

167 Selected Answers Step : Assume that k + is divisible b for some positive integer k. This means that k + = r for some positive integer r. Step : k + = r k = r - k + = 0r - k + + = 0r - k + + = (r - ) Since r is a positive integer, r - is a positive integer. Thus, k + + is divisible b, so the statement is true for n = k +. Therefore, n + is divisible b for all positive integers n. 7. Sample answer: n = 9. Step : When n =, the left side of the given [() + ] equation is. The right side is _ or, so the equation is true for n =.Step : Assume k(k + ) + (k -) = _ for some positive integer k. Step : (k ) + k(k + ) [(k + ) - ] = _ + [(k + )-] k(k + ) + [(k + )-] = = k + k + k + - = k + 7k + (k + )(k + ) = (k + )[(k + )+] = The last epression is the right side of the equation to be proved, where n = k +. Thus, the equation is true for n = k +. Therefore, (n ) n(n + ) = _ for all positive integers n.. Step : When n =, the left side of the given equation is or [() - ][() + ]. The right side is or, so the equation is true for n =. Step : Assume (k - ) k(k - )(k + ) = for some positive integer k. Step : (k ) + [(k + ) - ] k(k - )(k + ) = + [(k + )-] k(k - )(k + ) + (k + ) = (k + )[k(k - ) + (k + )] = = (k + )( k - k + k + ) = (k + )( k + k + ) (k + )(k + )(k + ) = (k + )[(k+)-][(k + )+] = The last epression is the right side of the equation to be proved, where n = k +. Thus, the equation is true for n = k +. Therefore, (n -) = n(n - )(n + ) for all positive integers n.. Step : 9 - =, which is divisible b. The statement is true for n =. Step : Assume that 9 k - is divisible b for some positive integer k. This means that 9 k - = r for some whole number r. Step : 9 k - = r 9 k = r + 9 k + = 7r k + - = 7r + 9 k + - = (9r + ) Since r is a whole number, 9r + is a whole number. Thus, 9 k + - is divisible b, so the statement is true for n = k +. Therefore, 9 n - is divisible b for all positive integers n.. Step : When n =, the left side of the given equation is f. The right side is f -. Since f = and f = the equation becomes = - and is true for n =. Step : Assume f + f + + f k = f k + - for some positive integer k. Step : f + f + + f k + f k + = f k f k + = f k + + f k + - = f k + -, since Fibonacci numbers are produced b adding the two previous Fibonacci numbers. The last epression is the right side of the equation to be proved, where n = k +. Thus, the equation is true for n = k +. Therefore, f + f + + f n = f n + - for all positive integers n. 7. Sample answer: n = 9. Sample answer: n =. Sample answer: n =. Step : When n =, the left side of the given equation is _. The right side is _ ( - _ ) or _, so the equation is true for n =. Step : Assume _ + _ + _ + + _ = _ ( - _ k ) for some positive k integer k. Step : _ + _ + _ + + _ + _ k k + = _ ( - _ ) + _ k k + = _ - _ + _ k k + = k k + = _ k + - k + = _ ( k + _- ) k + = _ ( - _ ) k + The last epression is the right side of the equation to be proved, where n = k +. Thus, the equation is true for n = k +. Therefore, _ + _ + _ + + _ n = _ - ( _ ) n for all positive integers n.. Step : + =, which is divisible b. The statement is true for n =. Step : Assume that k + is divisible b for some positive integer k. This R Selected Answers

168 means that k + = r for some positive integer r. Step : k + = r k = r - k + = r - k + + = r - k + + = (r - ) Since r is a positive integer, r - is a positive integer. Thus, k + + is divisible b, so the statement is true for n = k +. Therefore, n + is divisible b for all positive integers n. 7. Step : When n =, the left side of the given equation is a. The right side is a ( - r ) _ or a - r, so the equation is true for n =. Step : Assume a + a r + a r + + a r k- = a ( - r k ) _ for some positive integer k. - r Step : a + a r + a r + + a r k- + a r k = a ( - r k ) _ + a - r r k = a ( - r k ) + ( - r) a r k - r = a - a r k + a r k - a r k + - r = a ( - r k + ) - r The last epression is the right side of the equation to be proved, where n = k +. Thus, the equation is true for n = k +. Therefore, a + a r + a r + + a r n- = a ( - r n ) _ for all positive integers n. 9. Sample - r answer: n -. An analog can be made between mathematical induction and a ladder with the positive integers on the steps. Showing that the statement is true for n = (Step ) corresponds to stepping on the first step. Assuming that the statement is true for some positive integer k and showing that it is true for k + (Steps and ) corresponds to knowing that ou can climb from one step to the net.. H. a 7-7 a b + a b - a b + a b - a b + 7ab - b 7 7., 0, 9. h Pages 7 7 Chapter Stud Guide and Review. partial sum. sigma notation. Binomial Theorem 7. arithmetic series ,,.,, 0, , 9. $79.7. _. _ _ 9. -,,,,.,,. $,0. r + 0 r s + 70 r s + 90 r s + rs + s 7. -,07, Step : When n =, the left side of the given equation is. The right side is - or, so the equation is true for n =. Step : Assume k = k - for some positive integer k. Step : k + (k + ) - = k - + (k + ) - = k - + k = k - = k + - The last epression is the right side of the equation to be proved, where n = k +. Thus, the equation is true for n = k +. Therefore, n - = n for all positive integers n.. Step : - = which is divisible b. The statement holds true for n =. Step : Assume that k - is divisible b for some positive integer k. This means that k - = r for some whole number r. Step : k - = r k = r + ( k ) = (r + ) k+ = r + k+ - = r + k+ - = (r + ) Since r is a whole number, r + is a whole number. Thus, k+ - is divisible b, so the statement is true for n = k +. Therefore, n - is divisible b for all positive integers n.. n =. n = Chapter Probabilit and Statistics Page Chapter Get Read. _. _. _ 7. _ 9. a + a b + ab + b. m - m n + 0m n - 0m n + mn - n. (h + t) = h + h t + 0h t + 0h t + ht + t Pages 7 9 Lesson -. independent independent. dependent ,. 7. Sample answer: buing a shirt that comes in sizes and colors A. Step : When n =, the left side of the given [() + ] equation is. The right side is _ or, so the equation is true for n =. k(k + ) Step : Assume (k +) = _ for some positive integer k. Step : (k +) + [k( + ) + ] + [(k... k(k + ) = _ + [(k + ) + ] k(k + ) + [(k + ) + ] = = k + k + k + + = k + k + (k + )(k + ) = (k + )[(k + ) + ] = Selected Answers Selected Answers R

169 Selected Answers The last epression is the right side of the equation to be proved, where n = k +. Thus, the equation is true for n = k +. Therefore, n(n + ) (n + ) = _ for all positive integers n.. 0a b 7. {-, } 9. {-, _. (, ) } Pages 9 9 Lesson permutation; permutation; ,70. permutation; 00. permutation; 0. combination; 7. combination; 9.,0. 7, ,09, 7. Sample answer: There are si people in a contest. How man was can the first, second, and third prizes be awarded? 9. Sometimes; the statement is true when r =.. Permutations and combinations can be used to find the number of different lineups. There are 9! different 9-person lineups available: 9 choices for the first plaer, choices for the second plaer, 7 for the third plaer, and so on. So, there are,0 different lineups. There are C(, 9) was to choose 9 plaers from : C(, 9) = _! or,0.. J 7!9! Sample answer: n = 9. > das. Pages Lesson -. _. _. _ 7. _ _ 7. _ 9 _ 0 ( ) _ + _( - ) =. _ 9 9. _. 9. _. _. _ _ 0 7. theoretical; _ 7 _. _ 0 7. _. _. theoretical; 9. C. permutation; 0. combination;. direct variation 7. _ 9. _. 9 _ 0 Pages Lesson -. _. _. _ 7. _ _. _ _ 7 9. _ 0. dependent; _ 7.. _ 9. dependent; _ or about 0 7. _ 9. _ 9. _ or about _ or about independent; _ or about 0. 9 _, or about 0.009,00,000. independent; _ or about Second Spin blue ellow red blue BB BY BR 9 YB 9 First Spin ellow 9 YY 9 red 9 YR 9 RB RY RR 9. _. 9_. _ 7 7. no 9. Sample,0,0 0, answer: putting on our socks, and then our shoes.. D. _ 7. 0 was 9. 0., -. _. _ 7. _ Pages 7 7 Lesson -. _. _. _ 7. mutuall eclusive; _ 9. _. _. _. _ 7. _ 0 9. _ inclusive; _. _ 7. _ _ mutuall eclusive; _ 9. _. 7_. 9 _. _. _ 0. Sample answer: mutuall eclusive events: tossing a coin and rolling a die; inclusive events: drawing a 7 or a diamond from a standard deck of cards. Probabilit can be used to estimate the percents of what teens do online. The events are inclusive because some people send/read and bu things online. Also, ou know that the events are inclusive because the sum of the percents is not 00%. 7. G 9. _. _.. ( + ) ( - )( + ) 7. direct variation 9..,, no mode, 7..7,, 0 and, 0..9,.9, no mode,.7 Pages 70 7 Lesson -. $79.0, $0.7. 0,..., ,. 9..,.. 9.,.9..,.. The median seems to represent the center of the data. 7. Mode; it is the least epensive price. 9. Mean; it is highest..,90,0;,0,000;,000,000. Mean; it is highest.. % Different scales are used on the vertical aes.. Sample answer: The second graph might be shown b the compan owner to a prospective buer of the compan. It looks like there is a dramatic rise in sales.. Sample answer: The variance of the set {0, } is 0., and the standard deviation is The first histogram is lower in the middle and higher on the ends, so it represents data that are more spread out. Since set B has the greater standard R Selected Answers

170 deviation, set B corresponds to the first histogram and set A corresponds to the second. 9. The statistic(s) that best represent a set of test scores depends on the distribution of the particular set of scores. Answers should include the following. The mean, median, and mode of the data set are 7.9, 7., 9. The mode is not representative at all because it is the highest score. The median is more representative than the mean because it is influenced less than the mean b the two ver low scores of and 9. Each measure is increased b.. J. mutuall eclusive; _ _ 7. _ Pages 7 7 Lesson -7. normall distributed..%., positivel skewed. Negativel skewed; the histogram is high at the right and has a tail to the left % 7. 0% 9.. %. %.. 7. Sample answer: the use of cassettes since CDs were introduced 9. If a large enough group of athletes is studied, some of the characteristics ma be normall distributed; others ma have skewed distributions. Since the histogram goes up and down several times, the data ma not be normall distributed. This ma be due to plaers who pla certain positions tending to be of similar large sizes while plaers who pla the other positions tend to be of similar smaller sizes. 0 Frequenc Height (in.). J..,.. _ Pages 7 7 Lesson App Never; The probabilit that will be greater than the mean is alwas.% for eponential distributions. 7. The poll will give ou a percent of people supporting the science wing addition. The percent of supporters represents the probabilit of success. You can use the formula for the epected number of success in a binomial distribution with the total number of students in the school to predict the number that will support the science wing addition. 9. G. 97.%. _ c d Pages Lesson -9. _. 7_. _ 7. about _. _,. _. _ 7. _ 9. _ 09. _,. _. _ 0 7. _ 9 9. _ 0. about _, _, _, _, _, _, _. normal distribution 7a. Each trial has more than two possible outcomes. 7b. The number of trials is not fied. 7c. The trials are not independent. 9. Getting a right answer and a wrong answer are the outcomes of a binomial eperiment. The probabilit is far greater that guessing will result in a low grade than in a high grade. Use (r + w) = r + r w + 0r w + 0r w + rw + w and the chart on page 79 to determine the probabilities of each combination of right and wrong. P( right): r = ( _ ) = _ or about 0.09%; 0 P( right, wrong): _ or about.%; 0 P( right, wrong): 0r w = 0 ( _ ) _ ( ) = _ or about.%; P( wrong, right): 0r w = 0 ( _ ) _ ( ) = _ or about.%; P( wrong, right): rw = ( ) ( ) = _ 0 or about 0 9.%; P( wrong): w = _ ( ) = _ or about.7%. 0. G. 0. Mean; it is highest Pages 77 7 Lesson -0. Yes; the last digits of social securit numbers are random.. 9%. % Yes; all seniors would have the same chance of being selected.. No; basketball plaers are more likel to be taller than the average high school student, so a sample of basketball plaetrs would not give representative heights for the whole school.. %. % 7. % 9. %. %. or. % 7. The margin of sampling error decreases when the p ( p) size of the sample n increases. As n increases, _ n decreases. 9. A. _. _. 97.% Selected Answers Selected Answers R7

171 Selected Answers Pages 70 7 Chapter Stud Guide and Review. probabilit. dependent events. mutuall eclusive events 7. sample space 9., passwords.. _ 7. independent; _ 7. dependent; _ 9. inclusive; _. mutuall 7 eclusive; _.. 7. % , 7, 7, _, _ 7. about %. _, _, _, _, _, Chapter Trigonometric Functions 9c. sin 0 = _ opp hp sin 0 = _ sine ratio sin 0 = _ Simplif.. about. 9. units. Replace opp with and hp with. Page 77 Chapter Getting Read ft 7. =, = Pages 7 77 Lesson -. sin θ = _ ; cos θ = _ ; tan θ = _ ; csc θ = 7_ 7 7 ; sec θ = 7_ ; cot θ = _. sin θ = _ ; cos θ = _ ; tan θ = _ ; csc θ = _ ; sec θ = _ ; cot θ = _. cos = _ ;. 7. B =, a =, c. 9. a., A 7, B.. m. sin θ = _ ; cos θ = _ 0 ; tan θ = _ 0 0 ; csc θ = _ ; sec θ = _ 0 ; cot θ = _ 0 0. sin θ = _ 7 ; cos θ = _ ; tan θ = _ 7 ; csc θ = _ 7 7 ; sec θ = _ ; cot θ = _ 7 7. cos 0 = _ 7, = 9. tan 7. = _ ; 7.. sin = _.7, 7. A =, a.7, c.. A = 7, a., b. 7. B =, a = 7, b = 7 9. about. ft. sin θ = _ ; cos θ = _ ; tan θ = _ ; csc θ = ; sec θ = _ ; cot θ =. A = 7, b., c.. A, B 7, a. 7. A, B 9, b =, c 0. 9a. sin 0 = _ opp sine ratio hp sin 0 = _ sin 0 = _ 9b. cos 0 = _ adj hp cos 0 = _ cos 0 = _ Replace opp with and hp with. Simplif. cosine ratio Replace adj with and hp with. 7. The sine and cosine ratios of acute angles of right triangles each have the longest measure of the triangle, the hpotenuse, as their denominator. A fraction whose denominator is greater than its numerator is less than. The tangent ratio of an acute angle of a right triangle does not involve the measure of the hpotenuse, opp _. If the measure of the opposite side adj is greater than the measure of the adjacent side, the tangent ratio is greater than. If the measure of the opposite side is less than the measure of the adjacent side, the tangent ratio is less than. 9. C. No; Band members ma be more likel to like the same kinds of music.. _. _ 7. {,, 0,, } 9. 0 qt. m Pages Lesson -... _ π 7. _ 97π h. Sample answer: 0, 00. Sample answer: _ 7π, _ π R Selected Answers

172 . π_. π_ Sample answer: 90, 0. Sample answer: _ π, π_. Sample answer: π_, _ π. about. m _ 9π. _ π _ 0 9 π Sample answer:,. Sample answer: π_, π_. Sample answer: _ π, 7π_. number sin θ = _, tan θ =, csc θ = _, sec θ =, cot θ = _. about. ft. sin θ = _, cos θ = _, tan θ = _, csc θ =, sec θ = _, cot θ = 7. sin θ = _, cos θ = _, tan θ = _, csc θ = _, sec θ = _, cot θ = _ 9. sin θ = 0, cos θ =, tan θ = 0, csc θ = undefined, sec θ =, cot θ = undefined. sin θ = _, cos θ = _, tan θ =, csc θ = _, sec θ =, cot θ = _.. 7. _ 9. _... ; 0 Selected Answers 9a. a + ( b) = a + b = 9b. b + a = a + b = 9c. b + ( a) = a + b =. An angle with a measure of more than 0 gives an indication of motion in a circular path that ended at a point more than halfwa around the circle from where it started. Negative angles conve the same meaning as positive angles, but in an opposite direction. The standard convention is that negative angles represent rotations in a clockwise direction. Rates over 0 per minute indicate that an object is rotating or revolving more than one revolution per minute.. J. A =, a.9, c.9 7. c = 0., A = 0, B = 0 9. about 7.07% 7. combination, 7. [g h]() = +, [h g]() = _ 77. _ _ 0 Pages 7 7 Lesson -. sin θ = _, cos θ = _, tan θ = _ 7 7, csc θ = _ 7, sec θ = 7_, cot θ = _. sin θ = _, cos θ = _, tan θ =, csc θ =, sec θ =, cot θ =. 7. _ 9. ; π_ ; π _ ; ; π_. sin θ = _, cos θ = _, csc θ =, sec θ = _, cot θ =. sin θ = _, cos θ = _, tan θ =, csc θ = _, sec θ = 7. ; or 90 ields the greatest value for sin θ. Selected Answers R9

173 Selected Answers 9. 0., 0, 0., 0, 0., 0, and 0.; or about., 0,., 0,., 0, and.. Sample answer: 00. Answers should include the following. The cosine of an angle is defined as _ r, where is the -coordinate of an point on the terminal ra of the angle and r is the distance from the origin to that point. This means that for angles with terminal sides to the left of the -ais, the cosine is negative, and those with terminal sides to the right of the -ais, the cosine is positive. Therefore the cosine function can be used to model real-world data that oscillate between being positive and negative. If we knew the length of the cable we could find the vertical distance from the top of the tower to the rider. Then if we knew the height of the tower we could subtract from it the vertical distance calculated previousl. This will leave the height of the rider from the ground.. F (, ) Pages Lesson in. C = 0, a.9, c.. B 0, A 0, a two; B, C 0, c.7; B, C, c. 9. one; B 9, C, c.9.. m. 7. ft.. m 7. B = 0, c.0, b. 9. B, C 7, b.. C = 97, a., b.. no. two; B 7, C 7, c.; B 0, C 9, c. 7. one; B = 90, C = 0, c. 9. two; B, C 7, c 9.; B, C, c... and. mi. C 7, B, b ft 7. Gabe; Dulce used the wrong angle. The Law of Sines must first be used to find B. Then m C can be found. nce m C is found, A = _ ba sin C will ield the area of the triangle. 9. If the height of the triangle is not given, but the measure of two sides and their included angle are given, then the formula for the area of a triangle using the sine function should be used. You might use this formula to find the area of a triangular piece of land, since it might be easier to measure two sides and use surveing equipment to measure the included angle than to measure the perpendicular distance from one verte to its opposite side.. F.. 0, 0 7. _ 7π, 7π_ Pages Lesson -. cosines; A 77, B, c.. sines; C 0, B 7, c m 7. sines; A = 0, b., c. 9. cosines; A 7, B 7, C 0. cosines; A 7, B, c.. cosines; A, C 7, b 7.9. no 7. cosines; A 0, B 9, C 9.. cm, 9.0 cm. cosines; A, B 0, C. sines; C = 0, b., c.. cosines; A 07, B, c. 7. about Since the step angle for the carnivore is closer to 0, it appears as though the carnivore made more forward progress with each step than the herbivore did.. a. Use the Law of Cosines to find the measure of one angle. Then use the Law of Sines or the Law of Cosines to find the measure of a second angle. Finall, subtract the sum of these two angles from 0 to find the measure of the third angle. b. Use the Law of Cosines to find the measure of the third side. Then use the Law of Sines or the Law of Cosines to find the measure of a second angle. Finall, subtract the sum of these two angles from 0 to find the measure of the third angle.. Sample answer:. Given the latitude of a point on the surface of Earth, ou can use the radius of the Earth and the orbiting height of a satellite in geosnchronous orbit to create a triangle. This triangle will have two known sides and the measure of the included angle. Find the third side using the Law of Cosines and then use the Law of Sines to determine the angles of the triangle. Subtract 90 degrees from the angle with its verte on Earth s surface to find the angle at which to aim the receiver dish. 7. F 9. sin θ = _, cos θ, tan θ = _, csc θ = _, sec θ = _ = _, cot θ = _. sin θ = -_, cos θ = _ 0, tan θ = _, csc θ = _, sec θ = _ 0, cot θ = _. { > 0.9}. 0, 7. 0, 0 9. _ 9π, π_ Pages 0 0 Lesson -. sin θ = _, cos θ = _. _. s 7. sin θ = _ ; cos θ = _ 9. sin θ = _ ; cos θ = _. sin θ 7 7 = _ ; cos θ = _. _ π. _ s. _ 7. _ ( _, _ ), ( _, _ ), (, 0), ( _, _ ), ( _, _ ). _. _ Sample answer: the motion of the minute hand on a clock; 0 s. sine: D = {all reals}, R = { }; cosine: D = {all reals}, R = { }. B. cosines: c., B 9, A in 9. does not eist.. 0 Pages 09 Lesson π does not eist south of west does not eist No; with 9 R90 Selected Answers

174 this point on the terminal side of the throwing angle θ, the measure of θ is found b solving the equation tan θ = 7_. Thus θ = 7_ tan- or about., which is greater than the 0 requirement. 9. Sin + Cos = π_ for all values of. Sample answer: Cos = _ ; _ Cos =. 0. Trigonometr is used to determine proper banking angles. Answers should include the following. Knowing the velocit of the cars to be traveling on a road and the radius of the curve to be built, then the banking angle can be determined. First find the ratio of the square of the velocit to the product of the acceleration due to gravit and the radius of the curve. Then determine the angle that had this ratio as its tangent. This will be the banking angle for the turn. If the speed limit were increased and the banking angle remained the same, then in order to maintain a safe road the curvature would have to be decreased. That is, the radius of the curve would also have to increase, which would make the road less curved. 7. J 9.. sines; B 9, C, c. or B, C 9, c.9., 9., 09 Pages Lesson - ; period 0 or π. amplitude: _. amplitude: _ ; period 0 or π. amplitude: does not eist; period: 0 or π Selected Answers Pages Chapter Stud Guide and Review. false; coterminal.. true. true 7. A, B, b. 9. A =, a., b.. A =, b 0., c ft. 7π_ , 00. π_ ; _ π. sin θ = _ 9 9, cos θ = _ 9, tan θ = _ 9, csc θ = _ 9, sec θ = _ 9, cot θ = _. 7. about. ft 9. two; B, C 7, c.; B 7, C, c.0. no. 07 mph. sines; C = 0, a., c. 7. sines; B, C 9, c 0.; B ; C, c.7 9. about. ft. _. _ Chapter Trigonometric Graphs and Identities Page Chapter Get Read. _. 0. _ 7. _ 9. _.. 0 ft. ( ) 7. ( + ) ( ) 9.,. 0,., 7. amplitude: ; period: 0 or π_ 9. amplitude: _ ; period: 70 or π Selected Answers R9

175 Selected Answers. 0; June. amplitude ; period: 0 or π. amplitude: does not eist; period: or π_. amplitude: does not eist; period: 0 or π. amplitude: does not eist; period: 0 or π 7. amplitude: does not eist; period: 0 or π. Sample answer: The amplitudes are the same. As the frequenc increases, the period decreases. 7. amplitude: ; period: 70 or π 9. amplitude: ; period: 0 or π 9. amplitude: does not eist; period: 90 or π_ R9 Selected Answers

176 . amplitude: _ 9 ; period: 00 or _ 0π. = 7_ cos θ cos. Vertical asmptotes located at π_, π_, π_, 7π_, etc. and π_, π_, π_, 7π_, etc. 9. Sample answer: = cos (θ). Jamile; the amplitude is, and the period is π.. Sample answer: Tides displa periodic behavior. This means that their pattern repeats at regular intervals. Tides rise and fall in a periodic manner, similar to the sine function.. G _. _.,, 7, 9,. Selected Answers 7. Pages Lesson -. ; π; π_ Selected Answers R9

177 Selected Answers. ; 0 ;. ; no amplitude; π_ ; π_. _ ; = _ ; ; 0. ; ; s. 7. no amplitude; 0 ; 0 7. ; = ; no amplitude; 0 9. ; π; π_ 9. 0; ; 0 ; 0 R9 Selected Answers

178 . ; 0 ; 7 9. ; ; 0 ; 0 Selected Answers. ; = ; no amplitude; ; does not eist; 70 ; 90. _ ; = _ ; no amplitude; 0. ; does not eist; 0 ;. 7..; =.; ; 0. ; does not eist; π; π_ Selected Answers R9

179 Selected Answers 7. 00;. r 9. The graphs are identical.. translation π_ units left and units up. c. Sample answer: = sin (θ + ) 7. Sample answer: You can use changes in amplitude and period along with vertical and horizontal shifts to show an animal population s starting point and displa changes to that population over a period of time. The equation shows a rabbit population that begins at 00, increases to a maimum of 0, then decreases to a minimum of 90 over a period of ears. 9. H. amplitude: ; period: 70 or π a (a )(a ) ( )( + ) 7. _ 9. _ 7.. Pages 9 Lesson -. _. _. 7. sec θ 9. sin θ = cos θ _ v gr. _.. _ 7. _ 9.. sin θ.. tan θ 7. P = I Rsin πft 9. _. _ 7. cot θ. 7. about m/s 7 9. E = _ I cos θ. Sample answer: The sine function R is negative in the third and fourth quadrants. Therefore, the terminal side of the angle must lie in one of those two quadrants.. _ 0π. Sample answer: You can use equations to find the height and the horizontal distance of a baseball after it has been hit. The equations involve using the initial angle the ball makes with the ground with the sine function. Both equations are quadratic in nature with a leading negative coefficient. Thus, both are inverted parabolas which model the path of a baseball. 7. F 9. ; = ; no amplitude; 0. amplitude: ; period: 0 or π_ Subtraction (=) 9. Substitution (=) R9 Selected Answers

180 Pages Lesson -. tan θ (cot θ + tan θ) sec θ + tan θ sec θ sec θ = sec θ cos. _ θ sin θ + sin θ _ sin θ sin θ + sin θ ( sin θ)( + sin θ) + sin θ sin θ + sin θ = + sin θ. _ sin θ sec θ tan θ + cot θ _ sin θ sec θ sin θ _ cos θ + cos θ sin θ _ sin θ sec θ sin θ + cos θ sin θ cos θ _ sin θ sec θ sin θ cos θ sin θ + cos θ _ sin θ sec θ _ sin θ cos θ _ sin θ sec θ = _ sin θ sec θ 7. D 9. cot θ (cot θ + tan θ ) csc θ cot θ + cot θ tan θ csc θ cot θ + _ sin θ cos θ _ cos θ sin θ csc θ cot θ + csc θ csc θ = csc θ. sin θ sec θ cot θ sin θ _ cos θ _ cos θ sin θ. = _ cos θ tan θ cot θ sin θ cos θ ( cos θ) cos θ tan θ cot θ sin θ cos θ sin θ cos θ tan θ cot θ sin θ cos θ _ sin θ sin θ cos θ _ cos θ tan θ cot θ sin θ cos θ _ sin θ cos θ _ cos θ tan θ cot θ sin θ tan θ cot θ = tan θ cot θ. sin θ + cos θ _ + tan θ sec θ _ sin θ cos θ sin θ + cos θ cos θ sin θ + cos θ cos θ sin θ + cos θ cos θ sin θ + cos θ sin θ + cos θ cos θ cos θ sin θ + cos θ = sin θ + cos θ. 9.7 m. _ sin θ cos θ + _ cos θ csc θ sin θ _ sin θ sin θ _ sin θ cos θ + _ cos θ cos θ _ cos θ csc θ sin θ sin θ sin θ ( cos θ) + cos θ + cos θ csc θ sin θ ( cos θ) sin θ + cos θ + cos θ csc θ sin θ ( cos θ) cos θ sin θ ( cos θ) csc θ ( cos θ) sin θ ( cos θ) csc θ _ sin θ csc θ _ sin θ cos θ + cos θ _ sin θ cos θ _ + cos θ + cos θ + cos θ sin θ ( + cos θ) + cos θ - cos θ sin θ ( + cos θ) + cos θ sin θ sin θ + cos θ cos θ + cos θ = + cos θ _ + tan θ + cot θ _ sin θ cos θ _ + _ sin θ cos θ + _ cos θ sin θ sin θ + cos θ cos θ sin θ + cos θ sin θ _ sin θ cos θ _ sin θ cos θ sin θ sin θ + cos θ _ sin θ cos θ csc θ = csc θ Selected Answers _ sin θ cos θ = _ sin θ cos θ Selected Answers R97

181 Selected Answers. + _ cos θ _ tan θ sec θ + _ cos θ _ tan θ sec θ _ sec θ + sec θ + + _ cos θ tan θ (sec θ + ) sec θ + _ cos θ tan θ (sec θ + ) tan θ + _ cos θ sec θ + + _ cos θ = + _ cos θ 7. cos θ sin θ cos θ sin θ 9. (cos θ sin θ)(cos θ + sin θ) cos θ sin θ (cos θ sin θ) cos θ sin θ cos θ sin θ = cos θ sin θ _ cos θ + sin θ + _ cos θ sin θ sec θ _ cos θ + sin θ _ sin θ sin θ + _ cos θ sin θ _ + sin θ + sin θ sec θ cos θ ( sin θ) + cos θ ( + sin θ) sec θ ( + sin θ)( sin θ) cos θ sin θ cos θ + cos θ + sin θ cos θ sin θ. [ 0, 0] scl: 90 b [, ] scl: ; ma be [0, 0] scl: 90 b [, ] scl:. [ 0, 0] scl: 90 b [, ] scl: ; ma be sec θ _ cos θ cos θ sec θ _ cos θ sec θ sec θ = sec θ. [ 0, 0] scl: 90 b [, ] scl: ; is not [0, 0] scl: 90 b [, ] scl: 7. sin θ cos θ = sin θ does not belong with the others. The other equations are identities, but sin θ cos θ = sin θ is not. sin θ cos θ = sin θ - would be an identit. 9. Sample answer: The epressions have not et been shown to be equal, so ou could not use the properties of equalit on them. Graphing two epressions could result in identical graphs for a set interval, that are different elsewhere.. G. _. _ 7 7. ; 0 ; 9. _ 0 7.,.. _ Pages Lesson -. _ +. _. _ 9. sin ( θ + π _ ) cos θ 7. + sin θ cos _ π + cos θ sin _ π cos θ sin θ 0 + cos θ cos θ cos θ = cos θ. _. _ -. _ - 7. _ 9. _. _. 0. E. 0.7 E _ 7. _ [0, 0] scl: 90 b [, ] scl: 7. sin (70 θ) sin 70 cos θ cos 70 cos θ 0 = cos θ 9. cos (90 θ) cos 90 cos θ + sin 90 sin θ 0 cos θ + sin θ = sin θ R9 Selected Answers

182 . sin (θ + π_ ) cos θ sin θ cos π_ + cos θ sin π_ cos θ sin θ 0 + cos θ ( ) cos θ 0 + ( cos θ) cos θ cos θ = cos θ. cos (π + θ) cos θ cos π cos θ [sin π sin θ] cos θ cos θ [0 sin θ] cos θ cos θ 0 cos θ cos θ = cos θ. sin (α β) tan (α β) _ cos (α β) sin α cos β cos α sin β cos α cos β + sin α sin β _ sin α cos β -_ cos α sin β cos α cos β cos α cos β cos α cos β + _ sin α sin β cos α cos β cos α cos β tan α tan β = + tan α tan β. A 7. cot θ + sec θ cos θ + sin θ sin θ cos θ cos cot θ + sec θ _ θ sin θ cos θ + _ sin θ sin θ cos θ cot θ + sec θ _ cos θ sin θ + _ cos θ cot θ + sec θ = cot θ + sec θ Selected Answers 7. sin (0 + θ) + sin (0 θ) sin 0 cos θ + cos 0 sin θ + sin 0 cos θ cos 0 sin θ _ cos θ + _ sin θ + _ cos θ _ sin θ = cos θ 9. sin ( α + β ) sin ( α β ) sin α sin β (sin α cos β + cos α sin β )(sin α cos β cos α sin β ) sin α cos β cos α sin β sin α ( sin β ) ( sin α ) sin β sin α sin α sin β sin β + sin α sin β = sin α sin β. Sample answer: α = _ π ; β = _ π sin (α + β). tan (α + β) _ cos (α + β) sin α cos β + cos α sin β cos α cos β - sin α sin β sin α cos β cos α sin β + cos α cos β cos α cos β cos α cos β _ sin α sin β cos α cos β cos α cos β tan α + tan β = tan α tan β 9. sin θ (sin θ + csc θ) cos θ sin θ + cos θ cos θ + cos θ cos θ + = cos θ.. sec θ. about mi 7. ± _ 9. ± _ Pages 7 9 Lesson -. _, - 7_, _, _. _, _, _ -,_ +. -_ cos + sin cos cos + sin =. -_, - _, _ 0, - _. _, 7_, _ 0 0, - _ _, - 7_, _ 0, _ 7. _ - 9. _ -. -_ -. cos _ + cos (± _ + cos ) + cos _ ( + cos ) + cos + cos = + cos. sin _ ( - cos ) sin _ [- ( - sin )] sin _ ( sin ) sin = sin Selected Answers R99

183 Selected Answers 7. sin cos - cos sin tan _ - cos sin cos tan _ sin sin cos tan _ sin cos tan tan = tan 9. _ tan θ. _ 0 9,_ 9 9, _, - _. _, 7_, _ +, -_ -. -_, 7_, + 0, ± 7. _ - cos L + cos L ± _ - cos L + cos L 9. Sample answer: If is in the third quadrant, then _ is between 90º and. Use the half-angle formula for cosine knowing that the value is negative.. Sample answer: ; cos ( ) = cos 90 or 0, cos = _ or. D. _ + 7. _ 9. _ +. cot θ sin θ cos θ csc θ sin θ sin θ csc θ cos θ _ cot θ sin sin θ θ sin θ sin θ _ sin θ cot θ sin θ cot θ sin θ cot θ sin θ = cot θ sin θ. 0 or 0. (a ) 7(a ) + 7. (d ) + (d ) n 7n + f.,. _, 7. 0, _ Pages Lesson -7. 0, 0, 0, 00. π_, π_, π_, π_. 0 + _ kπ k 0, 0 + k π_ + kπ, _ π + kπ or 0 + k 0, 0 + k , 00. 0, 0, 0, 0 7. π + kπ, π_ + kπ, π_ + kπ kπ. 0 + k k 0, 0 + k 0. 7π_ + kπ, _ π + kπ or 0 + k 0, 0 + k 0 7. π_ + kπ, π_ + kπ, π_ + kπ or 90 + k 0, 0 + k 0, 0 + k π_. π_, π_, π_, π_. 0 + kπ, π_ + kπ, π_ + kπ 7. π_ + k π, 7π_ + k π, π_ + k π, π_ + k π k 0, 0 + k k 0, 0 + k 0. π_ + kπ or 90 + k 70. π_ + k π, π_ + k π, π_ + k π, π_ + k π, or 0 + k 0, 0 + k 0, + k 0, + k 0 7. about 9. Sample answer: If sec θ = 0 then _ cos θ = 0. Since no value of θ makes _ cos θ = 0, there are no solutions.. Sample answer: The function is periodic with two solutions in each of its infinite number of periods.. D. _, 7_, _ 0 0, _ 0 7. _ 0, 7_, _, _ 9. _. _ Pages 7 70 Chapter Stud Guide and Review. phase shift. vertical shift. double-angle formula 7. trigonometric identit 9. amplitude. amplitude: ; period: 0 or π. amplitude: does not eist; period: 0 or π. amplitude: does not eist; period: or _ π 7., _, 0, , does not eist, π π _ 0 sin [( 0 )] 0 sec [ ( )] R00 Selected Answers

184 . p =,000 +,000 sin ( π _ t ). - _. cot θ 7. csc θ sin θ 9. _ tan θ + _ cos θ cos θ + sin θ cot θ _ sin θ + _ cos θ cos θ + sin θ _ cos θ sin θ _ sin θ _ cos θ + cos θ _ sin θ cos θ + sin θ sin θ cos θ cos θ + sin θ = cos θ + sin θ. cot θ sec θ + cot θ _ cos θ sin θ _ cos θ + cot θ _ sin θ + cot θ csc θ + cot θ + cot θ = + cot θ. I m cos θ = I m ( - _ csc θ) I m cos θ = I m ( - sin θ) I m cos θ = I m cos θ. _ - 7. _ - 9. _ - -. sin(0 - θ) = cos (0 + θ) sin 0 cos θ - cos 0 sin θ cos 0 cos θ - sin 0 sin θ _ cos θ - _ sin θ _ cos θ - _ sin θ sin (θ + π) -sin θ sin θ cos π + cos θ sin π -sin θ (sin θ)(-) + (cos θ)(0) -sin θ -sin θ = -sin θ. -cos θ cos(π + θ) -cos θ cos π cos θ - sin π sin θ -cos θ - cos θ - 0 sin θ -cos θ = -cos θ. _ 0 9,_ 9 9, _, _ _ 0 9,_ 9 9, _, -_ 9. 0 Selected Answers Selected Answers R0

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186 Photo Credits Cover: (b) Digital Vision/PunchStock; (t) Created b Michael Trott with Mathematica. From Graphica, Copright 999 Wolfram Media, Inc.; v David Dennison; viii i Bran Peterson/Gett Images; i Gen Umekita/Gett Images; ii iii Donovan Reese/Gett Images; iv v Ramond Gehman/ CRBIS; vi vii Jim Craigmle/Masterfile; viii i Kaz Chiba/Gett Images; i John P. Kell/Gett Images. Bran Peterson/Gett Images; CRBIS; Mark Harmel/Gett Images; Am C. Etra/PhotoEdit; Archivo Iconografico, S.A./CRBIS; And Lons/Gett Images; Michael Newman/ PhotoEdit; Robert Llewelln/Imagestate; 7 Robert Yager/Gett Images; Andrew Ward/Life File/Gett Images; Rudi Von Briel/PhotoEdit; Jack Dkinga/ Gett Images; William J. 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Souders/CRBIS; Bettmann/CRBIS; 70 Tui De Ro/Bruce Coleman, Inc.; 7 Brent Smith/Reuters/CRBIS; 79 Jean-Yves Ruszniewski/ CRBIS; Dennis Hallinan/Alam Images; 90 Michael Denora/Gett Images; 99 AGUILAR/ Reuters/CRBIS; 0 Reuters/CRBIS; 0 CRBIS; 0 Michael Keller/CRBIS; Volker Steger/Science Photo Librar/Photo Researchers; SuperStock/ Alam Images; 7 Kenneth Eward/Photo Researchers; Rafael Marcia/Photo Researchers; Mark Gibson/Inde Stock Imager; 0 Steve Dunwell/ Gett Images; Aidan Rourke; 0 Yagi Studio/ SuperStock; 7 Matthew McVa/Stock Boston; Kaluzn/Thatcher/Gett Images; Duomo/ CRBIS; 7 CRBIS; 7 Dimitri Iundt/TempSport/ CRBIS; Bruce Hands/Gett Images; 9 NASA; 9 Clive Brunskill/Gett Images; 97 Todd Rosenberg/Allsport/Gett Images; 99 Aaron Haupt; 0 Gu Grenier/Masterfile; AFP/CRBIS; K.G.Murti/Visuals Unlimited; 9 Larr Dale Gordon/Gett Images; Brownie Harris/CRBIS; 7 Joan Marcus; VCG/Gett Images; Michael Newman/PhotoEdit; Gregg Mancuso/Stock Boston; Boden/Ledingham/Masterfile; National Librar of Medicine/Mark Marten/Photo Researchers; 7 VCG/Gett Images; Cedar Point; Ed Bock/CRBIS; 9 David Stoecklein/CRBIS; 9 Gett Images; 97 Ramond Gehman/CRBIS; 9 Frank Rossotto/Stocktreck/CRBIS; 0 Gianni Dagli rti/crbis; 7 Andrea Comas/Reuters/ CRBIS; Lori Adamski Peek/Gett Images; 9 CRBIS; 0 NASA; Edward A. rnelas/ Reuters/CRBIS; Pascal Rondeau/Allsport/Gett Images; 7 JPL/TSAD/Tom Stack & Associates; 9 Geoff Butler; 70 Lnn M. Stone/Bruce Coleman, Inc.; 77 Terr Smith Images/Alam Images; 79 Hugh Threlfall/Alam Images; Yoshiko Kusano/AP/ Wide World Photos; Keith Wood/Gett Images; 9 Grant Smith/CRBIS; 0 Pierre Arsenault/ Masterfile; 0 Jeff Zaruba/CRBIS; (l)mark Jones/Minden Pictures; (r)jane Burton/Bruce Coleman, Inc.; David Weintraub/Photo Researchers; Phil Cantor/SuperStock; Bettmann/CRBIS; Richard Cummins/CRBIS; Jim Craigmle/ Masterfile; Masterfile; Richard T. Nowitz/ Photo Researchers; 7 Gett Images; 9 Karl Weatherl/CRBIS; 0 Paul Conklin/PhotoEdit; 7 (t)james Roone; (b)hisham F. Ibrahim/Gett Images; 7 SuperStock; 7 PunchStock; 7 Long Photograph/Gett Images; 0 Matt Meadows; Ra F. Hillstrom, Jr.; 7 James P. Blair/CRBIS; 9 9 CRBIS; 00 Roalt-Free/CRBIS; 07 (l)space Telescope Science Institute/NASA/ Science Photo Librar/Photo Researchers; (r)michael Newman/PhotoEdit; 9 View Stock/Alam Images; 0 Kaz Chiba/Gett Images; SuperStock; Slvan H. Witter/Visuals Unlimited; 9 Allen Matheson/photohome.com; 0 Michelle Bridwell/ PhotoEdit; NASA; 0 Bill Horseman/Stock Boston; David Kell Crow/PhotoEdit; 7 Hulton- Deutsch Collection/CRBIS; 0 In the Bleachers Steve Moore. Reprinted with permission of Universal Press Sndicate. All rights reserved.; Stock Montage/Gett Images; 9 Dr. Dennis Drenner/Gett Images; David Young-Wolff/PhotoEdit; Science Photo Librar/Photo Researchers; Ted S. Warren/ Associated Press; D.F. Harris; (t)mitch Kezar/ Gett Images; (b)age fotostock; 90 Mark C. Burnett/ Photo Researchers; 9 Sri Maiava Rusden/Pacific Stock; 9 Michal Venera/Gett Images; 97 CRBIS; 70 Food & Drug Administration/Science Photo Librar/Photo Researchers; 70 Duomo/CRBIS; 707 Gett Images; 70 Ian McKinnell/Gett Images; 7 SuperStock; 7 Marc Serota/Reuters/CRBIS; 77 CDC/PHIL/CRBIS; 7 Ton Sweet/Gett Images; 7 Chris Meara/AP/Wide World Photos; 7 Steve Chenn/CRBIS; 70 7 Aaron Haupt; 7 7 Ed and Chris Kumler; 7 Bill Ross/CRBIS; 7 Gett Images; 7 John P. 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187 Inde Inde A Absolute value equations,, Absolute value functions, 9 00, 0, 7, 7 77, 9 graphs of, 9 00, 0 Absolute value inequalities, 9,, 0 0 Absolute values, 7, 9, 0, 7, 0 equations,, epressions, 7 functions, 7, 7 77, 9 inequalities, 9, Addition Associative Propert of,, 7 Commutative Propert of,, 7 of comple numbers,,, 0 of fractions,, of functions,,, 0 of matrices, 9 70, 7 7,, of monomials, of polnomials,, 7, 0 of probabilities, 70 7, 77, 7, 77 of radicals, 0, of rational epressions, Addition Propert of Equalit, 9, Addition Propert of Inequalit,, 9 Additive identit matrices,, 7 Additive Identit Properties,, 7 Agnesi, Maria Gaetana, Algebra Labs Adding Comple Numbers, Adding Radicals, 0 Arithmetic Sequences, Completing the Square, 70 Distributive Propert, Fractals, Head versus Height, Inverses of Functions, 9 Investigating Ellipses, 0 Investigating Regular Polgons Using Trigonometr, 77 Locating Foci, Multipling Binomials, Parabolas, 9 Simulations, 7 Special Sequences, 9 0 Testing Hpotheses, 70 Algebraic epressions, 0,, 9 0 absolute value, 7 containing powers, 7, 7, 7 7 equivalent, 0,, 7, 0 rational, 9,, 9 90 simplifing,, 0, 7, 0, 9 verbal, 9 Algorithms, Alternate interior angles, 7 Alternative hpotheses, 70 Amortizations, 7 Amplitude, 7, 0, 7 Angles, 7 77, 77 7, alternate interior, 7 central, 77 complementar, 7 7, 79 congruent, 70 7 coterminal, 77 77, 0 degrees of, 7 77, of depression, 7 7 double-angle formulas,, 9,, 7, 70 of elevation, 7 7 half-angle formulas,, 7 of inclination, 9 initial sides of, 7, measures of, 7 77, quadrantal, 777 radians of, 79 77, reference, , 7 7, of rotation, 7 in standard position, 7 79, , 77, 7, , sum and difference formulas,, 7, 70 supplementar, 7 terminal sides of, 7 79, 77, 77 7, ,,, Angular velocit, 7, 77 Apothem, 77 Applications accounting, 9 acidit, activities, advertising, 07, 7 aeronautics, 79 aerospace, 9, 00, 0, 77, agriculture, 0, 97, 99, 9 airplanes, altitude, 0 amusement, amusement parks, 7,, 0 animals, 7, 70, 90 anthropolog, arcade games, 0 archaeolog, 99 archer, 9 architecture,, 77,,, 7, 09 area codes, art, 7,, 0, 99, 9 astronom, 7,,, 0, 9, 70,, 7, 9, 0,, 77, 9, 9 atmosphere, 9 audio book downloads, auto maintenance, 9 auto racing, automobile maintenance, automobiles, 7, 7 automotive, 7 average speed, 0 aviation, 00,7, 797,, 7, 9 bab-sitting, 9 bacteria, 7 baking,,, ballooning, 07, 79 banking,,, 7,, baseball,,, 9, 0, 7, 9, 0, 07, 70, 7, 7, 79,, 9, 90 basketball,, 7,, 9, 0,, 0,,,, 7 biccling, 9,, billiards, biolog,,, 0, 0, 70, 7, 90, 0, 9,, 0,,, 9 boating, 0, 0, 7 books, 7 bowling, bridge construction, 7 bridges,, 7, 7 building design, buildings, 7 bulbs, 0 R0 Inde

188 business,,, 9, 0,,, 7,, 9, 9, 07, 99, 9,, 9, 0, 0,, 7, cable TV, caffeine, cameras, 7 car epenses, car rental, 7 car sales, card collecting, card games, 70 carousels, 7 cars, 7, 77 cartograph, 9 catering, cell phones, 0 charit, chemistr, 7,,, 7,, 90, 9,,, child care, child development, chores, 707 cit planning, civil engineering, 79 clocks, clothing, clubs, 9 coffee, 0 coins, 7,, 7, 7 college, 0 comic books, commission, 70 communication, 7,,,, 9 communit service, computers, 0,, concerts, construction,,, 7,,, 9,, 9, 90, 9 cooking, 9 crafts, 97, 99 crptograph,,, ccling, decoration, deliveries, deliver, 7 design,, 7, 79 digital photos, 0 dining, 07 dining out, dinosaurs, 7, 797 distance, 9 diving, 7, 9 drawbridge, 0 driving, 7, 77, 90 DVDs, 70 earthquakes,,, 9, 7, 9 ecolog,, e-commerce, 9 economics,,, 9, 9,, 7 education, 0, 7, 70, 7, 97, 9, 9, 9, 97 election prediction, 7 elections, 0, 707, 70 electricit, 9,,,, 7, 0,,,, 9 electronics,, 0 , emergenc medicine, 79 emploment,, 9, 97, 9 energ,,, 0, 7, 9 engineering, 7,, 0 entertainment, 7, 9, 7,,, 77 entrance tests, 70 eercise, 0, 9 etreme sports, famil, farming, Ferris wheel, 0, figure skating, 90 finance, 90, 0,, 9 financial planning, 79 firefighting, 00 fireworks, 9 fish,,, fishing, 70 flagpoles, floor plan, flooring, flwheels, food, 9, 7, 77, 7 food service, football, 7,, 97, 0, 7, 7 footprints, 9 forestr, 7,, 79 fountains, 90, 0 frames, 0 framing, 7, freedoms, 70 fund-raising,,,, 00 furniture, games,,,, 7, 9 gardening, 0,, 97 gardens, gas mileage, 0 genealog, 7 genetics,, geograph, 0, 9,, 00,, geolog,, 7, 7 glaciers, 7 gold production, 09 golf, 7,, government,, 9, 9 gravit,, 70 guitar, 0 gmnastics, 9 health,, 9, 0,,, 77,, 7,, 7, 7, 0,, 77, 7,,, 9, 97, 9, 97 health insurance, 09 highwa safet,, hiking, 0 histor,, hocke, 9 home decorating, 77 home improvement,, home ownership, 9 home securit, hot-air balloons, 7 hotels, housing, 7 hurricanes, income, insurance, 00 interest, 9 interior design, Internet,, 7 intramurals, inventor, investments,, 0 job hunting, jobs, 7, kennel, 7 kites, 77 ladder, 77 landscaping, 0, 90, 99,,,, 77 languages, 9 laughter, 9 law enforcement, 0, 0,, 9 lawn care, 9 legends, 7 life epectanc, 97, 99 light, 0, lighthouses, 79 lighting, 0 literature, 7 loans, lotteries, 9, 70, 97 magnets, mail,, 77 manufacturing, 0,,,, 7, 7, 77, 9, 9, 9 maps, marathons, 00, 7 market price, marriage,, measurement, 97 mechanics, media, 7 medical research, 9 medicine, 9, 9,, 0, 7 Inde Inde R0

189 Inde meteorolog, 0 milk, miniature golf, 9 mirrors, models, 90 mone, 9,, 0, 0, 0,,,,, 9 mountain climbing, movie screens, 7 movies,, 9 museums, music, 9, 7,, 0, nature,, 7 navigation,, 9, 7, 7, newspapers, noise ordinance, number games, 9 nursing,, 9 nutrition, 00, ocean, oceanograph,, office space, 7 lmpics, 9 optics, 0, 7,, 9 organization, 700 packaging,, painting,, 9 paleontolog,, parking, 99 parks, part-time jobs,,, parties, 7 passwords,, 7 patterns, 7 pendulum, 7 personal finance,, 0 pets, 07,, 77 photograph, 7,,, 79, 9, 00, 709,0, 9 phsical science, 9 phsicians, 7 phsics, 9,, 0,, 9,, 9, 0,,,,,,,,, 0,,,, 0,,,, 9, 90, 9, 9 phsiolog, 7 pilot training, 0 planets, 90 plumbing, police, pollution, ponds, pool, population,, 00, 0, 0, 7,,,, 7, 9, 97, 9, 9 population growth, 9 pricing, 0 prisms, 70 production, profit, 9, 7, 7 puzzles, 9, 7 qualit control, 7 quarterback ratings, 0 racing, 7 radio, 97, 7, 0, 79 radioactivit, 7 railroads, rainfall, 7 ramps, 0 reading, real estate,, 9, recording, recreation, 9,, 7,, 79 reccling, 9 remodeling, 7, 07 rentals, renting, restaurants, 7 rides, 90 ringtones, 0 robotics, 7 rocketr, 7 rockets, 07 roller coasters, 00 safet, 9, 9 sailing, 7 salaries, 0, 0,, 9 sales,, 77, 9 sandbo, 79 sandwiches, 9 satellite TV, 70 satellites, 07 savings, 7,,, 7, 77 scheduling, 9 school,,, 7, 77,,,, 77, 7, 7, 7, 77,, school clubs, school shopping, science,, science museum, scrapbooks, 7 sculpting, 7 seating, 7 shadows, 0 shipping, 7, 0 shopping,, 0,,,, 9, 0, 7 shopping malls, 7 skateboarding, skiing, 7,, 7 skcoasting, 7 soft drinks, 90 sound,,, space, 7,, space eploration, 7 space science, 9 spam, 0 speed limits,, 97 speed skating, 7 sports,, 7,,,, 00,, 7, 77, 70, 9 sprinklers, 9 stamp collecting, star light, stars, 7 state fairs, 7, 0 states, 7 stocks, storms, 7 structural design, 9 submarines, 9 subs, sundial, 7 surveing, 7, 797,, 0 surves, 0, 7 sweepstakes, 77 swim meet, 79 swimming, 7,, swings, 7 taes, 70, 7 tai ride, 07 teaching,, technolog, 9 telephone rates, 00 telephones, 9, 7 television, temperature, 9, tennis, 0 test grades, theater, 9, 00, 7 tides, time,, 770 tourism, 9 Tower of Pisa, tos, track and field, 0 training, transportation, travel, 7, 7, 7, 0, 9,, 0, 7, 09, 9, 9 trucks, 7 tunnels,, umbrellas, 7 used cars, utilities, 70, 7 vacation das, 7 vacations, vending, 77 veterinar medicine, 0 voting, 9 walking, Washington Monument, 7 water, 0 water pressure, 7 water suppl, 70 water treatment, R0 Inde

190 waves, weather,,,,,,, 90, 9 weightlifting, 7 White House, 7 wind chill, wireless Internet, 0 woodworking,,, 790 work,, 70, 7,,, 9 world cultures, 7, 79 world records, writing, 70 zoolog, Arccosine, 07, Arcs, intercepted, 77 Arcsine, 07 0 Arctangent, 07, 09 0 Area of circles, 9 diagram, 70 surface,, of trapezoids,, 9 of triangles,, 97,, 7 7, 790, 79, 9 Area diagram, 70 Arithmetic means,, Arithmetic sequences, 9, 7 7 common differences,,, 7 Arithmetic series, 9, 7 7 derivation of summation formulas, Associative Propert of Addition,, 7 Associative Propert of Multiplication,,, 0 Asmptotes of eponential functions, 99 of hperbolas, 9, 9 9, of logarithmic functions, of rational functions, 7, 7, 9 of trigonometric functions, Augmented matrices, Aes conjugate, 9, 9 major, 7, 09, minor,, 7 of smmetr, 7,,, 9 9, 0, 7 7, transverse, 9 9, 09 -ais, -ais,, Ais of smmetr, 7,,, 9 9, 0, 7 7, B Bar graphs, Bar notation, Bases of logarithms, 0 natural, of powers, 9 Bell curve, 7 7 Bias, 7 Binar fission, 9 Binomial distribution, 70 7 Binomial epansions,, 7, 7, 7 7 Binomial eperiments, 7 79, 7, 79 Binomial Theorem, 7, 7, 7 in factorial notation, 7, 7 in sigma notation, 7, 7 epanding binomial epressions, 9 Binomials, 7 difference of two cubes,, 9 0, difference of two squares,, 9 0,, 77 epansion of,, 7, 7, 7 7 factoring, 7, 9 0,,,, 90, 77 7 multipling,, 7,, 7 77 sum of two cubes, 9 0, Bivariate data, Boundaries, 0 0, 0, 0 Bounded regions, 0 Bo-and-whisker plots, 9 90 Bole s Law, 9 Break-even points, 7 C Careers archaeologists, 99 atmospheric scientists, chemists, cost analsts, 9 designers, electrical engineers, financial analsts, 90 industrial designers, land surveors, 7 landscape architects, 99 loan officers, meteorologist, 9 paleontologists, phsician, 70 pilot, 00 sound technicians, teachers, travel agents, 9 Cartesian coordinate plane, angles on, 7 79, , origin of,, 7 7, 7 79, 77, 70, quadrants of,, 77 7 unit circle on, 79, ais of,, 7 79, 777, -ais of, Cells, Celsius, 9, Celsius, Anders, 9 Centers of circles, 7 79, of hperbolas, 9 Centimeters, 97 Central angles, 77 Change of Base Formula, 0, Charles law, 9 Circles, 7, 7 79, 9 0, 09, area of, 9 centers of, 7 79, circumference of, 79 equations of, 7 79, 9 0, 09, graphs of, 7, 7 7, 99 0, radii of, 7 79,, 77 sectors of, 77 unit, 79 Circular functions, 00 0 cosine, sine, Circular permutations, 9 Circumference, 79 Coefficient matrices, 7 Coefficients, 7 in binar epansions, leading, linear correlation, 9 Inde Inde R07

191 Inde Column matrices, Combinations, 9 9, 7, 7 7 using to compute probabilities, 9 9, 97 9 Common denominators, least,, 79 0 Common differences,,, 7 Common logarithms, Common ratios,, 7 Commutative Propert of Addition,,, 7 Commutative Propert of Multiplication,, 0, 0, 0 Comparisons of real numbers, 7 Complementar angles, 7 7, 79 Complements, 70 Completing the square, 9 7, 7, 0,, 0, 0,, 70, 7,, 9, to write equations of conic sections, 70, 7,, 9, 9 Comple conjugates,, 0 Comple Conjugates Theorem,, 7 Comple fractions, 7 Comple numbers,, 7, 79, 0,, adding,,, 0 conjugates,, 0,, 7 dividing,, 0 graphing,, multipling, standard form of, subtracting,, Composition of functions, 90, 9, 0, iterations, 0, 7 Compound events, 70 Compound inequalities, 9,, conjunctions, disjunctions, Compound interest, 0,, continuousl, 9, Conditional probabilit, 70 Cones surface area of, volume of, Congruent angles, 7 79 Congruent figures, 7 0 Congruent sides, 7 Conic sections, 7 circles, 7, 7 79, 9 0, 09, ellipses, 7, 0, 9, 9 0, 0 0, 09, hperbolas, 7, 90 0, 09, inequalities, 0 0 parabolas, 7 7, 9 0, 09 sstems of, 0 09, Conjugate aes, 9, 9 Conjugates,, 0, Conjunctions, Consistent equations, Constant functions, 9, 9 00, 7, 7, 9 graphs of, 9, 9 00 Constant matrices, 7 Constant of variation, Constant polnomial, Constant terms, Constants, 7 Constraints, Continuit, 7 Continuous functions, 99, absolute value, 9 00, 0, 7, 7 77, 9 cosine, 0,,, 7 eponential functions, 99 0, 0 0, 09 logarithmic functions, polnomial, 7,, 0 7, 7, 7, 7, 7, 9 quadratic,,, 0 0,, 97, 7 77, 9, 9 sine, 0, 0,, 7 square root, 97 0,, 7, 7, 9 Continuous probabilit distribution, 7 7 bell curve, 7 7 normal distributions, 7 7, 7, 7 skewed distributions, 7 7 Continuous relations, 9 Continuousl compound interest, 9, Convergent series, Coordinate matrices, Coordinate sstem, angles on, 7 79, , origin,, 7 7, 7 79, 77, 70, quadrants of,, 77 7 unit circle on, 79, ais of,, 7 79, 777, -ais, Corollaries,, 9, 7 Correlations negative, no, positive, Corresponding parts, 7 79 Cosecant, 79 7, 7 7, , 779 7,, 7, 9 70 graphs of,, 7, Cosine, 79 7, 7 77, 77 77, 77 7, 79, 79 0, 0 0, 07,,, 7 graphs of, 0,,, 7 law of, 79 79, Cotangent, 79 7, 7 7, , 779 7,,, 7,, 7, 9 graphs of,, 7, Coterminal angles, 77 77, 0 Countereamples, 7, 7 7 Cramer s Rule, 0 0, 7 Cross-Curricular Projects,,,, 0, 7, 0,, 7, 9, 0, 7,, 7, 9, 0, 7, 0, 9,, 7, 7 Cubes difference of,, 9 0, sum of, 9 0, volume of, 07 Cubic function, Cubic polnomial, Curve of Agnesi, Curve of best fit, 7, 9 Clinders surface area of, 9 volume of, 7, 7, 7 D Data bivariate, interquartile range (IQR) of, 9 90 means of, 77, 70 7, 7, 7, 7, R0 Inde

192 medians of, 77, 70 7, 7, 7,, 9 modes of, 77, 70 7, 7, 7, organizing with matrices, 0,, 70 organizing with spreadsheets, outliers,, 77, 7, 9 90 quartiles of, 9 90 range of, 7, scatter plots of, 7 9, 0, 09, 7 standard deviations of, 7 7, 7 7, 7, 77 univariate, 77 variances of, 7 7 Data collection device, 9, Deca eponential, 00,,, Decimals, percents to, repeating,, 0, terminating,, 0 Degree of a polnomial, 0,, Degrees of angles, 7 77, of monomials, 7 of polnomials, 0,, Denominators,, common, rationalizing, 09,, of zero,, 7 Dependent equations, Dependent events, 7, 70 70, 7, 77 Dependent variables,, Depressed polnomials, 7, 7 Depression, angles of, 7 7 Descartes, René, Descartes Rule of Signs,, 70 Determinants, 9 0, 0, 7 Cramer s Rule, 0 0, 7 second-order, 9 third-order, 9 99 Diagrams area, 70 tree, Venn, Difference of two cubes,, 9 0, Difference of two squares,, 9 0,, 77 Differences, common,,, 7 Dilations, 7, 9 90,, 7 with matrices, 7, 9 90, Dimensional analsis,, 9 Dimensions,, 9 7, 77,, Direct variations,, 7, 7, 9 Directi, 7, 9 70, 7, Discontinuit, 7, Discrete probabilit distributions, 7 Discrete random variables, 99 Discrete relations, 9, Discriminant, 79 Disjunctions, Dispersions, 7 Distance Formula,, 7, 7,, 90, Distributions continuous probabilit, 7 7 discrete probabilit, 7 negativel skewed, 7 77 normal, 7 7, 7, 7 positivel skewed, 7, 7 7 probabilit, 99, 7 skewed, 7 7 uniform, 99 Distributive Propert,,, 7, 0,,, 7, 7 77 Division of comple numbers,, 0 of fractions,, 9 of functions,,, 0 long,,, of monomials, 7 of polnomials, 0, 9, 7 7 propert, 9,, 9 of radicals, 0 09,, 0 of rational epressions,, 9 remainders,,, 7 of square roots, 9, snthetic, 7, 9, 7 b zero, 777 Division algorithm, Division Propert of Equalit, 9 Division Propert of Inequalit,, 9 Domains,, 9, 97, 0 07, 0, 9,, 9, 97, 9 99, of Arcsine, 07 of trigonometric functions, 70, 07 Double-angle formulas,, 9,, 7, 70 Double bar graphs, Double roots,, 0, Double subscript notation, Dole Log Rule, 7 E e, Elements,, 9, 7 7, 7, 9, Elevation, angles of, 7 7 Elimination method,,,,, 0 Ellipses, 7, 0, 9 0, 0 0, 09, equations of, 0, 09, foci of, 7 graphs of,,, 7, 9, 00 0, 0 0, major aes of, 7, 07, minor aes of,, 7 vertices of, Empt set,,,,, 97 End behavior, 7 Equal matrices,, Equations, absolute value,, of asmptotes, 9, 9 9, of aes of smmetr, 7,,, 9 9, 0 base e, 7 of circles, 7 79, 9 0, 09, direct variation,, 9 of ellipses,, 9, 9 0, 09, eponential, 0 0, 0 0, 07 0, 9, of hperbolas, 90 0, 09, inverse variation, 7, 9 joint variation,, 9 linear, 70, 7 7, 79, 7 9, 0 09, logarithmic,,, 9,, involving matrices, Inde Inde R09

193 Inde matri, 0 of parabolas, 7, 9 0, 09 0 point-slope form, 0, 7, 0, 09 polnomial,,, 7 prediction, 9, 0, 09 quadratic,,, 0,, 9, 7 97, 0 0 in quadratic form, radical,,, 0, rational, 79, 9, 9 regression, 9 9, of relations, 0 roots of,, slope-intercept form, 79, 9, 0, solving, 9, 9,,,,, 0,, 9, 7, 0 0,,,, 7,,, 0,, 79,, 9, 9, 0 0, 0 0,,, 9,, 7,, 0, 70 standard form of, 7 9, 0 07,,,, 70, 7,, 9, 9, 9, 09 sstems of, 9,,, trigonometric, 0, 70 Equilateral triangles, 77 Equilibrium price, Equivalent epressions, 0,, 7, 0 Estimation, 0 Even-degree functions, 7, 9 Even functions, 7 Events, compound, 70 dependent, 7, 70 70, 7, 77 inclusive, 7 7, 7 independent, 7, , 70, 7, 77 mutual eclusive, 70 7, 7 7, 7, 77 simple, 70 Ecluded values,, Epansion of minors, 9, 97 9, 7 Epected value, 7 Eperimental probabilit, 70 Eponential deca, 00,,, Eponential distribution, 79 7 Eponential equations, 0 0, 0 0, 07 0, 9, Eponential form, 0, Eponential functions, 9 0, 0 0, 09 as inverse of logarithmic functions, 09, 7, 9, natural base, 7 Propert of Equalit, 0 0 Propert of Inequalit, 0 writing, 00 0, 0 0 Eponential growth, 00 0, 0 0, 9,, compound interest, 0,, Eponential inequalities, 0 0 Eponents, 9, 7, 0 Inverse Propert, negative,, 7 proofs of the laws, rational,, 0, zero as, Epressions absolute value, 7 algebraic, 0,, 9 0 containing powers, 7, 7 7 equivalent, 0,, 7, 0 evaluating, 0, logarithmic, 0, powers, 7 rational, 9,, 9 90 simplifing,, 0, 7, 0, 9, 0, 9 verbal, 9 Etraneous solutions,, 0,,, 9, Etrapolation, 7 F Factor Theorem, 7, 7 proof of, 7 Factorials,,, 90 9, 97 9 Factoring,, 70 binomials, 7, 9 0,,,, 90, 77 monomials,, 0, 90 polnomials,, 9, 7,, 0, 90, 7 77 trinomials,, 0, 9 0,,, 77 Factors, greatest common,, 9 0, Fahrenheit, 9, Fahrenheit, Gabriel Daniel, 9 Failure, 97 Families of graphs, 7 absolute value functions, 97 eponential functions, 99 linear functions, 7, 7 parabolas, 7, 0 parent graph, 7, 7, 97 square root functions, 97 Feasible regions, Fibonacci sequence, 0, Finite sample spaces, Foci of ellipses, 7 of hperbolas, 90, 9 9, of parabolas, 7, 9 70, 7, FIL method,,,, 7 7 Foldables,,,,,, 0,, 0, 9, 0, 0,, 7, 0 Formulas, 9, for angular velocit, 7, 77 for area, 9,,,, 9, 97,,, 77, 9, 9 Benford, change of base, 0, for combinations, 9 9 for converting centimeters to inches, 97 for converting temperatures, 9, distance,, 7, 7,, 90, double-angle,, 9,, 7, 70 half-angle,, 7 Hero s, 9 for margin of sampling error, 7, 70 midpoint,, 09 for nth terms,, 7, 7 for permutations, 90 9 for probabilit, 97 9, 70 70, 70 7, 7 7 for probabilit of dependent events, 70, 7 for probabilit of inclusive events, 7, 7 for probabilit of independent events, 70 70, 7 R0 Inde

194 for probabilit of mutuall eclusive events, 70 7, 7 quadratic, 7, 0, 0,, recursive, 9, 7, 77 for simple interest, slope, 7 7, 79,, 7, 0 09 solving for variables,,, for standard deviations, 7, 7, 9 sum and difference of angles,, 7, 70 for surface area,,, for volume,,, 7, 7, 7 Fractals, von Koch snowflakes, Fraction bars, 7 0 Fractional eponents,, 0, laws of, polnomials,, rational epressions, 0, simplifing epressions with, 7 0, Fractions adding,, bar, 7 0 comple, 7 dividing,, 9 multipling,,, 9 subtracting,, Frequenc tables, 7 Function notation,, Functions, 70, 9 0, 0 07 absolute value, 9 00, 0, 7, 7 77, 9 adding,,, 0 Arccosine, 07, Arcsine, 07 0 Arctangent, 07, 09 0 circular, 00 0 cosecant, 79 7, 7 7, , 779 7,,, 7,, 7, 9 70 cosine, 79 7, 7 77, , 779 7, 79, 79 0, 0 0, 07,,, 7 cotangent, 79 7, 7 7, , 779 7,,, 7,, 7, 9 classes of, 7 7, 9 composition of, 90, 9, 0,, 0 constant, 9, 9 00, 7, 7, 9 continuous, 99, cubic, direct variation, 7 7, 9 dividing,,, 0 domains of,, 9, 97, 0 equations of, 0 evaluating,, 7, 9, 7 even, 7 even-degree, 7, 9 eponential, 9 0, 0 0, 09 graphs of, 9 0,, 9 00, 07, 0,,, 0, 9 9, 97 0, 7 77, 9, 9 9, 9 00, 0 0, 09,, 9, greatest integer, 9, 7 7, 7 77, 9, 9 identit, 9, 9, 7, 9, inverse, 9 97, 0, 09, 7,, 77, 7 7, 0, inverse variation, 7, 7 77, 9 iterations, 0, 7 linear, 70, 7, 9, 9, logarithmic,, 7, mappings of, 9, natural logarithmic, 7, notation,, odd-degree, 7 one-to-one, 9, 99, 09, operations on,,, 0 period of, 0 0, 7, 0, 7 periodic, 0 0,, 7 piecewise, polnomial, 7,, 0 7, 7, 7, 7, 7, 9 quadratic,,, 0 0,, 97, 7 77, 9, 9 ranges of, 9,, 9, 97, 0, rational, 7, 7, 7, 9, 9 related,, 0 0 secant, 79 7, 7 7, , 779 7,,, 7, 9,, 7, 7, 9 70 sine, 79 77, , 779 0, 0 07,,, 7 special, 9 0 square root, 97 0,, 7, 7, 9 step, 9 9, 9 0, 7 7, 7 77, 9, 9 subtracting,,, 0 tangent, 79 77, , 779 7, 07, 09 0,, 7, 9, 7, 9 7,, 0,, 7, 9 trigonometric, 79 77, , 779 0, 0 7 vertical line test, 9, 9 zero, 9 zeros of,, 0,, 9,, 7, 7 Fundamental Counting Principle,, 70, 7 Fundamental Theorem of Algebra,, 7 G Geometric means, 0 Geometric sequences,, 7, 7 common ratio,, 7 limits, Geometric series,, 0, 7, 7 77 convergent, derivation of summation formulas, finite, 9 infinite, 0, 7, 77 Geometr angles, 7 77, 77 7, area, 9,,,, 9,, 7 7, 790, 79 circles, 9 cones,, congruent figures, 79 0 clinders, 7, 7, 7 equilateral triangles, 77 isosceles triangles, 7 parallel lines, 7 prisms, pramids,, 7 Pthagorean Theorem, right triangles, 7 77,, similar figures, 79 0 surface area,, trapezoids,, 9 triangles,,, 7 77, 77, 7 79,, volume,,, 7, 7, 7 Glide reflections, 90 Golden ratio, 7 Golden rectangle, 7 Inde Inde R

195 Inde Graphing Calculator Labs, Augmented Matrices, Cooling, Factoring Polnomials, Families of Eponential Functions, 99 Famil of Absolute Value Graphs, 97 The Famil of Linear Functions, 7 The Famil of Parabolas, Graphing Rational Functions, Horizontal Translations, 9 Limits, Lines of Regression, 9 9 Lines with the Same Slope, 7 Matri perations, 7 Maimum and Minimum Points, Modeling Data Using Polnomial Functions, 7 Modeling Motion, 9 Modeling Using Eponential Functions, 9 Modeling Using Quadratic Functions, ne Variable Statistics, 79 Period and Amplitude, Quadratic Sstems, 0 Sine and Cosine on the Unit Circle, 00 Solving Eponential Equations and Inequalities with Graphs and Tables, 07 0 Solving Inequalities, Solving Logarithmic Equations and Inequalities with Graphs and Tables, Solving Radical Equations and Inequalities b Graphing and Tables, 9 Solving Rational Equations and Inequalities with Graphs and Tables, 7 Solving Trigonometric Equations, 0 Square Root Functions, 99 Sstems of Linear Inequalities, Sstems of Three Equations in Three Variables, 9 Graphs of absolute value functions, 9 00, 0, 7, 7 77 of absolute value inequalities, 0 0 amplitudes, 7, 0, 7 asmptotes, 7, 7, 9, 99,, 9, 9 9,, bar, boundaries, 0 0, 0, 0 bo-and-whisker plots, 9 90 of circles, 7, 7 7, 99 0, of constant functions, 9, 9 00, 7, 7 continuit, 7 of cosecant functions,, 7, of cosine functions, 0,,, 7 of cotangent functions,, 7, curve of Agnesi, dilations, 7, 9 90, of direct variation functions,, 7 7 distance on,, 09 0 double bar, of ellipses,, 7, 9, 00 0, 0 0, end behavior of, 7 of equivalent functions, of eponential functions, 9 00, 0 0, 09, 9 families of, 7, 7, 97, 97, 99 of functions, 9 0,, 9 00, 07, 0,,, 0, 9 9, 97 0, 7 77, 9, 9 9, 9 00, 0 0, 09,, 9,, 0, 0,, 7 of greatest integer functions, 9, 7 7, 7 77, 9 of hperbolas, 90 97, 99 0, of identit function, 9, 7, 9 of inequalities,,, 0 0, 0, 9 9, 99 00,, of inverse functions, 9 9 of inverse variations, 7, 7 77 line, of linear inequalities, 0 0, 0 of lines,, 9, 9, 9, 9, 0,, 7 7 of logarithmic functions,, midpoints,, 09 0 parabolas,,, 0, 7 77, 9, 7 7, 99 0, 0 parent, 7, 7, 97, 97 of periodic functions, 0 0,, 7 phase shift, 9 0,,, 7 point discontinuit, 7,, 7 of polnomials functions, 7,, 0,, 7, 7 of quadratic functions,,, 0, 7 77, 9 of quadratic inequalities, 9 9 of rational functions, 7, 7, 7, 9 reflections, 9, of relations,, 07 rotations, 90,, scatter plots, 9, 0, 09, 7, 9 of secant functions,, 7, 9, of sine functions, 0, 0,, 7 slopes of, 7 77, 79, 7, 9, 0, 0 09,, 7 for solving sstems of equations, 7, for solving sstems of inequalities, 0,, of square root functions, 97 0,, 7, 7 of square root inequalities, of step functions, 9 9, 9 00, 7 7, 7 77, 9 of sstem of equations, 0 07, 09, of tangent functions, 7, 9,, 7 transformations, 9,,,, 9, 7 translations, 7, 9, 9,, 9, 7 of trigonometric functions, 0, 0,, 7 -intercepts,, 7 7 -intercepts,, 7 7, 79 Greatest common factors (GCF),, 9 0, Greatest integer functions, 9, 7 7, 7 77, 9, 9 Growth, eponential, 00 0, 0 0, 9,, H Half-angle formulas,, 7 Half-life, Harmonic means, R Inde

196 Hero s formula, 9 Identit Propert, Intercept form, Histograms, 7 relative-frequenc, Hooke s Law, 9 Horizontal line test, 9 Horizontal lines,, 7 7, 9 slope of, 7 7 -ais, Horizontal translations, 9,, 7 Hperbolas, 7, 90 0, 09, asmptotes of, 9, 9 9, centers of, 9 conjugate aes of, 9, 9 equations of, 90 0, 09, foci of, 90, 9 9, graphs of, 90 97, 99 0, nonrectangular, 9 rectangular, 9 transverse aes of, 9 9, 09 vertices of, 9 9, 9 9, Hpotenuse, 77, 79 7, Hpotheses alternate, 70 null, 70 testing, 70 I i, 0, 7, 0, 0 Identities, 7 9,, 7, 9 70 double-angle formulas,, 9,, 7, 70 to find value of trigonometric functions,, 9, 9, 70 half-angle formulas,, 7 Pthagorean, 7 9,,,, 9 quotient, 7 9,,, 9 reciprocal, 7 9, 9 to simplif epressions, 0, 9 sum and difference of angles fromulas,, 7, 70 verifing, 7, 0, 7, 9 70 Identit function, 9, 9, 7, 9, graph of, 9 Identit matrices, 0 09, Images, Imaginar numbers, 0, 7, 79, 0, 0,,, 7 adding,,, 0 conjugates,, 0 dividing,, 0 multipling, 0, standard form of, subtracting,, Imaginar unit, 0, 0 Inches, 97 Inclusive events, 7 7, 7 Inconsistent equations,,, 9 Independent equations, Independent events, 7, , 7, 7 Independent variables,, 7, Inde f radiacals, 0, 09 0, 9 of summation, Inde of summation, Indicated sums, 9 Indirect measurement, 7 7 Inequalities, 9 absolute value, 9,, 0 0 base e, 7 compound, 9,, epontential, 0 0 graphing,,, 0 0, 0, 9 9, 99 00,, linear, 0 0, 0 logarithmic,, properties of,, 9 quadratic, 9 00, 0, 0 0 radical, rational,, solving, 9,, 9 00, 0,,,, 0 0, 0,, 0,, 7, square root, sstems of, 0,, Infinite geometric series, 0, 7, 77 Infinit smbol, Initial sides, 7, Inscribed polgons, 77 Integers,, 9 0, 9 greatest, 9, 7 7, 7 77, 9, 9 Integral Zero Theorem, 9, 7 Intercepted arcs, 77 Interest compound, 0,, simple, Interior angles, alternate, 7 Interpolation, 7 Interquartile range (IQR), 9 90 Intersections of sets,, 9 Inverse functions, 9 97, 0, 09, 7, graphs of, 9 9 Inverse matrices, 09,,, finding, 0, Inverse Propert of eponents, of real numbers, Inverse relations, 9 9, 0, 09, 7,, 77, 7 7, 0, Inverse variations, 7 7, 7, 9, 9 Irrational numbers,, 9, 0, 9 Isosceles triangles, 7 Iterations, 0, 7 J Johannes Kepler s third law, 70 Joint variations,, 7, 9 K Kelvin, Kepler, Johannes, 70 Kepler s third law, 70 L Latus rectum, 9 7 Law of Cosines, 79 79,, Law of Sines, 7 79,, Law of Universal Gravitation, 70 Laws of eponents, proofs of, Leading coefficients, Least common denominators Inde Inde R

197 Inde (LCD),, 79 0 Least common multiples (LCM), 0 Legs, 77, 79 70, Light-ears, Like radical epressions, 0 Like terms,, 7 Limits, Line graphs, Line of best fit, 9 Line of fit, 9 best, 9 Linear correlation coefficients, 9 Linear equations, 70, 7 7, 79, 0 09, point-slope form, 0, 7, 0, 09 slope-intercept form, 79, 9, 0, standard form, 7 9, 0 07 Linear functions, 70, 9, 9, graphs of, 7, 9, 9 Linear inequalities, 0 0, 0 Linear permutations, 90, 9 Linear polnomials, Linear programming, 0,, Linear terms, Lines of best fit, 9 directi, 7, 9 70, 7 of fit, 9, 9 graphs of, 9, 9, 9, 9, 0,, 7 7 horizontal,, 7 7, 9 number,,, 97 9, oblique, 7 parallel, 7, 7, 0, 0, 9, 7 perpendicular, 7 7,, 0 regression, 9 slopes of, 7 77, 79, 7, 9, 0, 0 09, vertical,, 7 7, 79 Like terms, 7 Links real-world,, 9,,,, 0,,,,,, 7, 9,, 00, 0,, 7,, 0,, 0, 0,, 7, 79, 9, 0, 0, 0, 7,, 0,, 0, 7, 7,, 9, 97, 0,,, 7, 0,,, 7,, 9, 9, 9, 00,, 7, 0,, 0,,,, 7, 70, 77,, 9, 0,,,,, 9, 0, 7, 7,, 7, 9, 9, 0, 0,,, 0,, 0,, 7,, 9,,,, 9, 70, 70, 7, 77, 7, 7, 7, 7, 7, 7, 7, 79, 79, 79, 797, 0, 0, 0, 0,,, 0,,, vocabular, 9,, Location Principle, 0 Logarithmic equations,,, 9,, Logarithmic epressions, 0, Logarithmic form, 0, Logarithmic functions, natural, 7, Propert of Equalit, Propert of Inequalit, as inverse of eponential functions, 09, 7, 9, Logarithmic inequalities,, Logarithms, 0, 0 Change of Base Formula, 0, common, natural, 7 Power Propert,, Product Propert, 0 Quotient Propert,,, Long division,,, Long division of polnomials, 0 Lower quartile, 9 90 M Major aes, 7, 09, Mappings, 9, Margin of sampling error, 7 7, 70 Mathematical induction, 70 7, 7 Matrices, 9 adding, 9 70, 7 7,, additive identit, 7 augmented, coefficient, 7 column, constant, 7 Cramer s Rule, 0 0, 7 determinants of, 9 0, 0, 7 dilations with, 7, 9 90, dimensions of,, 9 7, 77,, elements of,, 9, 7 7, 7, 9, equal,, equations involving, identit, 0 09, inverse, 09,,, multipling, 77,, multipling b a scalar, 7 7, 7, operations with 9, properties of operations, 7 reflection, reflections with, 9, rotation, rotations with, 90,, row, to solve sstems of equations, 0, 0 square, subtracting, 7, transformations with, 9,,, translation,, translations with 7, 9, 9, variable, 7 verte,,, zero,, 7 Matri equations, 0 Maima of a function, 0 Maimum values,,,,, 0 relative, 0, 7 Means arithmetic,, of data, 77, 70 7, 7, 7, 7, geometric, 0 harmonic, Measurement of angles, 7 77, area, 9,,,, 9,,, 7 7, 790, 79, 9 centimeters, 97 circumference, 79 degrees, 7 77, dimensional analsis,, 9 indirect, 7 7 inches, 97 light-ears, nautical miles, 7 7 R Inde

198 radians, 79 77, surface area,,,, 9 temperature, 9 volume,,, 07, 7, 7, 7 Measures of central tendenc, 77, 70 7 means, 77, 70 7, 7, 7, 7, medians, 77, 70 7, 7, 7,, 9 modes, 77, 70 7, 7, 7, Measures of variation, 7 7 range, 7, standard deviation, 7 7, 7 7, 7, 77 variance, 7 7 Medians, 77, 70 7, 7, 7,, 9 Mid-Chapter Quizzes,,, 7, 9, 7,, 07, 7, 7, 9,, 7, 7, 7 Midlines, Midpoint Formula,, 09 Midpoints,, 09 0 Minima of a function, 0 Minimum values,,, 9, relative, 0, 7 Minor aes,, 7 of binomials,,, 7,,7 77 commutative propert of,, 0, 09, 0 of comple numbers, FIL method,,,, 7 7 of fractions,,, 9 of imaginar numbers, 0, of matrices, 77,, of monomials,, 7, 7 7 of polnomials,,, 7 7, of probabilities, , 7 77, 7, 77 of radicals, 0, 0, 0, of rational epressions, 7, 9 90 scalar, 7 7, 7, of square roots, 9 0, Multiplication Propert of Equalit, 9 0 Multiplication Propert of Inequalit,, 9 Multiplicative inverses, Mutuall eclusive events, 70 7, 7 7, 7, 77 Notation scientific, 7 standard, nth powers, 0 nth roots, 0 0, 0, nth terms, 7, 7 0, 7 Null hpotheses, 70 Null set, Number lines bo-and-whisker plots, 9 90 graphs of inequalities,,, 97 9, Numbers comple,, 7, 79, 0,, imaginar, 0, 7, 79, 0, 0,,, 7 integers,, 9 0, 9 irrational,, 9, 0, 9 natural,, 9 0 opposites,, 7 prime, 9 pure imaginar, 0, 0 rational,, 9 0, 09 real, 7,,, 9 0, 9, 97, 0,, 97,, 99, scientific notation, 7 standard notation, whole,, 9 0 Numerators,, Inde Minors, 9 Mied Problem Solving, 9 99 Modes, 77, 70 7, 7, 7, Monomials, 7 adding, 0 coefficients of, 7 constants, 7 degrees of, 7 dividing, 7 dividing into polnomials,, 9 factoring,, 0, 90 least common multiples (LCM) of, 0 multipling,, 7, 7 7 powers of, 7, 7 simplest form, Multiple-choice questions, 9 9 Multiples, least common, 0 Multiplication associative propert of,,, 0 N Natural base, Natural base eponential function, 7 Natural logarithmic function, 7, Natural logarithms, 7 Natural numbers,, 9 0 Nautical miles, 7 7 Negative correlations, Negative eponents,, 7 Negative slopes, 7 Negativel skewed distributions, 7 77 No correlation, Nonrectangular hperbolas, 9 Normal distributions, 7 7, 7, 7 Normall distributed random variable, 7 blique lines, 7 dd-degree functions, 7 ne-to-one functions, 9 eponential functions, 99 0, 0 0, 09 logarithmic functions, pen sentences, pposite reciprocals, 7 7,, 0 pposites,, 7 rder of operations,, 7 of real numbers, 7 rder of operations,, 7 rdered pairs, 9, rdered triples, rigin,, 7 7, 7 79, 77, 70, utcomes, utliers,, 77, 7, 9 90 Inde R

199 Inde P Parabolas,,, 0, 7 77, 9, 7 7, 9 0, 09 aes of smmetr, 7,,, 9 9, 0, 7 7, direction of opening, 9,, 7 9, 0, 0,, 70 7, directri of, 7, 9 70, 7, equations of, 7, 9 0, 09 families of, 7, 0 focus of, 7, 9 70, 7, graphs of, 7 7, 99 0, 0 latus rectum of, 9 7 maimum values,, 0 minimum values, 9, vertices of, 7, 9,, 9, 0, 0, 7 7 -intercepts, 7, Parallel lines, 9. 7 slopes of, 7, 0, 0, 9 -intercepts of, 9 Parent graphs, 7, 7, 97, 97 Partial sums, 0 Pascal, Blaise, Pascal s triangle,, 7, Patterns arithmetic sequences, 9, 7 7 Fibonacci sequence, 0, geometric sequences,, 7, 7 Pascal s triangle,, 7 sequences, 9,,, 7 7 Percents, Perfect square trinomials,, 70, 7, 9 0, 77 Periodic functions, 0 0 amplitude of, 7, 0, 7 cosecant,, 7, cosine, 799 0,,, 7 cotangent,, 7, phase shift of, 9 0,,, 7 secant,, 7, 9, sine, 799 0,, 7 tangent, 7, 9,, 7 translations of, 9, 7 Periods, 0 0, 7, 0, 7 Permutations, 90 9, 9 99, 7 circular, 9 linear, 90, 9 using to compute probabilities, 90 9, 9 99 with repetitions, 9 Perpendicular lines slopes of, 7 7,, 0 writing equations for, Phase shift, 9 0,,, 7 Pi, Piecewise functions, Point discontinuit, 7,, 7 Point-slope form, 0, 7, 0, 09 Points break-even, 7 foci, 7, 9 70, 7, 7, 90, 9 9, midpoint,, 09 0 turning, 0, 7 vertices, 7 7,, 9 9, 9 9 Polgons inscribed, 77 quadrilaterals,, 9 regular, 77 triangles,,, 7 77, 77, 7 79,,, 9 Polnomial equations,,, 7 Polnomial functions, 7, 7, 7, 9 cubic, end behavior, 7 graphs of, 7,, 0,, 7, 7 quadratic, Polnomial in one variable, Polnomials, 7 adding,, 7, 0 binomials, 7, 7,, 7 7, 7 77 constant, cubic, degrees of, 0, depressed, 7, 7 difference of two cubes,, 9 0, difference of two squares,, 9 0,, 77 dividing, 0, 9, 7 7 factoring,, 0, 9, 7,, 0, 90, 7 77 general epression, least common multiples (LCM) of, 0 linear, long division, 0 monomials, 7, 7, multipling,,, 7 7,, 7 77 in one variable, perfect square trinomials, 9 0 prime, 9, quadratic, quadratic form, simplifing, 0, 9 subtracting,, 7 sum of two cubes, 9 0, terms of, 7 trinomials, 7, 7 77 with comple coefficients, 77, Positive correlations, Positive slopes, 7 Positivel skewed distributions, 7, 7 7 Power of a Power, Power of a Product, Power of a Quotient, Power Propert of Logarithms,, Powers, 7 of monomials, 7, 7 multipling,, 7, 7 7 nth, 0 power of, of products, product of, properties of, of quotients, quotients of, simplifing, 7, 7 Practice Tests,,, 7, 9, 07, 79,, 9, 7,, 79, 7, 7, 7 Prediction equations, 9, 0, 09 R Inde

200 Preimages, Preparing for Standardized Tests, 9 9 Etended response practice, 9 9 Etended response questions, 9 9 Gridded response practice, 9 97 Gridded response questions, 9 9 Multiple choice practice, 9 Multiple choice questions, 9 Short response practice, 90 9 Short response questions, 9 99 Prerequisite Skills, 7 90 Bar and Line Graphs, Bo-and-Whisker Plots, 9 90 Congruent and Similar Figures, 79 0 Factoring Polnomials, 77 7 The FIL Method, 7 Frequenc Tables and Histograms, 7 Mean, Median, and Mode, Pthagorean Theorem, Stem-and-Leaf Plots, Prime numbers, 9 Prime polnomials, 9 Principal roots, 0 Principal values, 0 07 Prisms cubes, 07 volume of,, 07 Probabilit, 7, 70 7 adding, 70 7, 7, 7, 77 area diagrams, 70 Benford formula, binomial eperiments, 7 79, 7, 79 combinations, 9 9, 7, 7 7 complements, 70 compound events, 70 conditional, 70 continuous probabilit distributions, 7 7 dependent events, 7, 70 70, 7, 77 discrete probabilit distributions, 7 distributions, 99, 7 events, 7, 70 7 epected values, 7 eperimental, 70 failure, 97 Fundamental Counting Principle,, 70, 7 inclusive events, 7 7, 7 independent events, 7, , 7, 7 linear permutations, 90, 9 multipling probabilities, , 7 77, 7, 77 mutuall eclusive events, 70 7, 7 7, 7, 77 outcomes, permutations, 90 9, 9 99, 7 ratios, 97 7, 7 7, 7 77 sample spaces, simple events, 70 simulations, 7 success, 97 tables, theoretical, 70 tree diagrams, of two dependent events, 70 70, 7, 77 of two independent events, , 7, 7, 77 uniform distribution, 99 Probabilit distributions, 99, 7 Problem solving dimensional analsis,, 9 mied, 9 99 Product of Powers Propert,, 0 Product Propert of logarithms, 0 of radicals, 0, 0, Projects,, 9, 7, 9, 0,, 7, 0, 7,, 7, 7 Proofs countereamples, 7, 7 7 mathematical induction, 70 7, 7 Properties addition of equalit, 9, addition of inequalit,, 9 additive identit,, 7 associative of addition,, 7 associative of multiplication,,, 0 commutative of addition,,, 7 commutative of multiplication,,, 09, 0 distributive,,, 7, 0,,, 7, 7 77 division of equalit, 9 division of inequalit,, 9 of equalit, 9, 0 0, of eponents,, 0 identit, of inequalities,, 9, 0, inverse,, of logarithms, 0, 9, of matri operations,, 0, 09 multiplication of equalit, 9 0 multiplication of inequalit,, 9 power,, of powers,, 7 product, 0, 0, product of powers, 0 quotient, 0 09, 0 of radicals, 0, 0 of real numbers,, 7, 0 reflective, 9 square root, 0, 9, 7 7, 0 substitution, 9 0, subtraction of equalit, 9 subtraction of inequalit,, 9 smmetric, 9 transitive, 9 trichotom, zero product,, 0,,,,,, 70 Propert of Equalit for eponential functions, 0 0 for logarithmic functions, Propert of Inequalit for eponential functions, 0 for logarithmic functions, Proportional sides, 7 79 Proportions, similar figures, 7 0 Punnett squares, Pure imaginar numbers, 0, 0 Pramids surface area of,, volume of, 7 Pthagoras, Pthagorean identities, 7 9,,,, 9 Pthagorean Theorem,,,, 77 7, 7, , 70, 79, Inde Inde R7

201 Inde Q Quadrants,, 77 7 Quadratal angles, 777 Quadratic equations,,, 7 97, 0 0 intercept form of, solving b completing the square, 7 7, 0, 0 solving b factoring,, 0, 0 solving b graphing,, 0, 0 solving in the comple number sstem, solving using Quadratic Formula, 77 solving using Square Root Propert, 0,, 9, 7 7, 0 standard form of,, Quadratic form, Quadratic Formula, 7, 0, 0,, derivation of, 7 discriminant, 79 Quadratic functions,,, 0 0,, 7 77, 9 effect of a coefficient on the graph, effect of a, b, and c var in = a( b) + c,, 9 graphing,,, 0 inverse of, 97 verte form of,, 9, 0 Quadratic inequalities, 9 00, 0, 0 0 graphing, 9 9 solving, 9 00, 0 Quadratic polnomials, Quadratic terms, Quadrilaterals trapezoids,, 9 Quadruple roots, Quartiles, 9 lower, 9 90 median, 9 90 upper, 9 90 Quick Quizzes,, 7,,,,,,, 97,,,, 77, Quick Reviews,, 7,,,,,,, 97,,,, 77, Quizzes mid-chapter,,, 7, 9, 7,, 07, 7, 7, 9,, 7, 7, 7 quick,, 7,,,,,,, 97,,,, 77, Quotient identities, 7 9,,, 9 Quotient of Powers, Quotient Propert of logarithms,,, of radicals, 0 09, 0 R Radians, 79 77, Radical equations,,, 0, Radical inequalities, Radical signs, 0, 7 Radicals, 0, 0, adding, 0, approimating, 0 0 conjugates, dividing, 0 09,, 0 like epressions, 0 multipling, 0, 0, 0, operations with, 0, 0, and rational eponents,, 0, simplifing, 0,, 77 subtracting,, Radicand, 97, 0, 0 0, Radii, 7 79,, 77 Random samples, 7, 7 Random variables, 99 Ranges of Arcsine, 07 of data, 7, interquartile, 9 90 of relations, 9,, 9, 97, 0 07, 0, 9,,, 9, 97, 9 99, Rates of change, 7,, of deca, of growth, initial sides, 7, slope, 7 77, 79, 7, 9, 0, 0 09,, 7 terminal sides, 7 79, 77, 77 7, ,,, Rational equations, 79, 9, 9 Rational eponents,, 0, simplifing epressions with, 7 0, Rational epressions, 9,, 9 90 adding, comple fractions, 7 dividing,, 9 evaluating, 0 ecluded values, multipling, 7, 9 90 simplifing,, subtracting,, 90 Rational functions, 7, 7, 7, 9, 9 graphing, 7, 9 Rational inequalities,, Rational numbers,, 9 0, 09 integers,, 9 0 natural numbers,, 9 0 whole numbers,, 9 0 Rational Zero Theorem, 9 Rationalizing the denominators, 09,, Ratios, common,, 7 golden, 7 probabilit, 79 7, 97 7, 7 77 Reading Math, 0, 0, 7, 79, 9, Angle of Rotation, 7 Comple Numbers, Composite Functions, Dimensional Analsis, 9 Discrete and Continuous Functions in the Real World, Double Meanings, Element, Ellipse, 9 Function Notation, Functions, Greek Letters,, 0 Matrices, Maimum and Minimum, 0 Notation, 97 R Inde

202 blique, 7 pposites, Permutations, 90 Permutations and Combinations, 9 Predictions, 7 Radian Measure, 770 Random Variables, 99 Roots, Roots of Equations and Zeros of Functions, Roots, Zeros, Intercepts, Standard Form, 9 Smbols, 7 Theta Prime, 77 Trigonometr, 79 Real numbers, 7,,, 9 0, 9, 97, 0,, 97,, 99, comparing, 7 integers,, 9 0 irrational numbers,, 9 0, 0, 9 natural numbers,, 9 0 ordering, 7 properties of,, 7, 79 rational numbers,, 9 0, 09 whole numbers,, 9 0 Real-World Careers archaeologists, 99 atmospheric scientists, chemists, cost analsts, 9 designers, electrical engineers, financial analsts, 90 industrial designers, land surveors, 7 landscape architects, 99 loan officers, meteorologist, 9 paleontologists, phsician, 70 pilot, 00 sound technicians, teachers, travel agents, 9 Real-World Links, 9,,,, 0,,,,, 7, 9,, 00, 0,, 0,, 0,, 7, 79, 9, 0, 0,, 7, 0,, 0, 7, 7,, 9, 97,, 7, 0,, 7, 9, 9, 9, 00,, 7, 0,,,,, 7, 70, 77,, 0,,,,, 9, 7, 7,, 7, 9, 9, 0,,, 0,, 0,, 7,, 9,,, 9, 70, 7, 77, 7, 7, 7, 7, 7, 7, 79, 79, 79, 797, 0, 0, 0,,,, 0,,, approval polls, attendance figures, buildings 7 cell phone charges, chambered nautilus, 0 compact discs, 7 data organization, 0 Descartes, The Ellipse, 0 genetics, intensit of light, 0 music, 0 power generation, 0 seismograph, 9 suspension bridges, trill rides, underground temperature, Reciprocal identities, 7 9, 9 Reciprocals,, 79, 7 opposite, 7 7,, 0 Rectangles golden, 7 Rectangular hperbolas, 9 Recursive formulas, 9, 7, 77 Reference angles, , 7 7, Reflection matrices, Reflections, 9,, 7, 99, 09, glide, 9 inverse, 9 9, 0 with matrices, 9, Refleive Propert, 9 Regions bounded, 0 feasible, unbounded, 9 Regression equations, 9 9, linear correlation coefficient, 9 Regression lines, 9 9 Regular polgons, 77 Relations, 70 continuous, 9 discrete, 9, domain of,, 9, 97, 0 07, 0,, 9, 97, 9 99, equations of, 0 functions, 70, 7, 9 0, 0 07, 0,,,, 0, 7, 7, 7, 90, 9 0, 0, 7, 7 7, 9, 9 9, 9 0, 0 0, 09,, 9,, 7,, 0, 7 graphs of,, 07 inverse, 09, 7, mappings of, 9, range of, 9,, 9, 97, 0 07, 0,, 9, 97, 9 99, Relative-frequenc histograms, Relative maimum, 0, 7 Relative minimum, 0, 7 Remainder Theorem, 7 Remainders,,, 7 Repeated roots, 0 Repeating decimals,, 0, Review Vocabular countereample, 7 inconsistent sstem equations, inverse function, 09 inverse relation, 09 Reviews chapter 9, 0 0,,, 0 0, 7 7, 0, 9 9,, 09, 7 7, 7 70,, 7 70 quick,, 7,,,,,,, 97,,,, 77, vocabular,, 09, 7, Right triangles, hpotenuse of, 77, 79 7, legs of, 77, 79 70, special, 7, 7 7 solving, 7 7, Rise, 7 Roots and the discriminant, 79 double,, 0, of equations,, 0,, imaginar, 7, 7 0,, 7 irrational, 9, 7 79 nth, 0 0, 0, principal, 0 quadruple, repeated, square, 9,, 97 0, 0 0 Inde Inde R9

203 triple, proportional, 7 79 Special Right Triangles, 7 Inde Rotation matrices, Rotations, 90 with matrices, 90,, Row matrices, Run, 7 S Sample space, Samples margin of error, 7 7, 70 random, 7, 7 unbiased, 7 Scalar multiplication, 7 7, 7, Scalars, 7 Scatter plots, 9, 0, 09,, 7, 9 outliers, prediction equations,, 9, 0, 09 Scientific notation, 7 Secant, 79 7, 7 7, , 779 7,, 7, 9, 7, 9 7,, 0,, 9 70 graphs of,, 7, 9, Second-order determinants, 9 Sectors, 77 area of, Sequences, 9,,, 7 7 arithmetic, 9, 7 7 Fibonacci, 0, geometric,, 7, 7 terms of, 9,, 7 7 Series, 9,, 7 77 arithmetic, 9, 7 7 convergent, geometric,, 0, 7, 7 77 infinite, 0, 7, 77 terms of, 9,, 7 7 Set-builder notation, Sets empt,,,,, 97 intersections of,, 9 null, unions of,, 9 Sides congruent, 7 Sigma notation,, 9,, 7, 7, 7, 7 inde of summation, Similar figures, 70, 7 0 and dilations, 7 Simple events, 70 Simple interest, Simplest form of rational epressions,, Simplifing epressions, 7, 0, 9 Simulations, 7 Simultaneous linear sstems,, Sine, 79 77, , 779 0, 0 07,,, 7 graphs of, 0, 0,, 7 law of, 7 79,, Skewed distributions, 7 7 Slope-intercept form, 79, 9, 0, Slopes, 7 77, 79, 7, 9, 0, 0 09,, 7 of horizontal lines, 7 7 negative, 7 of parallel lines, 7, 0, 0, 9 of perpendicular lines, 7 7,, 0 positive, 7 undefined, 7, 79 of vertical lines, 7, 79 of zero, 7 7 Snell s law, SH-CAH-TA, 70 Solids cones,, clinders, 7, 7, 7, 9 prisms,, 07 pramids,, 7 spheres, 9 Solutions, 9, etraneous,, 0,,, 9, Solving triangles, 7 7, 7 79, 79 79, Special right triangles, 7, 7 7 Spheres surface area of, 9 Spreadsheet Labs Amortizing Loans, 7 rganizing Data, Spreadsheets cells of, for organizing data, Square matrices, Square root functions, 97 0,, 7, 7, 9 Square root inequalities, Square Root Propert, 0, 9, 7 7, 0 Square roots, 9,, 97 0, 0 0, 7 simplifing, 9 0, Squares differences of,, 9 0,, 77 perfect,, 70, 7, 9 0, 77 Punnett, Standard deviations, 7 7, 7 7, 7, 77 Standard form of comple numbers, of conic section equations,,,, 70, 7,, 9, 9, 9, Standard notation, Standard position, 7 79, , 77 7, , Standardized Test Practice,,, 9, 0, 0 09, 0, 7, 9 9, 9, 7, 0, 7 7, 9, 7 7 Statistics, 77 7, 7 7, 7 79 bar graphs, bell curve, 7 7 bias, 7 bo-and-whisker plots, 9 90 continuous probabilit distributions, 7 7 curve of best fit, 9 discrete probabilit distributions, 7 dispersion, 7 double bar graphs, histograms, 99 70, 7 interquartile range (IQR), 9 90 line graphs, margin of sampling error, 7 7, 70 means, 77, 70 7, 7, 7, 7, R0 Inde

204 measures of central tendenc, 77, 70 7, 7, 7, 7,, 9 measures of variation, 7 7, 7 7, 7, 7, medians, 77, 70 7, 7, 7,, 9 modes, 77, 70 7, 7, 7, normal distributions, 7 7, 7, 7 outliers, 77, 7, 9 90 prediction equations, 9, 0, 09 quartiles, 9 90 random samples, 7, 7 ranges, 7, relative-frequenc histograms, scatter plots, 9, 0, 09,, 7, 9 skewed distributions, 7 7 standard deviations, 7 7, 7 7, 7, 77 stem-and-leaf plots, testing hpotheses, 70 unbiased samples, 7 univariate, data, 77 variance, 7 7 Stem-and-leaf plots, Step functions, 9 9, 9 0 graphs of, 9 9, 9 00 Stud Guides and Reviews, 9, 0 0,,, 0 0, 7 7, 0, 9 9,, 09, 7 7, 7 70,, 7 70 Stud Tips,,, 7, 70, A is acute, 7 absolute value, 0 absolute values and inequalities, absolute value function, 97 additive identit, 7 alternative method,,,,,,,, 9, 70, 7, 79 alternative representations, 7 amplitude and period, angle measure, 0 area formula, 97 bar notation, check,, check our solution, checking reasonableness, 00 checking solutions, 7, choosing a committee, 7 choosing the independent variable, 7 choosing the sign, coefficient of, coefficients, combining functions, 7 common factors, common misconception,, 9, 9, 7, 9, 7, 7, complement, 70 composing functions, conditional probabilit, 70 continuous relations, 9 continuousl compounded interest, coterminal angles, 77 deck of cards, 9 depressed polnomial, 7 Descartes Rule of Signs, 70 dilations, 7 distance, domain, double roots, elimination, equations of ellipses, equations with ln, 9 error in measurement, 7 ecluded values, eponential growth and deca, 00 epressing solutions as multiples, etraneous solutions, 0, factor first, factoring, finding a term, 7 finding zeros, focus of a parabola, 7 formula, 70 formula for sum if < r <, fraction bar, 7 function values, graphing, graphing calculator, 0,, 9, 0,, graphing polnomial functions, 9 graphing quadratic functions, 7 graphing quadratic inequalities, 0 graphing rational functions, 9 graphs of linear sstems, graphs of piecewise functions, 9 greatest integer function, 9 horizontal lines, 7 identit matri, independent and dependent variables, indicated sum, 9 inverse functions, 9 location of roots, look back, 0, 0, 0,, 9,, 0,, 0,, 99,,,, 0, 0,, 77, 7, 779, 07 math smbols, matri operations, 7 memorize trigonometric ratios, 70 notation, messages, midpoints, missing steps, Multiplication and Division Properties of Equalit, 0 multipling matrices, 7 negative base, normal distributions, 7 number of zeros, one real solution, 7 outliers, parallel lines, 9 permutations and combinations, 9 Quadratic Formula, 77 radian measure, 79 random sample, 7 rate of change, rationalizing the denominator, 09 reasonableness, remembering relationships, 00 sequences, sides and angles, 79 simplifing epressions with e, skewed distributions, 7 slope, 7 slope-intercept form, 79 slope is constant, 7 solutions to inequalities, solving quadratic inequalities algebraicall, 97 solving quadratic inequalities b graphing, 9 special values, step, 70 smmetr, technolog, terms, terms of geometric sequences, using logarithms, 9 using the Quadratic Formula, 7 verifing a graph, 0 verifing inverses, 09 vertical and horizontal lines, Inde Inde R

205 Inde vertical line test, 0 vertices of ellipses, writing an equation, zero at the origin, Subscript notation double, Substitution method,, 7,, 0, propert, 9 0, snthetic, 7, Substitution Propert, 9 0, Subtraction of comple numbers,, of fractions,, of functions,,, 0 of matrices, 9 7, of polnomials,, 7 of radicals,, of rational epressions,, 90 Subtraction Propert of Equalit, 9 Subtraction Propert of Inequalit,, 9 Success, 97 Sum and difference of angles formulas,, 7, 70 Sum of two cubes, 9 0, Sums of arithmetic series, 9, 7 7 of geometric series,, 0, 7, 7 77 indicated, 9 of infinite geometric series,, 7, 77 partial, 0 sigma notation,, 9,,, 7, 7, 7, 7 of two cubes, 9 0, Supplementar angles, 7 Surface area of cones, of clinders, 9 of pramids,, Smbols for combinations, 9 for congruent to, 79 0 for elements, for empt set, for greatest integer function, 9 for inequalities, 0 for infinit,, for inverse functions, 9 for permutations, 90, 97 for minus or plus, 9, 7 for plus or minus, 0, 0, 9,, 7 for probabilit, 97 for random variables, 99 sigma,, 9,, 7, 7, 7, 7 for similar to, 79 for sums,, 9,, 7, 7, 7, 7 for terms of sequences,, 7, for variance, 7 Smmetric Propert, 9 Smmetr, aes of, 7,,, 9 9, 0, 7 7, of bell curve, 7 Snthetic division, 7, 9, 7 Snthetic substitution, 7, Sstems of equations, 9,,, classifing, conic sections, 0 07, 09, consistent, dependent, inconsistent,,, 9 independent, solving using augmented matrices, solving using Cramer s Rule, 0 0, 7 solving using elimination,,,,, 0 solving using graphs, 7, solving using matrices,, solving using substitution,, 7,, 0, solving using tables,, 0 in three variables,,, in two variables, 9, Sstems of inequalities, 0,, linear programming, 0,, T Tables, for solving sstems of equations,, 0 Tangent, 79 77, , 779 7, 07, 09 0,, 7, 9, 7, 9 7,, 0,, 7, 9 graphs of, 7, 9,, 7 Temperature, 9, Terminal sides, 7 79, 77, 77 7, 799,,, Terminating decimals,, 0 Terms of binomial epansions, constant, like, 7,, 7 linear, nth, 7, 7 0, 7 of polnomials, 7 quadratic, of sequences, 9,, 7 7 of series, 9,, 7 7 Test-Taking Tips, 0,,,,,,,,,, 70, using properties, Tests practice,,, 7, 9, 07, 79,, 9, 7,, 79, 7, 7, 7 standardized practice,,, 9, 0, 0 09, 0, 7, 9 9, 9, 7, 0, 7 7, 9, 7 7 vertical line, 9 Theorems binomial, 7, 7, 7 comple conjugates,, 7 factor, 7, 7 fundamental,, 7 integral zero, 9, 7 Pthagorean,,,77 7, 7, , 70, 790, rational zero, 9 remainder, 7 Theoretical probabilit, 70 Third-order determinants, 9 99 using diagonals, 9, 9 R Inde

206 epansion of minors, 9, 97 9, 7 Three-dimensional figures cones,, clinders, 7, 7, 7, 9 prisms,, 07 pramids,, 7 spheres, 9 Tips Stud, 7,, 0,,,, 9, 0,, 7, 7, 7, 79,, 7,, 9, 97, 9, 0, 7,, 9,,,, 0, 9,,, 7, 7, 7, 9, 0, 09,,,, 7,, 9, 7,,,,,, 7, 77, 7,, 7,, 9, 9, 97,,, 0,,, 9, 7,,,,, 70,, 7, 9, 0, 0, 09,,,,,,,, 9, 0,, 9, 99, 00,,,,,,, 9,,, 9,,,, 7,, 70,,, 9, 0, 0, 0,,, 9,, 7,,, 0,,, 0,,, 70,, 9, 9, 70, 70, 70, 7, 7, 77, 7, 7, 7, 7, 70, 7, 79,, 77, 779, 7, 7, 79, 79, 00, 07, 0,, 0,,,,,, Test-Taking,, 0,,,,,,,,,, 70, Transformations, 9, dilations, 7, 9 9,,, 7 with matrices, 7, 9, 9,,, reflections, 9,,, 7 rotations, 90,, translations, 7, 9, 9,,, 7, 0, 9, 7 Transitive Propert, 9 Translation matrices,, Translations, 7,, 7, 0, 9, 7 horizontal, 9,, 7 with matrices, 7, 9, 9, vertical,, 7 Transverse aes, 9 9, 09 Trapezoids,, 9 Tree diagrams, Triangles area of,, 97,, 7 7, 790, 79, 9 equilateral, 77 isosceles, 7 Pascal s,, 7, right, 7 77,, similar, 70, 79 0 solving, 7 7, 7 79, Trichotom Propert, Trigonometric equations, 0, 70 Trigonometric functions, 79 77, , 779 0, 0 7 calculators, 7 7 cosecant, 79 7, 7 7, , 779 7,,, 7,, 7, 9 70 cosine, 79 7, 7 77, , 779 7, 79, 79 0, 0 0, 07,,, 7 cotangent, 79 7, 7 7, , 779 7,,, 7,, 7, 9 domains of, 70 inverses of, 7 7, 0, secants, 79 7, 7 7, , 779 7,,, 7, 9,, 7, 7, 9 70 sine, 79 77, , 779 0, 0 07,,, 7 tangent, 79 77, , 779 7, 07, 09 0,, 7, 9, 7, 9 7,, 0,, 7, 9 Trigonometric identities, 7 9,, 7, 9 70 double-angle formulas,, 9,, 7, 70 to find value of trigonometric functions,, 9, 9, 70 half-angle formulas, 9, 7 Pthagorean, 7 9,,,, 9 quotient, 7 9,,, 99 reciprocal, 7 9, 9 to simplif epressions, 0, 9 sum and difference formulas,, 7, 70 verifing, 7, 0, 7, 9 70 Trigonometr, 7 7 angle measurement, 7 77, Arccosine, 07, Arcsine, 07 0 Arctangent, 07, 09 0 circular functions, cosecant, 79 7, 7 7, , 779 7,,, 7,, 7, 9 70 cosine, 79 7, 7 77, 77 77, 77 7, 79, 79 0, 0 0, 07,,, 7 cotangent, 79 7, 7 7, , 779 7,,, 7,, 7, 9 double-angle formulas,, 9,, 7, 70 equations, 0, 70 graphs, 0, 0,, 7 half-angle formulas,, 7 identities, 7 9,, 7, 9 70 inverse functions, 7 7, 0, Law of Cosines, 79 79,, Law of Sines, 7 79,, periodic functions, 0 0,, 7 quadrantal angles, 777 reference angles, , 7 7, and regular polgons, 77 right triangle, 79 77, secant, 79 7, 7 7, , 779 7,,, 7, 9,, 7, 7, 9 70 sine, 79 77, , 779 0, 0 07,,, 7 solving triangles, 7 79, 79 79, sum and difference of angles formulas,, 7, 70 tangent, 79 77, , 779 7, 07, 09 0,, 7, 9, 7, 9 7,, 0,, 7, 9 unit circles, 79, Trinomials, 7 Inde Inde R

207 Inde factoring,, 0, 9 0,,,,, 7 77 least common multiples (LCM) of, perfect square,, 70, 7, 9 0, 77 Triple roots, Turning points, 0, 7 U Unbiased samples, 7 Unbounded regions, 9 Uniform distributions, 99 Unions,, 9 Unit circles, 79, Univariate data, 77 Upper quartiles, 9 90 V Values absolute, 7, 9, 0, 7, 0 ecluded,, Variable matrices, 7 Variables, 7 dependent,, independent,, 7, polnomials in one, random, 99 solving for,,, Variance, 7 7 Variation direct,, 7, 7, 9 inverse, 7 7, 7, 9, 9 joint,, 7, 9 Velocit, angular, 7, 77 Venn diagrams, Verbal epressions,, 9 Verte form,, 9, 0 Verte matrices,,, Vertical line test, 9, 9 Vertical lines,, 7 7, 79 slopes of, 7, 79 -ais, Vertical translations,, 7 midlines, Vertices of ellipses, of hperbolas, 9 9, 9 9, of parabolas, 7, 9,, 9, 0, 0, 7 7 Vocabular Links intersection, smmetric, 9 union, Volume of cones, of cubes, 07 of clinders, 7, 7, 7 of prisms, of pramids, 7 von Koch snowflakes, W Whiskers, 9 Whole numbers,, 9 0 -ais,, 7 79, 777, -intercepts,, 7 7,, 0, 9 -ais,, X Y -intercepts,, 7 7, 79, 9, 99 of parabolas, 7, of parallel lines, 9 Z Zero function, 9 Zero matrices,, 7 Zero Product Propert,, 0,,,,,, 70 Zeros denominators of,, 7 division b, 777 as eponents, of functions,, 0,, 9,, 7, 7 locating, 0, Location Principle, 0 as slopes, 7 7 R Inde