Solving Simple Equations (pages 7 9) 23. k = = b, b = 360; $60. Solving Multi-Step Equations (pages 14 and 15) x

Transcription

1 Section. Solving Simple Equations (pages 7 9). + and are inverses. and are inverses.. x = ; It is the onl equation that does not have x = as a solution.. x = 7 7. x = 9. p =. x = 9π. d = 7. a. = x + ; x = 9. n =.9 b. no; Because = 9, ou did not knock down the last pin with the second ball of the frame. 9. n =. m = 7.π. k =. p = 7. The should have added. to each side. 9..x =.; $. per hour. + k = = b, b = ; $ k = k = 9.7. h = 7. q =. 7. x = 9 9. greater than; Because a negative number divided b a negative number is a positive number.. mg. 8 in.. 7x 7. g Section. Solving Multi-Step Equations (pages and ). + x = 7; x =. k = ;,, 9. b = 9; 9,, 9, 9, 7. c =. 9. h = 9. x = 9. watches. (b + ) = ; in <. > x = ; people Section. Solving Equations with Variables on Both Sides (pages and ). no; When is substituted for x, the left side simplifies to and the right side simplifies to.. x =. in.. x = 7. in. 7. k =.7 9. p = 8. n =.. x = A

2 . The should have been added to the 7. +.m = +.m; mi right side units x = x + x x = x + x x = x + = + x =. Remember that the box is with priorit mail and the envelope is with express mail.. ml. square: units; triangle: units, 9 units, 9 units 7. in. 9. C Lesson.b Solutions of Linear Equations (pages A and B). no solution. x = 7. no; There is no solution to the equation stating the areas are equal, x + = x. Section.. no solution 9. no solution. infinitel man solutions. x =. no solution 7. infinitel man solutions 9. x = Rewriting Equations and Formulas (pages 8 and 9). no; The equation onl contains one variable.. a. A = bh b. b = A c. b = mm h. = x 7. = x 9. = x. 9 I. The should have a negative sign in front of it.. a. t = Pr x = = x + b. t = r = x e. m = c 9. a. F = + (K 7.) b. F c. liquid nitrogen 7. = A πw w. r V = π ; r =. in w = g A

3 Section. Converting Units of Measure (pages 7). es; Because centimeter is equal to.. ft; The other three represent the same length. millimeters, the conversion factor equals.. d, ft a. about.7 m b. about 8. km. about.99 ml/sec a. spine-tailed swift; mallard b. es, It is faster than all of the other birds in the table. Its dive speed is about. miles per hour..,88.,,,.. 7. a. in. 9., mm.. B b. 8 tissues 8 (, ) 8 O x (, 8) 8 Section. Graphing Linear Equations (pages and ). a line. Sample answer: x = x = x x (, ). = x 7. (, ) = x x 9. = 7x. x = x x. 8 (,.7) =.7 x. = x 7. = x + 9. = x 9 = x + = x 9 x x A

4 . a. = +.x Balance (dollars) = +.x 8 x Number of months. a. = x b. mo b. Sample answer:. (, ) 7. (, ) 9. B If ou are ears old, the sea level has risen millimeters since ou were born. Rise in sea level (mm) = x 8 x Number of ears Section. Slope of a Line (pages 9 ). a. B and C. The line is horizontal. b. A c. no; All of the slopes are different.. x The lines are parallel (7, ) (, ) (, 8) (, ) 7 x (, 8) (, ) 7. The should be because it goes down. (, ) Slope = 9.. red and green; The both have a slope of.. no; Opposite sides have different slopes.. a. x (, ) b. The cost increases b $ for ever miles ou drive, or the cost increases b $.7 for ever mile ou drive. 7. You can draw the slide in a coordinate plane and let the x-axis be the ground to find the slope. 9. = x 9. B x 9 A

5 Lesson.b Triangles and Slope (pages A and B). similar; Corresponding leg lengths are proportional.. The ratios are equal; Sample answer: Using the similar triangles in the Ke Idea: AB DE = AC DF AB DF = DE AC AB AC = DE DF. es; The ratios of the corresponding leg lengths in the right triangles are proportional. Section. Graphing Linear Equations in Slope-Intercept Form (pages and 7). Find the x-coordinate of the point where the graph crosses the x-axis.. Sample answer: The amount of gasoline (in gallons) left in our tank after ou travel x miles is = x +. The slope of means the car uses gallon of gas for ever miles driven. The -intercept of means there is originall gallons of gas in the tank.. A; slope: ; -intercept: 7. slope: ; -intercept: 9. slope: ; -intercept:. slope: ; -intercept:. slope: ; -intercept:.. slope:.; -intercept: 7. a. Height (feet) = x + x Time (seconds) b. The x-intercept of means the skdiver lands on the ground after seconds. The slope of means that the skdiver falls to the ground at a rate of feet per second x = x 7 x-intercept: 7. =.x. x-intercept: 7 x = x x-intercept: x A

6 . =.7x + 7. =.x + 9. = x + =.7x x =.x x. = x. B Section. Graphing Linear Equations in Standard Form (pages 7 and 7). no; The equation is in slope-intercept form.. x = pounds of peaches. = x = pounds of apples 7. = x + = x = x x. x-intercept: -intercept:. x-intercept: none -intercept:. a. x = b. $9 x = 8 x (, 8) 7 x + = 8 (, ) x 9. x-intercept: 9. a. 9.x + 7. =. -intercept: 7 b. Number of DVDs 9 8 (, 7) 7 x + 8 = (9, ) x Number of CDs Hours worked as server x + 7. =. 8 8 x Hours worked as host. a. = x + 7. x 7 b. x-intercept: ; It will not be on the graph x 8 because ou cannot have a negative time. c. 8 = x + 7 x A

7 Section. Sstems of Linear Equations (pages 8 and 8). es; The equations are linear and in the same variables.. x C 8 9 R (, ). (.,.) 7. (, ) 9. a. R = x b. rides. (, ). (, ). (8, ) 7. a. h b. 9 mi 9. es. no Section. Special Sstems of Linear Equations (pages 8 and 87). The graph of the sstem with no solution has two parallel lines, and the graph of a sstem with infinitel man solutions is one line.. one solution; because the lines are not parallel and will not be the same equation. no solution 7. infinitel man solutions; all points on the line = x + 9. one solution; (, ). no solution. no; because the are running at the same speed and our pig had a head start. no solution 7. a. h b. You both work the same number of hours. 9. a. Sample answer: = 7. x = b. Sample answer: = x. B c. Sample answer: x = Section.7 Solving Equations b Graphing (pages 9 and 9). algebraic method; Graphing fractions is harder than solving the equation.. x =. x = 7. x = 9. es; Because a solution of x + = x exists (x = ).. x =. The two lines are parallel, which means there is no solution. Using an algebraic method, ou obtain = 8, which is not true and means that there is no solution.. Organize the home and awa games for last ear and this ear in a table before solving A A

8 Section. Writing Equations in Slope-Intercept Form (pages and ). Sample answer: Find the ratio of the rise to the run between the intercepts.. = x + ; = x ; = ; =. = x + 7. = x + 9. = x. The x-intercept was used instead of the -intercept. = x. =. = 7. a b. Speed (mi/h) 7 (, ) (, ) 7 x Braking time (seconds) (, ) represents the speed of the automobile before braking. (, ) represents the amount of time it takes to stop. The line represents the speed of the automobile after x seconds of braking. c. = x + 9. Be sure to check that our rate. of growth will not lead to a -ear-old tree with a negative height. 7 (, 7) O x (, ) Section. Writing Equations Using a Slope and a Point (pages and 7). Sample answer: slope and a point. = x +. = x = x + 9. = 7 x. = x. V = T +. The rate of change is. degree per chirp. 7. a. =.x B b. g/cm c. Sample answer: Eventuall =, which means the astronaut s bones will be ver weak. A7

9 Section. Writing Equations Using Two Points (pages and ). Plot both points and draw the line that passes through them. Use the graph to find the slope and -intercept. Then write the equation in slope-intercept form.. slope = ; -intercept: ; = x. slope = ; -intercept: ; = x 7. = x 9. = x. = x +. = x. The switched the slope and -intercept in the equation. = x 7. a. π π π π π π O b. = πx (, π) (, π) x 9. a. = x +, b. Value (dollars), 8,,, x Years c. $,; the original price of the car. a. = x 8. b. m. 7. D Section. Solving Real-Life Problems (pages and ). The -intercept is because the line crosses the -axis at the point (, ). The x-intercept is because the line crosses the x-axis at the point (, ). You can use these two points to find the slope. change in Slope = change in x = =. Sample answer: the rate at which something is happening. Sample answer: On a visit to Mexico, ou spend pesos ever week. After weeks, ou have no pesos left. 7. a. slope:.; -intercept: 9 b. =.x + 9 c. 9 F 9. a. Antananarivo: 9 S, 7 E; Denver: 9 N, W; Brasilia: S, 8 W; London: N, W; Beijing: N, E b. = x + 87 c. a place that is on the prime meridian. infinitel man solutions. no solution Pesos remaining 8 9 Denver x Weeks W 8 O 8 Brasilia Antananarivo N S London Beijing E A8

10 Section. Writing Sstems of Linear Equations (pages and 7). because its graph is a line. You can use a table to see when the two equations are equal. You can use a graph to see whether or not the two lines intersect. You can use algebra and set the equations equal to each other to see when the have the same value.. a. x + = c. Tulips Cost Number 8 (8, ) 8 x Lilies d. x = x ; x + = x = 8, = ; b. x 7 8 = x = x lilies and tulips 8 lilies and tulips 7. a. no; You need to know how man more dimes there are than nickels or how man coins there are total. b. Sample answer: 9 dimes and nickel 8 lilies and tulips 9. no; A linear sstem must have either one, none, or infinitel man solutions. Lines cannot intersect at exactl two points.. Each equation is the same. So, the graph of the sstem is the same line.. (, ), (, ), (, ). = x 7. B Section. Domain and Range of a Function (pages and ). no; The equation is not solved for.. a. = x b. domain:,,, ; range:,,, c. x = is not in the domain because it would make negative, and it is not possible to bu a negative number of headbands.. domain:,,,, ; range:,, 7. The domain and range are switched. The domain is,,, and. The range is,,, and. 9. x 8. x.. domain:,,, domain:,,, range:,, 8, range:.,,., A9

11 Section. Domain and Range of a Function (continued) (pages and ). Rewrite the percent as a fraction or decimal before writing an equation.. 8 O x 7. x 9. D Section. Discrete and Continuous Domains (pages 8 and 9). A discrete domain consists of onl certain numbers in an interval, whereas a continuous domain consists of all numbers in an interval.. domain: x and x. range: and ; continuous 9. The domain is discrete because onl certain numbers are inputs. Marbles (, ) (, ) x Bags (, ) discrete 7. Volume (in. ) (, ) 7 (, ) 9 x Width (in.) (, ) continuous. The function with an input of length has a continuous domain because ou can use an length, but ou cannot have half a shirt.. Area (in. ) A h Height (in.) continuous. Before writing a function, draw one possible arrangement to understand the problem C Section. Linear Function Patterns (pages and 7). words, equation, table, graph. = π x; x is the diameter;. = x +. a. b. = x (, ) (, ) is the circumference = (, ) c. $9 π π π π π x 9. = x Cost (dollars) (, ) x Number of Movies discrete A

12 . Substitute 8 for t in the equation.. % 7. B Section. Comparing Linear and Nonlinear Functions (pages 7 and 7). A linear function has a constant rate of change. A nonlinear function does not have a constant rate of change.. 8 x linear. 8 x nonlinear 7. linear; The graph is a line. 9. linear; As x increases b, increases b.. nonlinear; As x increases b, V increases b different amounts.. linear; The equation can be written in slope-intercept form.. Because ou want the table to represent a linear function and is half-wa between and, the missing value is half-wa between.8 and.. 7. nonlinear; The graph is not a line. 9. linear. straight. right Lesson.b Comparing Rates (pages 7A and 7B). a. fingernails b. Growth (millimeters) Fingernails Toenails x Time (weeks) The graph that represents fingernails is steeper than the graph that represents toenails. So, fingernails grow faster than toenails. A

13 Section. Classifing Angles (pages 88 and 89). The sum of the measures of two complementar angles is 9. The sum of the measures of two supplementar angles is 8.. sometimes; Either x or ma be obtuse.. never; Because x and must both be less than 9 and greater than. 7. complementar 9. supplementar. neither. 8. Vertical angles are congruent. The value of x is a. CBD and DBE ; ABF and FBE b. ABE and CBE ; ABD and CBD ; CBF and ABF.. 7x = 8; x + = 9; x = ; = B Section. Angles and Sides of Triangles (pages 9 and 9). An equilateral triangle has three congruent sides. An isosceles triangle has at least two congruent sides. So, an equilateral triangle is a specific tpe of isosceles triangle.. right isosceles triangle. obtuse isosceles triangle 7. 9; obtuse triangle 9. 7.; acute isosceles triangle. ; obtuse isosceles triangle. a. 7 b. acute isosceles triangle. no; es 9. If two angle measures of a triangle were greater than or equal to 9, the sum of those two angle measures would be greater than or equal to 8. The sum of the three angle measures would be greater than 8, which is not possible.. x + x + x = 8; 7. x + π =. or x = ; Section. Angles of Polgons (pages ).. What is the measure of an angle of a regular pentagon?; 8 ; no; The angle measures given add up to, but the sum of the angle measures of a pentagon is A

14 9. The sum of the angle measures should have been divided b the number of angles,. = ; The measure of each angle is.. sides. convex; No line segment connecting two vertices lies outside the polgon.. no; All of the angles would not be congruent You can determine if it is a linear function b writing an equation or b graphing the points D Section. Using Similar Triangles (pages and ). Write a proportion that uses the missing measurement because the ratios of corresponding side lengths are equal.. Student should draw a triangle with the same angle measures as the textbook. The ratio of student s triangle length the corresponding side lengths,, should be greater than one. book s triangle length. es; The triangles have the same angle measures, 7, 9, and. 7. no; The triangles do not have the same angle measures. 9. The numerators of the fractions should be from the same triangle. 8 = x 8 x = x = 9.. no; Each side increases b %, so each side is multiplied b a factor of. The area is ( ) = 9 or % of the original area, which is a % increase.. When two triangles are similar, the ratios of corresponding sides are equal. 7. linear; The equation can be rewritten in slope-intercept form. 9. nonlinear; The equation cannot be rewritten in slope-intercept form. Section.. Sample answer: Parallel Lines and Transversals (pages 7 9) a b. m and n t = 7, = 7 9. = 9, =. ; Corresponding angles are congruent. A

15 Section. Parallel Lines and Transversals (continued) (pages 7 9).,,, and 7 are congruent.,,, and 8 are congruent.. = ; and the given angle are vertical angles. = 9 and 7 = 9 ; and 7 are supplementar to the given angle. = ; and the given angle are corresponding angles. = ; and are vertical angles. = 9 and = 9 ; and are supplementar to. 7. = 9 ; and the given angle are vertical angles. = 9 and = 9 ; and are supplementar to the given angle. = 9 ; and the given angle are corresponding angles. = 9 ; and are vertical angles. = 9 and 7 = 9 ; and 7 are supplementar to. 9. ; Sample answer: and are alternate interior angles and and are supplementar.. ; Sample answer: and 8 are alternate exterior angles... ; Sample answer: and are alternate interior angles and and are supplementar.. The are all right angles because perpendicular lines form 9 angles a. no; The look like the are spreading apart. b. Check students work.... B Section. Finding Square Roots (pages and ). no; There is no integer whose square is.. represents the positive square root because there is not a or a ± in front... km 7. and 9. and.. and 7. The positive and negative square roots should have been given. ± = and because a negative radius does not make sense.. and. 7. = 9. 9 ft. 8 m/sec.. ft B A

16 Section. The Pthagorean Theorem (pages and ). The hpotenuse is the longest side and the legs are the other two sides.. cm. 9 in. 7. ft 9. The length of the hpotenuse was substituted. cm for the wrong variable.. ft a + b = c 7 + b =. 8. cm 9 + b = b = 7 b = 7. a. Sample answer: b. ft 9. and You.. C x Friend Section. Approximating Square Roots (pages 9 ). A rational number can be written as the ratio of two integers. An irrational number cannot be written as the ratio of two integers.. all rational and irrational numbers; Sample answer:, 8, 7. es 7. no 9. rational;. is a repeating decimal.. irrational; 7 is not a perfect square.. rational; 8 can be written as the ratio of two integers. 9. is a perfect square. So, is rational. 7. a. natural number b. irrational number c. irrational number ; is to the right of. 7. ; is to the right of. 9..;. is to the right of... 8 ft. Sample answer: m/sec a = 8, b = Falling objects do not fall at a linear rate. Their speed increases with each second the are falling.. x +. k 9 A

17 Lesson.b Real Numbers (pages A and B) cm..... Create a table of integers whose cubes are close to the radicand. Determine which two integers the cube root is between. Then create another table of numbers between those two integers whose cubes are close to the radicand. Determine which cube is closest to the radicand;. 7. < 9. < 8 Section. Simplifing Square Roots (pages and 7). Sample answer: The square root is like a variable. So, ou add or subtract the number in front to simplif.. about.; es. about.; no You do not add the radicands. + = in ft. a. 88 ft b. 8 ft. Remember to take the square root of each side when solving for r.. in. 7. C. 7 7 Section. Using the Pthagorean Theorem (pages and ). Sample answer: You can plot a point at the origin and then draw lengths that represent the legs. Then, ou can use the Pthagorean Theorem to find the hpotenuse of the triangle m.. d units ft.. m. es. no 7. es 9..8 ft. a. Sample answer: in., 7 in., in. b. Sample answer: BC 8. in.; AB 9. in. c. Check students work.. mean: ; median:.; mode:. mean: 8; median: 9; mode: 9 A

18 Section 7. Measures of Central Tendenc (pages 78 and 79). no; The definition of an outlier means that it is not in the center of the data.. If the outlier is greater than the mean, removing it will decrease the mean. If the outlier is less than the mean, removing it will increase the mean. 9. mean: ; median: ; mode: 7. mean: h; median: h; modes: h and h 9. The calculated the mean, not the median. Test scores: 8, 8, 9, 9, 9, Median = = = 9... a. F b. mean 7. The mean and median both decrease b $.. There is still no mode. 9. 8,,,,, 7. B Section 7.. %; % Box-and-Whisker Plots (pages 8 and 8). The length gives the range of the data set. This tells how much the data var Hours Length (inches) range = 7 7. Elevation (feet). a Calories burned b. 9 calories c. Calories burned d. The outlier makes the right whisker longer, increases the length of the box, increases the third quartile, and increases the median. In this case, the first quartile and the left whisker were not affected.. Sample answer:,,,,,,. Sample answer:, 7, 9,,,, 7. = x + 9. = x. B A7

19 Section 7. Scatter Plots and Lines of Best Fit (pages 9 9). The must be ordered pairs so there are equal amounts of x- and -values.. a b. Weight (pounds) x Pints c. Sample answer: =.7x d. Sample answer: 7. lb e. Sample answer: $.88. a.. h b. $8 c. There is a positive relationship between hours worked and earnings. 7. positive relationship 9. negative relationship. a b. Distance (miles) x Hours c. Sample answer: = x + d. Sample answer: mi. a. positive relationship b. The more time spent studing, the better the test score.. The slope of the line of best fit should be close to Lesson 7.b Two-Wa Tables (pages 9A 9B). a. b. students are attending the dance; students are not attending the dance; students are attending the football game; students are not attending the football game; 7 students were surveed c. about % A8

20 Section 7. Choosing a Data Displa (pages and ). es; Different displas ma show different aspects of the data.. Sample answer:. Sample answer: Line graph: shows changes Notebooks Sold in One Week over time. Number of notebooks Red Pink Black Green Other White Orange Purple Yellow Blue Color A bar graph shows the data in different color categories.. Sample answer: bar graph; Each bar can represent a different vegetable.. Sample answer: line plot 7. Sample answer: Line graph: shows changes changes over time. 9. The pictures of the bikes are larger on Monda, which makes it seem like the distance is the same each da.. The intervals are not the same size. 7. Does one displa better show the differences in digits? 9. 8x = Section 8. Writing and Graphing Inequalities (pages and 7). An open circle would be used because is not a solution.. no; x 9 is all values of x greater than or equal to 9. 9 x is all values of x less than or equal to 9.. x < ; all values of x < 9. k 8. > 8 less than. es. es. no 7.. es x. a. a ; s ; b. es; You satisf the swimming requirement of the course because () = and. t ; 8 7. a. m < n; n p b. m < p c. no; Because n is no more than p and m is less than n, m cannot be equal to p D A9

21 Section 8. Solving Inequalities Using Addition or Subtraction (pages and ). no; The solution of r 8 is r and the solution of 8 r is r.. Sample answer: A =, C = 7, Y =, T =, N =. Sample answer: A =, C = 8, Y =, T = 8, N = 7. t > ; 9. a > 8; > d;. m ;. h <.; u; a. + V 7; V in. b. V 7 in.. x + > ; x > 8.. a. + x,; x 7 points b. This changes the number added to x b %, so the inequalit becomes 7 + x,. So, ou need less points to advance to the next level. 7. π h + π π ; h. mm 9.. Section 8. Solving Inequalities Using Multiplication or Division (pages ). Multipl each side of the inequalit b.. Sample answer: x <. x 7. x 9. x. c ; x < 8; k > ; 7. ; 9. The inequalit sign should not have been reversed. x < x < ( ) x <. x < ; x <. x > ; x > 8..x.; x.; You can make at most copies. A

22 7. n ; 9. h ;. > ; 7 8. m > ; 9 8. b > ; 7. no; You need to solve the inequalit for x. The solution is x <. Therefore, numbers greater than are not solutions. 9. x ; x 8. cm. x < 8; x < $. Answer should include, but is not limited to: Using the correct number of months that the CD has been out. In part (d), an acceptable answer could be never because the top selling CD could have a higher monthl average.. n and n ; 7. m < ; Section 8. Solving Multi-Step Inequalities (pages 8 and 9). Sample answer: The use the same techniques, but when solving an inequalit, ou must be careful to reverse the inequalit smbol when ou multipl or divide b a negative number.. k > and k units. b ; 7. m ;. The did not perform the operations in proper order.. ; 9 9. p < ; x + x x. u < 7; z >.9; x + ; x > and x 8 lines 9. x ; 7 8. Remember to add the height of the truck to find the height the ladder can reach.. r units 7. π in. 9. A A

23 Section 9. Exponents (pages and ). An exponent describes the number of times the base is used as a factor. A power is the entire expression (base and exponent). A power tells ou the value of the factor and the number of factors. No, the two cannot be used interchangeabl... (... ) 7. π x 9. 8 b 7. The exponent describes how man times the base should be used as a factor. Three should not appear as a factor in the product. = = 9. ( ) h h ; The option h pas ou h 7 more mone when h >. h 8 9. Remember to add the black kes when finding how man notes ou travel.. Associative Propert of Multiplication. B Section 9. Product of Powers Propert (pages and ). When multipling powers with the same base.. ( ) 7. h 7 9. ( 7) The bases should not be multiplied. 9 = + 9 = 7. g 9. k. r t. no; + = = and = , 9. a. π. in. b. 9π.88 in. Squaring each of the dimensions causes the volume to be times larger.. Use the Commutative and Associative Properties of Multiplication to group the powers B A

24 Section 9. Quotient of Powers Propert (pages and 7). To divide powers means to divide out the common factors of the numerator and denominator. To divide powers with the same base, write the power with the common base and an exponent found b subtracting the exponent in the denominator from the exponent in the numerator... ( ) ( 7). (.). b. You should subtract the exponents instead of dividing them. = = π 8. k. x. a b 7. x 7 9. You are checking to see if there is a constant rate of change in the prices, not if it is a linear function.. galaxies B Section 9.. no; An nonzero base raised to the zero power is alwas..,,. n n = = = = Zero and Negative Exponents (pages 7 and 7) 7. One-fifth of ; = ( ) = The negative sign goes with the exponent, not the base. () = = 9. ;. a7. b. 7. w 9 9., micrometers.,, micrometers. Convert the blood donation to cubic millimeters before answering the parts.. If a =, then n =. Because ou can not divide b, the expression is undefined D A

25 Section 9. Reading Scientific Notation (pages 8 and 8). Scientific notation uses a factor of at least one but less than multiplied b a power of. A number in standard form is written out with all the zeros and place values included... m., mm 7. es; The factor is at least and less than. The power of has an integer exponent. 9. no; The factor is greater than.. es; The factor is at least and less than. The power of has an integer exponent.. no; The factor is less than.. 7,, ,,,. 9,7,. a. 8,, platelets 7. a. Bellatrix b.,,,, platelets b. Betelgeuse 9. km. Be sure to convert some of the speeds so that the all have the same units.. 7. Section 9. Writing Scientific Notation (pages 8 and 87). If the number is greater than or equal to, the exponent will be positive. If the number is less than and greater than, the exponent will be negative is not less than. The decimal point needs to move one more place to the left m.. cm N m per sec 7. Answer should include, but is not limited to: Make sure calculations using scientific notation are done correctl. 9. a.. 8 b... Lesson 9.b Scientific Notation (pages 87A and 87B) about times greater A

26 Topic Transformations (pages 98 ). 8 P 7 P O Q R Q R x. P P 9 Q 7 R Q O R x P (, 8), Q (, ), R (, 7) P (, ), Q (, 8), R (, ). a. side AB and side CD, side AD and side BC b. Check students work. c. es; Sample answer: A translation creates a congruent figure, so the sides remain parallel. 7. L (, ), M (, ), N (7, ), P (7, ) 9. H (, 7), I (, ), J (, ), K (, 8). a. es; Sample answer: The image is also a rectangle, so each angle measure is 9. b. es; Sample answer: The image is congruent to the original, so side CD is the same length as side C D.. L (, ), M (, ), N (, ), P (, ). O x F G F G E E H E (, ), F (, H ) (, G, ), H (, ); reduction 7. a. es; Triangle JKL is a 9 counterclockwise rotation about the origin of triangle XYZ. b. es; Sample answer: You can create triangle PQR b rotating triangle XYZ 9 counterclockwise about the origin and then dilating the image using a scale factor of. Topic Volume (pages ). π 97.8 m. π.9 in.. π 7.9 cm 7. π 7 cm A

27