Polynomials. Polynomials

Transcription

1 Preview of Algebra 1 Polynomials 1A Introduction to Polynomials 1-1 Polynomials LAB Model Polynomials 1- Simplifying Polynomials 1B Polynomial Operations LAB Model Polynomial Addition 1-3 Adding Polynomials LAB Model Polynomial Subtraction 1- Subtracting Polynomials 1-5 Multiplying Polynomials by Monomials LAB Multiply Binomials 1-6 Multiplying Binomials KEYWORD: MT8CA Ch1 Polynomials can be used to calculate the height of fireworks. Walt Disney Concert Hall, Los Angeles 586 Chapter 1

2 Associative Vocabulary Property Choose the best term from the list to complete each sentence. coefficient 1.? have the same variables raised to the same powers. Distributive. In the epression, is the?. Property 3. 5 ( 3) (5 ) 3 by the?. like terms ( ) by the?. Commutative Property Complete these eercises to review skills you will need for this chapter. Integer Operations Add or subtract () (5) (5) (19) (5) Evaluate Epressions Evaluate the epression for the given value of the variable. 1. ( y ) z for 8, y 3, z 15. 7ab 5 for a 3, b 16. (n 3) for n (t ) for t Simplify Algebraic Epressions Simplify each algebraic epression b a 11 3a 1 0. n 10m 9n Area of Squares, Rectangles, and Triangles Find the area of each figure cm 6 in. 36 cm m 15 in. m Polynomials 587

3 The information below unpacks the standards. The Academic Vocabulary is highlighted and defined to help you understand the language of the standards. Refer to the lessons listed after each standard for help with the math terms and phrases. The Chapter Concept shows how the standard is applied in this chapter. California Standard Preview of Algebra Students add, subtract, multiply, and divide monomials and polynomials. Students solve multistep problems, including word problems, by using these techniques. (Lessons 1-3, 1-, 1-5, 1-6; Labs 1-3, 1-, 1-6) Academic Vocabulary multistep more than one step technique a way of doing something Chapter Concept You use your knowledge of eponents to add, subtract, and multiply polynomials, and you use polynomials to solve problems. Eample: You simplify epressions such as and (3 5 3 ). Standards AF1. and AF1.3 are also covered in this chapter. To see these standards unpacked, go to Chapter 1, p. (AF1.) and Chapter 3, p. 11 (AF1.3). 588 Chapter 1

4 Study Strategy: Study for a Final Eam A cumulative final eam will cover material you have learned over the course of the year. You must be prepared if you want to be successful. It may help you to make a study timeline like the one below. weeks before the final: Look at previous eams and homework to determine areas I need to focus on; rework problems that were incorrect or incomplete. Make a list of all formulas I need to know for the final. Create a practice eam using problems from the book that are similar to problems from each eam. 1 week before the final: Take the practice eam and check it. For each problem I miss, find two or three similar problems and work those. Work with a friend in the class to quiz each other on formulas from my list. 1 day before the final: Make sure I have pencils and scratch paper. Try This Complete the following to help you prepare for your cumulative test. 1. Create a timeline that you will use to study for your final eam. Polynomials 589

5 1-1 Polynomials California Standards Preview of Algebra 1 Preparation for 10.0 Students add, subtract, multiply, and divide monomials and polynomials. Students solve multistep problems, including word problems, by using these techniques. Also covered: 7AF1. Why learn this? You can use polynomials to find the height of a firework when it eplodes. (See Eample.) Recall that a monomial is a number, variable, or a product of numbers and variables with eponents that are whole numbers. Monomials n, 3, a b 3, 7 Not monomials p.,,, g 5 EXAMPLE 1 Vocabulary polynomial bionomial trinomial degree of a polynomial Identifying Monomials Determine whether each epression is a monomial. 1 3 y 7 10y 0.3 monomial not a monomial and 7 are whole numbers. 0.3 is not a whole number. A polynomial is one monomial or the sum or difference of monomials. A simplified polynomial can be classified by the number of monomials, or terms, that it contains. A monomial has 1 term, a binomial has terms, and a trinomial has 3 terms. EXAMPLE Classifying Polynomials by the Number of Terms Classify each epression as a monomial, a binomial, a trinomial, or not a polynomial h 19.55g binomial Polynomial with terms 3 y monomial Polynomial with 1 term 6 y can be written as 1, where the not a polynomial eponent is not a whole number. 7mn m 5n trinomial Polynomial with 3 terms 590 Chapter 1 Polynomials

6 The degree of a term is the sum of the eponents of the variables in the term. The degree of a polynomial is the same as the degree of the term with the greatest degree. A polynomial can be classified by its degree. 5 y { { Degree Degree 5 Degree Degree 0 13 Degree 5 EXAMPLE 3 Classifying Polynomials by Their Degrees Find the degree of each polynomial Degree Degree 1 Degree 0 The greatest degree is, so the degree of 6 3 is. 6 3m m 5 6 3m m 5 Degree 0 Degree Degree 5 The greatest degree is 5, so the degree of 6 3m m 5 is 5. To evaluate a polynomial, substitute the given number for each variable. EXAMPLE A polynomial is an algebraic epression. For help with evaluating algebraic epressions, see Lesson 1-1. Physics Application The height in feet of a firework launched straight up into the air from s feet off the ground at velocity v after t seconds is given by the polynomial 16t vt s. Find the height of a firework launched from a 10 ft platform at 00 ft/s after 5 seconds. 16t vt s Write the polynomial epression for height. 16(5) 00(5) 10 Substitute 5 for t, 00 for v, and 10 for s Simplify. The firework is 610 feet high 5 seconds after launching. Think and Discuss 1. Describe two ways you can classify a polynomial. Give a polynomial with three terms, and classify it two ways.. Eplain why 5 3 is a polynomial but 5 3 is not. 1-1 Polynomials 591

7 1-1 Eercises See Eample 1 GUIDED PRACTICE California Standards Practice Preparation for Algebra ; 7AF1. Determine whether each epression is a monomial. 1. y KEYWORD: MT8CA 1-1 KEYWORD: MT8CA Parent See Eample See Eample 3 See Eample Classify each epression as a monomial, a binomial, a trinomial, or not a polynomial y 6. 5r 3r Find the degree of each polynomial. 9. 7m 5 3m The trinomial 16t t 7 describes the height in feet of a ball thrown straight up from a 7 ft platform with a velocity of ft/s after t seconds. What is the ball s height after seconds? See Eample 1 See Eample See Eample 3 See Eample INDEPENDENT PRACTICE Determine whether each epression is a monomial y y Classify each epression as a monomial, a binomial, a trinomial, or not a polynomial m n g 3 1 h a v 3 s Find the degree of each polynomial m m p 7p 9. n 30. 3y The volume of a bo with height, length, and width 3 5 is given by the trinomial What is the volume of the bo if its height is inches? Etra Practice See page EP. PRACTICE AND PROBLEM SOLVING 3. Transportation The distance in feet required for a car traveling at r r mi/h to come to a stop can be approimated by the binomial r. 0 About how many feet will be required for a car to stop if it is traveling at 70 mi/h? 59 Chapter 1 Polynomials

8 Classify each epression as a monomial, a binomial, a trinomial, or not a polynomial. If it is a polynomial, give its degree y 6y 37. f 3 5f 5 f b 9b 8b Transportation Gas mileage at speed s in miles per hour can be estimated using the given polynomials. Evaluate the polynomials to complete the table. Compact Midsize Van 0.05s +.5s s + 1.5s s +.9s 53 Gas Mileage (mi/gal) 0 mi/h 50 mi/h 60 mi/h 6. Reasoning Without evaluating, tell which of the following binomials has the greatest value when 10. Eplain what method you used. A B C 3 8 D What s the Error? A student says that the degree of the polynomial b 5 7b 9 6b is 5. What is the error? 8. Write About It Give some eamples of words that start with mono-, bi-, tri-, and poly-, and relate the meaning of each to polynomials. 9. Challenge The base of a triangle is described by the binomial, and its height is described by the trinomial 3 7. What is the area of the triangle if 5? NS1.1, NS., AF Multiple Choice The height in feet of a soccer ball kicked straight up into the air from s feet off the ground at velocity v after t seconds is given by the trinomial 16t vt s. What is the height of the soccer ball kicked from feet off the ground at 90 ft/s after 3 seconds? A 3 ft B 15 ft C 90 ft D 18 ft 51. Gridded Response What is the degree of the polynomial 6 7k 8k 9? Write each number in scientific notation. (Lesson -5) 5.,080, ,910,000,000 Find the two square roots of each number. (Lesson -6) Polynomials 593

9 Model Polynomials 1-1 Use with Lesson 1-1 KEY REMEMBER KEYWORD: MT8CA Lab1 0 California Standards Preview of Algebra 1 Preparation for 10.0 Students add, subtract, multiply, and divide monomials and polynomials. Students solve multistep problems, including word problems, by using these techniques. You can use algebra tiles to model polynomials. To model the polynomial 3, you need four -tiles, one -tile, and three 1-tiles Activity 1 1 Use algebra tiles to model the polynomial 6. All signs are positive, so use all yellow tiles Chapter 1 Polynomials

10 Use algebra tiles to model the polynomial 6. Modeling 6 is similar to modeling 6. Remember to use red tiles for negative values Think and Discuss 1. How do you know when to use red tiles? Try This Use algebra tiles to model each polynomial Activity 1 Write the polynomial modeled by the algebra tiles below The polynomial modeled by the tiles is Think and Discuss 1. How do you know the coefficient of the -term in Activity? Try This Write a polynomial modeled by each group of algebra tiles Hands-On Lab 595

11 1- Simplifying Polynomials California Standards Preview of Algebra 1 Preparation for 10.0 Students add, subtract, multiply, and divide monomials and polynomials. Students solve multistep problems, including word problems, by using these techniques. Also covered: 7AF1.3 Why learn this? You can simplify polynomials to determine the amount of lumber that can be harvested from a tree. (See Eample.) You can simplify a polynomial by adding or subtracting like terms. Like terms The variables have the same powers. Not like terms The variables have different powers. EXAMPLE 1 Identifying Like Terms Identify the like terms in each polynomial. a a 3 5a 6a a a 3 5a 6a Like terms: a and 5a; a and 6a 5 y y y 3 5 y y y 3 Like terms: 5 y 3, 1 5 y 3, and 6 5 y 3 5m 3mn m 5m 3mn m There are no like terms. Identify like terms. Identify like terms. Identify like terms. To simplify a polynomial, combine like terms. First arrange the terms from highest degree to lowest degree by using the Commutative Property. EXAMPLE When you rearrange terms, move the operation symbol in front of each term with that term. Simplifying Polynomials by Combining Like Terms Simplify Identify like terms. Commutative Property Combine coefficients: and Chapter 1 Polynomials

12 Simplify. 5a b 1ab a b ab 3ab 5a b 1ab a b ab 3ab Identify like terms. 5a b a b 1ab ab 3ab 9a b 11ab 3ab Commutative Property Combine coefficients: 5 9 and You may need to use the Distributive Property to simplify a polynomial. EXAMPLE 3 Simplifying Polynomials by Using the Distributive Property Simplify. (3 5) (3 5) Distributive Property (3 ) (5) 1 0 No like terms (ab 5b) 3ab 6 (ab 5b) 3ab 6 (ab ) (5b) 3ab 6 8ab 10b 3ab 6 11ab 10b 6 Distributive Property Identify like terms. Combine coefficients. EXAMPLE Business Application A board foot is equal to the volume of a 1 ft by 1 ft by 1 in. piece of lumber. The amount of lumber that can be harvested from a tree with diameter d in. is approimately (d 3 30d 300d 1000) board feet. Use the Distributive Property to write an equivalent epression (d 3 30d 300d 1000) d d 1.5d d d 1.5d Think and Discuss 1. Tell how you know when you can combine like terms.. Give an eample of an epression that you could simplify by using the Distributive Property. Then give an epression that you could simplify by combining like terms. 1- Simplifying Polynomials 597

13 1- Eercises California Standards Practice Preparation for Algebra ; 7AF1.3 KEYWORD: MT8CA 1- KEYWORD: MT8CA Parent GUIDED PRACTICE See Eample 1 Identify the like terms in each polynomial. 1. 3b 5b b b 6. 7mn 5m n 8m n m n See Eample Simplify b b 7b 9 b 3b See Eample 3 See Eample 5. (3 8) 6. 7( ) 7. 5(3a 5a) a a 8. The level of nitric oide emissions, in parts per million, from a car engine is approimated by the polynomial 0,000 5(800 ), where is the air-fuel ratio. Use the Distributive Property to write an equivalent epression. INDEPENDENT PRACTICE See Eample 1 Identify the like terms in each polynomial. 9. t t 5t 5t 10. 8rs 3r s 5r s rs 5 See Eample Simplify. 11. p 3p 5p 1p 1. 3fg f g fg 3fg f g 6fg See Eample 3 See Eample Etra Practice See page EP ( 5) 7 1. (b 3) 5b 3b (6y3 8) 3y The concentration of a certain medication in an average person s bloodstream h hours after injection can be estimated using the epression 6(0.03h 0.00h 0.01h 3 ). Use the Distributive Property to write an equivalent epression. PRACTICE AND PROBLEM SOLVING Simplify. 17. s 3s 10s 5s gh g h g h g h 19. ( 5 ) ( 5 3 ) 3 1. (m 3m ) 7(3m m). 6b b 3(b 6) 3. 5mn 3m 3 n 3(m 3 n mn). 3( y) (3 y) 598 Chapter 1 Polynomials 5. Life Science The rate of flow in cm/s of blood in an artery at d cm from the center is given by the polynomial 1000(0.0 d ). Use the Distributive Property to write an equivalent epression.

14 Art Abstract artists often use geometric shapes, such as cubes, prisms, pyramids, and spheres, to create sculptures. 6. Suppose the volume of a sculpture is approimately s 3 0.5s s s 3 cm 3 and the surface area is approimately 6s 3.1s 7.6s 3.s cm. a. Simplify the polynomial epression for the volume of the sculpture, and find the volume of the sculpture for s 5. b. Simplify the polynomial epression for the surface area of the sculpture, and find the surface area of the sculpture for s 5. Balanced/Unbalanced O by Fletcher Benton 7. A sculpture features a large ring with an outer lateral surface area of about y in, an inner lateral surface area of about 38y in, and bases, each with an area of about 1y in. Write and simplify a polynomial that epresses the surface area of the ring. 8. Challenge The volume of the ring on the sculpture from Eercise 7 is 9πy 36πy in 3. Simplify the polynomial, and find the volume for 1 and y 7.5. Give your answer both in terms of π and to the nearest tenth. Pyramid Balancing Cube and Sphere, artist unknown KEYWORD: MT8CA Art NS1.3, AF Multiple Choice Simplify the epression A B C D Short Response Identify the like terms in the polynomial 3 5. Then simplify the polynomial. Find each percent to the nearest tenth. (Lesson 6-3) 31. What percent of 8 is? 3. What percent of 195 is 16? Create a table for each quadratic function, and use it to graph the function. (Lesson 7- ) 33. y 1 3. y 1 1- Simplifying Polynomials 599

15 Quiz for Lessons 1-1 Through Polynomials Determine whether each epression is a monomial c d 8 Classify each epression as a monomial, a binomial, a trinomial, or not a polynomial a 3 a y Find the degree of each polynomial. 7. u c c 5 c The depth, in feet below the ocean surface, of a submerging eploration submarine after y minutes can be approimated by the polynomial 0.001y 0.1y 3 3.6y. Estimate the depth after 5 minutes. 1- Simplifying Polynomials Identify the like terms in each polynomial y y y 1. z 7z z z t 8 t ab 3ac 5bc ac 6ab Simplify b 5 b 3 7 5b y y 7y y ( 7) y 5 5y (5y ) 19. The area of one face of a cube is given by the epression 3s 5s. Write a polynomial to represent the total surface area of the cube. 0. The area of each lateral face of a regular square pyramid is given by the epression 1 b b. Write a polynomial to represent the lateral surface area of the pyramid. 600 Chapter 1 Polynomials

16 California Standards MR.1 Use estimation to verify the reasonableness of calculated results. Also covered: NS1.7 Look Back Estimate to check that your answer is reasonable Before you solve a word problem, you can often read through the problem and make an estimate of the correct answer. Make sure your answer is reasonable for the situation in the problem. After you have solved the problem, compare your answer with the original estimate. If your answer is not close to your estimate, check your work again. Each problem below has an incorrect answer given. Eplain why the answer is not reasonable, and give your own estimate of the correct answer. 1 The perimeter of rectangle ABCD is 8 cm. What is the value of? A 9 B C Answer: 5 D A patio layer can use 6y ft of accent edging to divide a patio into three sections measuring ft long by y ft wide. If each section must be at least 15 ft long and have an area of at least 165 ft, what is the minimum amount of edging needed for the patio? 3 y ft ft A baseball is thrown straight up from a height of 3 ft at 30 mi/h. The height of the baseball in feet after t seconds is 16t t 3. How long will it take the baseball to reach its maimum height? Answer: 5 minutes Jacob deposited $000 in a savings account that earns 6% simple interest. How much money will he have in the account after 7 years? Answer: $195 Answer: 5 ft Focus on Problem Solving 601

17 1-3 Model Polynomial Addition Use with Lesson 1-3 KEY REMEMBER KEYWORD: MT8CA Lab1 0 California Standards Preview of Algebra Students add, subtract, multiply, and divide monomials and polynomials. Students solve multistep problems, including word problems, by using these techniques. You can use algebra tiles to model polynomial addition. Activity 1 Use algebra tiles to find ( 3) ( 5). 3 5 Use tiles to represent all terms from both epressions. Remove any zero pairs. The remaining tiles represent the sum 3. 3 Think and Discuss 1. Eplain what happens when you add the -terms in ( 5) ( ). Try This Use algebra tiles to find each sum. 1. (3m m 6) (m m 3). (5b b 1) (b 1) 60 Chapter 1 Polynomials

18 1-3 Adding Polynomials California Standards Preview of Algebra Students add, subtract, multiply, and divide monomials and polynomials. Students solve multistep problems, including word problems, by using these techniques. Also covered: 7AF1.3 Why learn this? You can add polynomials to find the amount of material needed to mat and frame a picture. (See Eample 3.) Adding polynomials is similar to simplifying polynomials. One way to add polynomials is to write them horizontally. First write the polynomials as one polynomial, and then use the Commutative Property to combine like terms. EXAMPLE 1 Adding Polynomials Horizontally Add. (6 3 ) (7 6) (cd 3cd 6) (7cd 6cd 6) cd 3cd 6 7cd 6cd 6 cd 6cd 3cd 7cd cd cd (ab a) (3ab a 3) (a 5) ab a 3ab a 3 a 5 ab 3ab a a a 3 5 ab 9a Write as one polynomial. Commutative Property Combine like terms. Write as one polynomial. Commutative Property Combine like terms. Write as one polynomial. Commutative Property Combine like terms. You can also add polynomials in a vertical format. Write the second polynomial below the first one. Be sure to line up the like terms. If the terms are rearranged, remember to keep the correct sign with each term. 1-3 Adding Polynomials 603

19 EXAMPLE Adding Polynomials Vertically Add. (5a a ) (a 3a 1) 5a a a 3a 1 Place like terms in columns. 9a 7a 3 Combine like terms. (y 3 y) (8y 3) y 3 y 8y 3 Place like terms in columns. 10y y 3 Combine like terms. (a b 3a 6ab) (ab a 5) (3 7ab) a b 3a 6ab a ab 5 7ab 3 Place like terms in columns. a b a 3ab Combine like terms. EXAMPLE 3 Reasoning Art Application 1 in. Mina is putting a mat of width m and a frame of width f around f 11 in. an 11-inch by 1-inch picture. Find m m f an epression for the amount of framing material she needs. m The amount of material Mina f needs equals the perimeter of the outside of the frame. Draw a diagram to help you determine the outer dimensions of the frame. Width 1 m m f f 1 m f P (11 m f ) (1 m f ) m f 8 m f 50 8m 8f Length 11 m m f f 11 m f P w She will need 50 8m 8f inches of framing material. f m Simplify. Combine like terms. Think and Discuss 1. Compare adding (5 ) (3 ) vertically with adding it horizontally.. Eplain how adding polynomials is similar to simplifying polynomials. 60 Chapter 1 Polynomials

20 1-3 Eercises See Eample 1 GUIDED PRACTICE Add. 1. ( ) (3 7) California Standards Practice Preview of Algebra ; 7AF1.3 KEYWORD: MT8CA 1-3 KEYWORD: MT8CA Parent. ( 6) (1 3) 3. (r s 3rs) (r s 8rs) (6r s 1rs) See Eample. (b 5b 10) (6b 7b 8) 5. (9ab 5ab 6a b) (8ab 1a b 6) (6ab 5a b 1) 6. (h j hj 3 hj 6) (5hj 3 5) (6h j 7hj) See Eample 3 7. Colette is putting a mat of width 3w and a frame of width w around a 16-inch by 8-inch poster. Find an epression for the amount of frame material she needs. 16 in. 3w 8 in. w w 3w See Eample 1 INDEPENDENT PRACTICE Add. 8. (5 y y 3) (7y 3 y) 9. (5g 9) (7g g 8) 10. (6bc b c 8bc ) (6bc 3bc ) 11. (9h 5h h 6 ) (h 6 6h 3h ) 1. (pq 5p q 9pq ) (6p q 11pq ) (pq 7pq 6p q) See Eample 13. (8t t 3) (5t 8t 9) 1. (5b 3 c 3b c bc) (8b 3 c 3bc 1) (b c 5bc 9) 15. (w 3w 5) (w 3w 1) (w w 6) See Eample Each side of an equilateral triangle has length w 3. Each side of a square has length w. Write an epression for the sum of the perimeter of the equilateral triangle and the perimeter of the square. w 3 w 1-3 Adding Polynomials 605

21 Etra Practice See page EP5. PRACTICE AND PROBLEM SOLVING Add. 17. (3w y 3wy wy) (5wy wy 7w y) (wy 5wy 3w y) 18. (p t 3pt 5) (p t pt 3pt) (1 5pt p t) Business 19. Geometry Write and simplify an epression for the combined volumes of a sphere with volume 3 πr 3, a cube with volume r 3, and a prism with volume r 3 r 5r. Use 3.1 for π. 0. Business The cost of producing n toys at a factory is given by the polynomial 0.5n 3n 1. The cost of packaging is 0.5n 5n. Write and simplify an epression for the total cost of producing and packaging n toys. According to the Toy Industry Association, $.6 billion was spent on toys worldwide in 000. KEYWORD: MT8CA Toys 1. Reasoning Two airplanes depart from the same airport, traveling in opposite directions. After hours, one airplane is 00 miles from the airport, and the other airplane is miles from the airport. How could you determine the distance between the two planes? Eplain.. Write two polynomials whose sum is 3m m Choose a Strategy What is the missing term? (6 3) (3 5) A B C 10 D 10. Write a Problem A plane leaves an airport heading north at 3 mi/h. At the same time, another plane leaves the same airport, heading south at mi/h. Write a problem using the speeds of both planes. 5. Write About It Eplain how to add polynomials. 6. Challenge What polynomial would have to be added to 6 5 so that the sum is 3 7? NS1.5, MG1. 7. Multiple Choice Debbie is putting a deck of width 5w around her 0 foot by 80 foot pool. Which is the epression for the perimeter of the pool and deck combined? A w w 00 0w 50 5w B C D 8. Gridded Response What is the sum of ( ), ( ), and ( )? Find the fraction equivalent of each decimal. (Lesson -1) Using the scale 1 in. 6 ft, find the height or length of each object. (Lesson 5-7) 33. a 1 in. tall model of an office building 3. a.5 in. long model of a train 606 Chapter 1 Polynomials

22 1- Use with Lesson 1- Model Polynomial Subtraction KEY REMEMBER KEYWORD: MT8CA Lab1 0 California Standards Preview of Algebra Students add, subtract, multiply, and divide monomials and polynomials. Students solve multistep problems, including word problems, by using these techniques. You can use algebra tiles to model polynomial subtraction. Activity 1 Use algebra tiles to find ( 3) ( 3). 3 3 Remember, subtracting is the same as adding the opposite. Use the opposite of each term in Remove any zero pairs. The remaining tiles represent the difference 3 6. Think and Discuss 1. Why do you have to add the opposite when subtracting? Try This Use algebra tiles to find each difference. 1. (6m m) (m ). (5b 9) (b 9) 1- Hands-On Lab 607

23 1- Subtracting Polynomials California Standards Preview of Algebra Students add, subtract, multiply, and divide monomials and polynomials. Students solve multistep problems, including word problems, by using these techniques. Also covered: 7AF1.3 Who uses this? Manufacturers can subtract polynomials to estimate the cost of making a product and the revenue from sales. (See Eample.) Recall that to subtract an integer, you add its opposite. To subtract a polynomial, you first need to find its opposite. EXAMPLE 1 Finding the Opposite of a Polynomial Find the opposite of each polynomial. 8 3 y 6 z (8 3 y 6 z) The opposite of a positive term 8 3 y 6 z is a negative term. 1 5 (1 5) 1 5 3ab ab 3 (3ab ab 3) 3ab ab 3 Distributive Property Distributive Property To subtract a polynomial, add its opposite. EXAMPLE Subtracting Polynomials Horizontally Subtract. (n 3 n 5n ) (7n n 9) (n 3 n 5n ) (7n n 9) Add the opposite. n 3 5n n n 7n 9 Commutative Property n 3 9n 8n 9 Combine like terms. (cd cd ) (7cd 5cd ) (cd cd ) (7cd 5cd) cd 7cd cd 5cd 5cd 6cd Add the opposite. Commutative Property Combine like terms. 608 Chapter 1 Polynomials

24 You can also subtract polynomials in a vertical format. Write the second polynomial below the first one, lining up the like terms. EXAMPLE 3 Subtracting Polynomials Vertically Subtract. ( 3 1) ( ) ( 3 1) 3 1 ( ) Add the opposite. 5 3 (m n 3mn m) (8m n 6mn 3) (m n 3mn m) m n 3mn m (8m n 6mn 3) 8m n 6mn 3 Add the 1m n 3mn m 3 opposite. ( y y 6) (7 5y 6) ( y y 6) y y 6 (7 5y 6) 5y 7 6 Rearrange terms y y 13 6 as needed. EXAMPLE Business Application Suppose the cost in dollars of producing model kits is given by the polynomial 3 00,000 and the revenue generated from sales is given by the polynomial Find a polynomial epression for the profit from making and selling model kits, and evaluate the epression for 00, (3 00,000) (3 00,00) , ,000 revenue cost Add the opposite. Commutative Property Combine like terms. The profit is given by the polynomial ,000. For 00,000, (00,000) 17(00,000) 00,000 1,00,000. The profit is $1,00,000, or $1. million. Think and Discuss 1. Eplain how to find the opposite of a polynomial.. Compare subtracting polynomials with adding polynomials. 1- Subtracting Polynomials 609

25 1- Eercises California Standards Practice Preview of Algebra ; 7AF1.3 KEYWORD: MT8CA 1- KEYWORD: MT8CA Parent GUIDED PRACTICE See Eample 1 Find the opposite of each polynomial. 1. y. 5 y y y y y See Eample Subtract. 7. (b 3 5b 8) (b 3 b 1) 8. 7b (b 3b 1) 9. (m n 7mn 3mn ) (5mn m n) See Eample (8 1) (5 3) 11. ( y y 3 ) (y 7 ) 1. (5ab ab 3a b) (7 5ab 3ab a b) See Eample 13. The volume of a rectangular prism, in cubic inches, is given by the epression The volume of a smaller rectangular prism is given by the epression How much greater is the volume of the larger rectangular prism? Evaluate the epression for 3. See Eample 1 INDEPENDENT PRACTICE Find the opposite of each polynomial. 1. rn 15. 3v 5v 16. m 6m 17. y y 18. 8n 6 5n 3 n 19. 9b b 9 See Eample Subtract. 0. (6w 3w 6) (3w w 5) 1. (1a a ) (8 a 9a). (7r s 5rs 6r s 7rs) (3rs 3r s 8rs) See Eample 3 3. ( 6 1) (3 9 5). (3a b ab a ) (a b 5a 3b 6) 5. (pt 6p 3 5p t ) (5p 6pt 7p t ) See Eample 6. The current in an electrical circuit at t seconds is t 3 5t t 00 amperes. The current in another electrical circuit is 3t 3 t 5t 100 amperes. Write an epression to show the difference in the two currents. 610 Chapter 1 Polynomials

26 Etra Practice See page EP5. PRACTICE AND PROBLEM SOLVING Subtract. 7. (6a 3b 5ab) (6a 5b 7ab) 8. (pq 6p q 3pq) (7pq 7p q 3pq) 9. (9y 5 y ) (3y 7 y ) 30. The area of the rectangle is a a 5 cm. The area of the square is a a 6 cm. What is the area of the shaded region? 31. The area of the square is 6 in. The area of the triangle is 5 in. What is the area of the shaded region? 3. Business The price in dollars of one share of stock after y years is modeled by the epression 3y 3 6y.5. The price of one share of another stock is modeled by 3y 3 y 5.5. What epression shows the difference in price of the two stocks after y years? 33. Choose a Strategy Which polynomial has the greatest value when 6? A B 3 8 C D Write About It Eplain how to subtract the polynomial from Challenge Find the values of a, b, c, and d that make the equation true. (t 3 at bt 6) (ct 3 t 7t 1) t 3 5t 15t d AF1., AF1.3, AF. 36. Multiple Choice What is the opposite of the polynomial a b 3ab 5ab? A a b 3ab 5ab C a b 3ab 5ab B a b 3ab 5ab D a b 3ab 5ab 37. Etended Response A square has an area of A triangle inside the square has an area of. Create an epression for the area of the square minus the area of the triangle. Evaluate the epression for 8. Multiply. (Lesson -) 38. (3)(6) 39. (9m 3 )(7m ) 0. (8ab )(5a ) 1. (r s)(r 6 s 9 ) Simplify. (Lesson 1-). 3 y y 3 y 3. (zy 3 zy) 3zy 5zy 3. 6(3 6 1) 1- Subtracting Polynomials 611

27 1-5 Multiplying Polynomials by Monomials California Standards Preview of Algebra Students add, subtract, multiply, and divide monomials and polynomials. Students solve multistep problems, including word problems, by using these techniques. Also covered: 7AF1., 7AF1.3, 7AF. Why learn this? You can multiply polynomials and monomials to determine the dimensions of a planter bo. (See Eample 3.) Remember that when you multiply two powers with the same bases, you add the eponents. To multiply two monomials, multiply the coefficients and add the eponents of the variables that are the same. (5m n 3 )(6m 3 n 6 ) 5 6 m 3 n m 5 n 9 EXAMPLE 1 Multiplying Monomials Multiply. (r 3 s )(6r 5 s 6 ) 6 r 3 5 s 6 Multiply coefficients. Add eponents that r 8 s 10 have the same base. (9 y)( 3 yz 6 ) 9 3 y 1 1 z 6 Multiply coefficients. Add eponents that 18 5 y z 6 have the same base. To multiply a polynomial by a monomial, use the Distributive Property. Multiply every term of the polynomial by the monomial. EXAMPLE Multiplying a Polynomial by a Monomial Multiply. 1 (y z) 1 (y z) Multiply each term in the parentheses by 1. 1 y 1 z When multiplying a polynomial by a negative monomial, be sure to distribute the negative sign. 5a b(3a b 3 6a b 3 ) 5a b(3a b 3 6a b 3 ) Multiply each term in the parentheses 15a 6 b 30a b by 5a b. 61 Chapter 1 Polynomials

28 Multiply. 5rs (r s 3rs 3 rst) 5rs (r s 3rs 3 rst) Multiply each term in the 5r 3 s 6 15r s 5 0r s 3 t parentheses by 5rs. EXAMPLE 3 PROBLEM SOLVING APPLICATION Chrystelle is making a planter bo with a square base. She wants the height of the bo to be 3 inches more than the side length of the base. If she wants the volume of the bo to be 680 in 3, what should the side length of the base be? Reasoning 1. 1 Understand the Problem If the side length of the base is s, then the height is s 3. The volume is s s (s 3) s (s 3). The answer will be a value of s that makes the volume of the bo equal to 680 in Make a Plan You can make a table of values for the polynomial to try to find the value of s. Use the Distributive Property to write the epression s (s 3) another way. Use substitution to complete the table Solve s (s 3) s 3 3s Distributive Property s s 3 3s (15) (16) (17) (18) The side length of the base should be 18 inches. 1. Look Back If the side length of the base were 18 inches and the height were 3 inches more, or 1 inches, then the volume would be in 3. The answer is reasonable. Think and Discuss 1. Compare multiplying two monomials with multiplying a polynomial by a monomial. 1-5 Multiplying Polynomials by Monomials 613

29 1-5 Eercises See Eample 1 See Eample GUIDED PRACTICE California Standards Practice Preview of Algebra ; 7AF1., 7AF1.3, 7AF. Multiply. 1. (5s t )(3st 3 ). ( y 3 )(6 y 3 ) 3. (5h j )(7h j 6 ). 6m(m 5 ) 5. 7p 3 r(5pr ) 6. 13g 5 h 3 (10g 5 h ) 7. h(3m h) 8. ab(a b ab ) KEYWORD: MT8CA 1-5 KEYWORD: MT8CA Parent 9. 3( 5 10) 10. 6c d(3cd 3 5c 3 d cd ) See Eample 3 See Eample The formula for the area of a trapezoid is A 1 h(b 1 b ), where h is the trapezoid s height and b 1 and b are the lengths of its bases. Use the Distributive Property to simplify the epression. Then use the epression to find the area of a trapezoid with height 1 in. and base lengths 9 in. and 7 in. INDEPENDENT PRACTICE Multiply. 1. (6 y 5 )(3y ) 13. (gh 3 )(g h 5 ) 1. (a b)(b 3 ) 15. (s t 3 )(st) y y 17..5j 3 (3h 5 j 7 ) See Eample See Eample 3 Etra Practice See page EP (3m 3 n )(1 5mn 5 ) 19. 3z(5z z) 0. 3h (6h 3h 3 ) 1. 3cd(c 3 d cd ). b(b 7b 10) 3. 3s t (s t 5st s t ). A rectangle has a base of length 3 y and a height of 3 y 3. Write and simplify an epression for the area of the rectangle. Then find the area of the rectangle if and y 1. PRACTICE AND PROBLEM SOLVING Multiply. 5. (3b )(8b ) 6. (m n)(mn ) 7. (a b )(3ab ) 8. 7g(g 5) 9. 3m (m 3 5m) 30. ab(3a b 3ab ) 31. ( 3 y 5 ) 3. m( 3) 33. f g (3 f g 3 ) 3. ( 9) 35. (m p )(5m p 3mp 3 6m p) 36. 3wz(5w z wz 6w z ) 37. Feli is building a cylindrical-shaped storage container. The height of the container is 3 y 3. Write and simplify an epression for the volume using the formula V πr h. Then find the volume with r 1 1 feet, 3, and y Chapter 1 Polynomials

30 38. Health The table gives some formulas for finding the target heart rate for a person of age a eercising at p percent of his or her maimum heart rate. Target Heart Rate Male Female Nonathletic p(0 a) p(6 a) Fit 1 p(10 a) 1 p( a) a. Use the Distributive Property to simplify each epression. b. Use your answer from part a to write an epression for the difference between the target heart rate for a fit male and for a fit female. Both people are age a and are eercising at p percent of their maimum heart rates. 39. What s the Question? A square prism has a base area of and a height of 3. If the answer is 3 3, what is the question? If the answer is 1 16, what is the question? 0. Write About It If a polynomial is multiplied by a monomial, what can you say about the number of terms in the answer? What can you say about the degree of the answer? 1. Challenge On a multiple-choice test, if the probability of guessing each question correctly is p, then the probability of guessing two or more correctly out of four is 6p (1 p p ) p 3 (1 p) p. Simplify the epression. Then write an epression for the probability of guessing fewer than two out of four correctly. AF1.3, MG.1. Multiple Choice The width of a rectangle is 13 feet less than twice its length. Which of the following shows an epression for the area of the rectangle? A 13 B 13 C 13 D Short Response A triangle has base 10cd and height 3c d cd. Write and simplify an epression for the area of the triangle. Then evaluate the epression for c and d 3. Combine like terms. (Lesson 3-). 8 3y 7 5. m n 7 n a 11 6b 10a 7b Find the surface area of each figure. Use 3.1 for π. (Lesson 10-) 7. a rectangular prism with base in. by 3 in. and height.5 in. 8. a cylinder with radius 10 cm and height 7 cm 1-5 Multiplying Polynomials by Monomials 615

31 Multiply Binomials 1-6 Use with Lesson 1-6 KEY REMEMBER The area of a rectangle with base b and height h is given by A bh. California Standards KEYWORD: MT8CA Lab1 Preview of Algebra Students add, subtract, multiply, and divide monomials and polynomials. Students solve multistep problems, including word problems, by using these techniques. 1 1 You can use algebra tiles to find the product of two binomials. Activity 1 1 To model ( 3)( 1) with algebra tiles, make a rectangle with base 3 and height Area ( 3)( 1) 7 3 Use algebra tiles to find ( )( 1). 1 Area ( )( 1) 3 Think and Discuss 1. Eplain how to determine the signs of each term in the product when you are multiplying ( 3)( ).. How can you use algebra tiles to find ( 3)( 3)? 616 Chapter 1 Polynomials

32 Try This Use algebra tiles to find each product. 1. ( )( ). ( 3)( ) 3. ( 5)( 3) Activity Write two binomials whose product is modeled by the algebra tiles below, and then write the product as a polynomial epression. The base of the rectangle is 5 and the height is, so the binomial product is ( 5)( ). The model shows one -tile, seven -tiles, and ten 1-tiles, so the polynomial epression is Think and Discuss 1. Write an epression modeled by the algebra tiles below. How many zero pairs are modeled? Describe them. Try This Write two binomials whose product is modeled by each set of algebra tiles below, and then write the product as a polynomial epression Hands-On Lab 617

33 1-6 Multiplying Binomials California Standards Preview of Algebra Students add, subtract, multiply, and divide monomials and polynomials. Students solve multistep problems, including word problems, by using these techniques. Vocabulary FOIL Why learn this? You can multiply binomials to determine the area of a walkway around a cactus garden. (See Eample.) You can use the Distributive Property to multiply two binomials. 678 ( y)( z) ( z) y( z) First z y yz The product can be simplified using the FOIL method: multiply the First terms, the Outer terms, the Inner terms, and the Last terms of the binomials. Last F O I L Inner Outer EXAMPLE 1 When you multiply two binomials, you will get four products. Then combine like terms. Multiplying Two Binomials Multiply. (p )(3 q) (m n)(p q) (p )(3 q) FOIL (m n)(p q) 3p pq 6 q mp mq np nq ( )( 5) (3m n)(m n) ( )( 5) FOIL (3m n)(m n) m 6mn mn n 7 10 Combine like terms. 3m 5mn n 618 Chapter 1 Polynomials

34 EXAMPLE Landscaping Application Find the area of a bark walkway of width ft around a 1 ft by 5 ft cactus garden. Area of Area of Walkway Total Area Flower Bed (5 )(1 ) (5)(1) The walkway area is 3 ft. Binomial products of the form (a b), (a b), and (a b)(a b) are often called special products. EXAMPLE 3 Special Products of Binomials Multiply. ( 3) (a b) ( 3)( 3) (a b)(a b) a ab ab b 6 9 a ab b (n 3)(n 3) (n 3)(n 3) n 3n 3n 3 n 9 3n 3n 0 Special Products of Binomials (a b) a ab ab b a ab b (a b) a ab ab b a ab b (a b)(a b) a ab ab b a b Think and Discuss 1. Give an eample of a product of two binomials that has terms, one that has 3 terms, and one that has terms. 1-6 Multiplying Binomials 619

35 1-6 Eercises California Standards Practice Preview of Algebra KEYWORD: MT8CA 1-6 KEYWORD: MT8CA Parent GUIDED PRACTICE See Eample 1 Multiply. 1. ( 5)(y ). ( 3)( 7) 3. (3m 5)(m 9). (h )(3h ) 5. (m )(m 7) 6. (b 3c)(b c) See Eample See Eample 3 7. A courtyard is 0 ft by 30 ft. There is a walkway of width all the way around the courtyard. Find the area of the walkway. Multiply. 8. ( ) 9. (b 3)(b 3) 10. ( ) 11. (3 5) See Eample 1 INDEPENDENT PRACTICE Multiply. 1. ( )( 3) 13. (v 1)(v 5) 1. (w 6)(w ) 15. (3 5)( 6) 16. (m 1)(3m ) 17. (3b c)(b 5c) 18. (3t 1)(t 1) 19. (3r s)(r 5s) 0. (5n 3b)(n b) See Eample See Eample 3 1. Construction The Gonzalez family is having a pool to swim laps built in their backyard. The pool will be 5 yards long by 5 yards wide. There will be a cement deck of width yards around the pool. Find the total area of the pool and the deck. Multiply.. ( 5) 3. (b 3). ( )( ) 5. ( 3)( 3) 6. ( 1) 7. (a 7) Etra Practice See page EP5. PRACTICE AND PROBLEM SOLVING Multiply. 8. (m 6)(m 6) 9. (b 5)(b 1) 30. (q 6)(q 5) 31. (t 9)(t ) 3. (g 3)(g 3) 33. (3b 7)(b ) 3. (3t 1)(6t 7) 35. (m n)(m 3n) 36. (3a 6b) 37. (r 5)(r 5) 38. (5q ) 39. (3r s)(5r s) 0. A metalworker makes a bo from a 15 in. by 0 in. piece of tin by cutting a square with side length out of each corner and folding up the sides. Write and simplify an epression for the area of the base of the bo. 60 Chapter 1 Polynomials

36 Life Science A. V. Hill ( ) was a biophysicist and pioneer in the study of how muscles work. He studied muscle contractions in frogs and came up with an equation relating the force generated by a muscle to the speed at which the muscle contracts. Hill epressed this relationship as (P a)(v b) c, where P is the force generated by the muscle, a is the force needed to make the muscle contract, V is the speed at which the muscle contracts, b is the smallest contraction rate of the muscle, and c is a constant. 1. Use the FOIL method to simplify Hill s equation.. Suppose the force a needed to make the muscle contract is approimately 1 the maimum force the muscle can generate. Use Hill s equation to write an equation for a muscle generating the maimum possible force M. Simplify the equation. 3. Write About It In Hill s equation, what happens to V as P increases? What happens to P as V increases? (Hint: You can substitute the value of 1 for a, b, and c to help you see the relationship between P and V.). Challenge Solve Hill s equation for P. Assume that no variables equal 0. The muscles on opposite sides of a bone work as a pair. Muscles in pairs alternately contract and rela to move your skeleton. AF1.3, AF.1 5. Multiple Choice Which polynomial shows the result of using the FOIL method to find ( )( 6)? A 1 B 6 1 C 1 D 6. Gridded Response Multiply 3a b and 5a 8b. What is the coefficient of ab? Solve. (Lesson -8) j y Simplify. (Lesson 1-) 51. (m 3m 6) 5. 3(a b a 3ab) ab 53. y (y 3 y y) 1-6 Multiplying Binomials 61

37 Quiz for Lessons 1-3 Through Adding Polynomials Add. 1. ( ) ( 6). (30 7) (1 5) 3. (7b 3 c 6b c 3bc) (8b 3 c 5bc 13) (b c 5bc 9). (w w 6) (3w w 5) (w ) 5. Each side of an equilateral triangle has length w. Each side of a square has length 3w. Write an epression for the sum of the perimeter of the equilateral triangle and the perimeter of the square. 1- Subtracting Polynomials w 3w Find the opposite of each polynomial y 3 7. m 6m v 7v Subtract b (3b 6b 8) 10. (13a a ) (9 a 7a) 11. (6 6) (3 7) 1. The population of a bacteria colony after h hours is h 3 5h h 00. The population of another bacteria colony is 3h 3 h 5h 00. Write an epression to show the difference between the two populations. Evaluate the epression for h Multiplying Polynomials by Monomials Multiply. 13. ( 3 y 3 )(3y 6 ) 1. (3hj 5 )(6h j 5 ) 15. s t (s t 3st s t ) 16. A triangle has a base of length y and a height of 3 y. Write and simplify an epression for the area of the triangle. Then find the area of the triangle if and y Multiplying Binomials Multiply. 17. ( )( 6) 18. (3m )(m 8) 19. (n 5)(n 3) 0. ( 6) 1. ( 5)( 5). (3 )(3 ) 3. A rug is placed in a 10 ft 0 ft room so that there is an uncovered strip of width all the way around the rug. Find the area of the rug. 6 Chapter 1 Polynomials

38 Cooking Up a New Kitchen Javier is a contractor who remodels kitchens. He drew the figure to help calculate the dimensions of a countertop surrounding a sink that is inches long and y inches wide. in. 1. Write a polynomial that Javier can use to find the perimeter of the outer edge of the countertop. 6 in. in. y 6 in.. Someone orders a countertop for a sink that is 18 inches long and 1 inches wide. Javier puts tape around the outer edge of the countertop to protect it while it is being moved. Use the polynomial to determine how many inches of tape are needed. 3. Write a polynomial that Javier can use to find the area of the countertop for any size sink.. The marble for the countertop costs $1.5 per square inch. Write a polynomial that gives the cost of the countertop. 5. Find the cost of the countertop for the 18-inch by 1-inch sink. Eplain your answer. Concept Connection 63

39 Short Cuts You can use properties of algebra to eplain many arithmetic shortcuts. For eample, to square a two-digit number that ends in 5, multiply the first digit by one more than the first digit, and then place a 5 at the end. To find 35, multiply the first digit, 3, by one more than the first digit,. You get 3 1. Place a 5 at the end, and you get 15. So Why does this shortcut work? You can use FOIL to multiply 35 by itself: (30 5)(30 5) First use the shortcut to find each square. Then use FOIL to multiply the number by itself Can you eplain why the shortcut works? Use FOIL to multiply each pair of numbers Write a shortcut for multiplying two-digit numbers with a first digit of 1. Rolling for Tiles For this game, you will need a number cube, a set of algebra tiles, and a game board. Roll the number cube, and draw an algebra tile: 1,, 3,, 5, 6. The goal is to model epressions that can be added, subtracted, multiplied, or divided to equal the polynomials on the game board. A complete set of rules and a game board are available online. KEYWORD: MT8CA Games 6 Chapter 1 Polynomials

40 Materials 3 sheets of decorative paper ruler compass scissors glue markers PROJECT Polynomial Petals A Pick a petal and find a fact about polynomials! Directions 1 Draw a 5-inch square on a sheet of decorative paper. Use a compass to make a semicircle on each side of the square. Cut out the shape. Figure A 3 5 Draw a 3 1 -inch square on another sheet of decorative paper. Use a compass to make a semicircle on each side of the square. Cut out the shape. Draw a 1 -inch square on the last sheet of decorative paper. Use a compass to make a semicircle on each side of the square. Cut out the shape. Glue the medium square onto the center of the large square so that the squares are at a 5 angle to each other. Figure B Glue the small square onto the center of the medium square in the same way. B Taking Note of the Math Write eamples of different types of polynomials on the petals. Then use the remaining petals to take notes on the key concepts from the chapter. When you re done, fold up the petals. 65

41 Vocabulary binomial degree of a polynomial FOIL polynomial trinomial Complete the sentences below with vocabulary words from the list above. 1. The epression is an eample of a? whose? is 3.. Use the? method to find the product of two?. 3. A polynomial with terms is called a?. A polynomial with 3 terms is called a?. 1-1 Polynomials (pp ) Preview of 1A10.0; 7AF1. EXAMPLE Classify each epression as a monomial, a binomial, a trinomial, or not a polynomial trinomial y 7 3 y not a polynomial Find the degree of each polynomial. 3 1 degree 3 n 3n 16n degree EXERCISES Classify each epression as a monomial, a binomial, a trinomial, or not a polynomial.. 5t 7t 8 5. r 3r g 7g 3 5 g 7. a b 3 c 5 8. y 9. 6st 7s Find the degree of each polynomial r 9r m m m Chapter 1 Polynomials

42 1- Simplifying Polynomials (pp ) Preview of 1A10.0; 7AF1.3 EXAMPLE Simplify ( 7) 5 EXERCISES Simplify. 15. t 6t 3t t 7t gh 5g h 7gh g h 17. (5mn 3m) 18. (a b) 6b 19. 5(st 6t) 16st 7t Adding Polynomials (pp ) Preview of 1A10.0; 7AF1.3 EXAMPLE Add. (3 ) (5 3 ) Identify like terms. 8 Combine like terms. (8t 3 t 6) (t 7t ) 8t 3 t 6 Place like terms t 7t in columns. 8t 3 t 3t Combine like terms. EXERCISES Add. 0. ( 3 7) ( 5 1) 1. (5 3 ) ( 5 9). (5h 5) (h 3) (3h 1) 3. (3y 5 y y) (3 y 6y y ). (n 6) (3n ) (8 6n ) 1- Subtracting Polynomials (pp ) Preview of 1A10.0; 7AF1.3 EXAMPLE Subtract. (6 5) (7 8 ) 6 5 (7 8 ) Add the opposite Associative Property 3 Combine like terms. EXERCISES Subtract. 5. ( ) ( 5 ) 6. (w w 6) (w 8w 8) 7. (3 8 9) (7 8 5) 8. (ab 5ab 7a b) (3a b 6ab) 9. (3p 3 q p q ) (pq p 3 q ) Study Guide: Review 67

43 1-5 EXAMPLE Multiply. (3 y 3 )(y ) (3 y 3 )(y ) Multiplying Polynomials by Monomials (pp ) 3 1 y y 5 Multiply the coefficients and add the eponents. EXERCISES Preview of 1A10.0; 7AF1., 7AF1.3, 7AF. Multiply. 30. (st 3 )(s 3st 8) 31. 6a b(a b 5ab 6a b) 3. m(m 8m 1) 33. 5h(3gh g 3 h 6h g) (ab )(a b 3ab 6a 8) 3. 1 j 3 k (j k 3jk j 3 k 3 ) y 5 (5 y y 9 8y y ) (ab )(a b 3ab 6a 8) 8a 3 b 6a b 3 1a b 16ab 1-6 Multiplying Binomials (pp ) Preview of 1A10.0 EXAMPLE Multiply. (r 8)(r 6) (r 8)(r 6) FOIL r 6r 8r 8 Combine like terms. r r 8 (b 6) (b 6)(b 6) FOIL EXERCISES Multiply. 36. (p 6)(p ) 37. (b )(b 6) 38. (3r 1)(r ) 39. (3a b)(a 5b) 0. (m 7) 1. (3t 6)(3t 6). (3b 7t)(b t) 3. (10 3)( ). ( y 11) b 6b 6b 36 b 1b 36 Combine like terms. 68 Chapter 1 Polynomials

44 Classify each epression as a monomial, a binomial, a trinomial, or not a polynomial. 1. t t a 3 b 6 3. m 5m 8 Find the degree of each polynomial.. 6 9b m y 7. The volume of a cube with side length is given by the polynomial What is the volume of the cube if 3? Simplify. 8. a b 5b 6a b 9. 3( 6 10) 10. y 3y y y 11. 6(b 7b) 3b 5b 1. The area of one face of a cube is given by the epression s 9s. Write a polynomial to represent the total surface area of the cube. Add. 13. ( 1) ( 5) 1. (1 5) (9 5) 15. (3bc b c 5bc ) (bc bc ) 16. (6h 5 3h 3 h 6 ) (h 6 h 5h ) 17. (b 3 c 8b c 5bc) (6b 3 c bc 3) (b c 3bc 11) 18. Harold is placing a mat of width w around a 16 in. by 0 in. portrait. Write an epression for the perimeter of the outer edge of the mat. Subtract. 19. (m n 5mn mn ) (mn m n) 0. (1a a ) (6 a 8a) 1. (3a b 5a b 6ab ) (a b 7a b). ( j 7j j) (5j 3 j 6j 1) 3. A circle whose area is 3 is cut from a rectangular piece of plywood with area 3 1 and discarded. Write an epression for the area of the remaining plywood. Evaluate the epression for in. Multiply.. (3)(5 ) 5. ( y)(5y 3 ) 6. (a b )(5a b 5 ) 7. a(a 3 a 5) 8. 3m 3 n (m 3 n 5m n ) 9. 3a 3 (ab ab 8a) 30. ( )( 1) 31. ( )( ) 3. (a 3)(a 7) 33. A student forms a bo from a 10 in. by 15 in. piece of cardboard by cutting a square with side length out of each corner and folding up the sides. Write and simplify an epression for the area of the base of the bo. Chapter 1 Test 69

45 KEYWORD: MT8CA Practice Cumulative Assessment, Chapters 1 1 Multiple Choice 1. Jerome walked on a treadmill for 5 minutes at a speed of. miles per hour. How far did Jerome walk? A 1.89 miles C 3.15 miles B.1 miles D 5.6 miles. Which line has a slope of 3? A y 3 C y 3 5. If rectangle MNQP is similar to rectangle ABDC, then what is the area of rectangle ABDC? 18 cm 3 M N A P A B Q cm C 10 cm 66 cm D 70 cm C B 10 cm D B 3. How much water can the cone-shaped cup hold? Use 3.1 for π. A B 0-5 y 10 cm -3 cm cm 3 C cm cm 3 D cm 3. Twenty-two percent of the sales of a general store are due to snack sales. If the store sold $1350 worth of goods, how much of the total was due to snack sales? A $167 C $1053 B $97 D $970 D 0 y 3 6. Which statement is modeled by 3f 16? A Two added to 3 times f is at least 16. B Three times the sum of f and is at most 16. C The sum of and 3 times f is more than 16. D The product of 3f and is no more than If the area of a circle is 9π and the circumference of the circle is 1π, what is the diameter of the circle? A 7 units C 1 units B 1 units D 9 units 8. Nationally, there were 17.8 million people age 18 and over and 53.3 million children ages 5 to 17 as of July 1, 003, according to the U.S. Census Bureau. How do you write the number of people age 5 and older in scientific notation? A C B D Chapter 1 Polynomials

46 9. There are 36 flowers in a bouquet. Two-thirds of the flowers are roses. One-fourth of the roses are red. What percent of the bouquet is made up of red roses? A 9% C 5% B 16 3 % D 66 3 % If a problem involves decimals, you may be able to eliminate answer choices that do not have the correct number of places after the decimal point. Gridded Response 10. The floor in the entrance way of Kendra s house is square and measures 6.5 feet on each side. Colored tiles have been set in the center of the floor in a square measuring feet on each side. The remaining floor consists of white tiles. Short Response 1. A quilt is made by connecting squares like the one below. 3 a. Write an epression for the area of the triangle and an epression for the area of the square. b. Write an epression for the area of the gray region. 15. Draw a model for the product of the two binomials ( 3) and ( 5) with the following tiles. Use the model to determine the product. ft 6.5 ft How many square feet of the entrance way floor consists of white tiles? 11. Rosalind purchased a sewing machine discounted 0%. The original selling price of the machine was $30. What was the sale price in dollars? 1. What is the length, in centimeters, of the diagonal of a square with side length 8 cm? Round your answer to the nearest hundredth. 13. The length of a rectangle is units greater than the width. The area of the rectangle is square units. What is its width? Etended Response 16. A cake pan is made by cutting four squares from a 18 cm by cm piece of tin and folding the sides as shown. 1 cm 18 cm a. Write an epression for the length, width, and height of the cake pan in terms of. b. Multiply the epressions from part a to find a polynomial that gives the volume of the cake pan. c. Evaluate the polynomial for 1,, 3, and. Which value of gives the cake pan with the largest volume? Give the dimensions and the volume of the largest cake pan. Cumulative Assessment, Chapters

47 Student Handbook Etra Practice Skills Bank EP SB Place Value to the Billions SB Round Whole Numbers and Decimals SB Compare and Order Whole Numbers SB3 Compare and Order Decimals SB3 Divisibility Rules SB Factors and Multiples SB Prime and Composite Numbers SB5 Prime Factorization SB5 Greatest Common Divisor (GCD) SB6 Least Common Multiple (LCM) SB6 Multiply and Divide by Powers of Ten SB7 Dividing Whole Numbers SB7 Plot Numbers on a Number Line SB8 Simplest Form of Fractions SB8 Mied Numbers and Improper Fractions SB9 Finding a Common Denominator SB9 Adding Fractions SB10 Subtracting Fractions SB10 63 Student Handbook

48 Multiplying Fractions SB11 Dividing Fractions SB11 Adding Decimals SB1 Subtracting Decimals SB1 Multiplying Decimals SB13 Dividing Decimals SB13 Order of Operations SB1 Measurement SB15 Polygons SB16 Geometric Patterns SB16 Classify Triangles and Quadrilaterals SB17 Bar Graphs SB18 Line Graphs SB19 Histograms SB0 Circle Graphs SB1 Sampling SB Bias SB Compound Events SB3 Inductive and Deductive Reasoning SB Selected Answers Glossary Inde Table of Formulas and Symbols SA1 G1 I inside back cover 633

49 Etra Practice Chapter 1 LESSON 1-1 Evaluate each epression for the given value(s) of the variable(s) for 5. 6m for m 3 3. (p 3) for p 8. y for 1, y 3 5. y for 3, y y for, y LESSON 1- Write an algebraic epression for each word phrase. 7. seven less than a number b 8. eight more than the product of 7 and a 9. a quotient of 8 and a number m 10. five times the sum of c and 18 Write a word phrase for each algebraic epression ( 1) Write a word problem that can be evaluated by the algebraic epression 1, and then evaluate the epression for 5. LESSON In a miniature golf game the scores of four brothers relative to par are Jesse 3, Jack, James 5, and Jarod 1. Use,, or to compare Jack s and Jarod s scores. Then list the brothers in order from the lowest score to the highest. Write the integers in order from least to greatest. 17., 6, 18. 1, 16, ,, 19 Simplify each epression LESSON 1- Add (8) 8. 6 () 9. 7 (11) Evaluate each epression for the given value of the variable for for for The middle school registrar is checking her records. Use the information in the table to find the net change in the number of students for this school for the week. EP Etra Practice Students Students Day Registering Withdrawing Monday Tuesday 6 7 Wednesday 5 5 Thursday 1 Friday 0

50 Etra Practice Chapter 1 LESSON 1-5 Subtract (3) (3) Evaluate each epression for the given value of the variable for s for s b for b for. 7 b for b m 6 for m 3. An elevator rises 351 feet above ground level and then drops 15 feet to the basement. What is the position of the elevator relative to ground level? LESSON 1-6 Multiply or divide. 5. 8(6) (3) 8. Simplify. 9. 8( 5) 50. 5(9) (16 ) (10 1) LESSON 1-7 Solve t m a p y k g Richard biked 39 miles on Saturday. This distance is 13 more miles than Trevor biked. How many miles did Trevor bike on Saturday? LESSON 1-8 Solve and check. 6. a c d p 66. 8b y c Jessica hiked a total of 36 miles on her vacation. This distance is times as far as she typically hikes. How many miles does Jessica typically hike? LESSON 1-9 Translate each sentence into an equation less than the product of 5 and a number is more than the quotient of a number t and 6 is 9. Solve m y 11 m Etra Practice EP3

51 Etra Practice Chapter LESSON -1 Write each fraction as a decimal Write each decimal as a fraction in simplest form Write each repeating decimal as a fraction in simplest form LESSON - Compare. Write,,or In a sewing class, students were instructed to measure and cut cloth to a width of 3 yards. While checking four students work, the teacher found that the four pieces of cloth were cut to the following measurements: 1 1 yards, and yards. List these measurements from least to greatest. LESSON -3. Hannah and Elizabeth drove to Niagara Falls for vacation. Hannah drove 98 3 miles, and Elizabeth drove 106. miles. How far did they drive together? Add or subtract. Write each answer in simplest form Evaluate each epression for the given value of the variable for a for a z for z 31 5 LESSON - Multiply. Write each answer in simplest form (8) 39..1(8.6) (5.) (.6). Rosie ate 1 bananas on Saturday. On Sunday she ate 1 as many bananas as she ate on Saturday. How many bananas did Rosie eat over the weekend? EP Etra Practice

52 Etra Practice Chapter LESSON -5 Divide. Write each answer in simplest form Evaluate each epression for the given value of the variable for for Yolanda is making bows that each take 1 1 inches of ribbon to make. She has 3 inches of ribbon. How many bows can she make? LESSON for 1. Add or subtract. Write each answer in simplest form Evaluate each epression for the given value of the variable for 9 6. n 1 9 for n y for y A container has 10 1 gallons of milk. If the children at a preschool drink 7 3 gallons of milk, how many gallons of milk are left in the container? LESSON -7 Solve. a p m w z Peter estimates that it will take him 9 3 hours to paint a room. If he gets two of his friends to help him and they work at the same rate as he does, how long will they take to paint the room? LESSON A bill from the plumber was $383. The plumber charged $175 for parts and $5 per hour for labor. How long did the plumber work at this job? Solve. 77. a m b k c d y Etra Practice EP5

53 Etra Practice Chapter 3 LESSON 3-1 Name the property that is illustrated in each equation (6 ) (5 6). 8 (1) (1) 8 3. m m Simplify each epression. Justify each step Write each product using the Distributive Property. Then simplify. 7. 3(9) 8. 8(7) 9. 6(5) LESSON 3- Combine like terms a b 6 b 5a 1. s 9t m n 6m n Simplify (y ) y 17. 3(3b 3) 3b 18. ( ) 3 8 LESSON 3-3 Solve. 19. a 5 a b 6 b g 9 g f 5 5f 6. r 8 7 6r 9 5. a b z f c A round-trip car ride took 1 hours. The first half of the trip took 7 hours at a rate of 5 miles per hour. What was the average rate of speed on the return trip? LESSON 3- Solve. 3. z z a a p 6 3 p c 3c 36. 7d 3 d 5d f 5f f f 38. 5k k 3k 6 k 39. w 5 8 w 7 8 w a a a a q q 6 5 q A cafeteria charges a fied price per ounce for the salad bar. A sandwich costs $3.10, and a large drink costs $1.75. If a 7-ounce salad and a drink cost the same as a -ounce salad and a sandwich, how much does the salad cost per ounce? EP6 Etra Practice

54 Etra Practice Chapter 3 LESSON 3-5 Write an inequality for each situation or statement. 3. The cafeteria could hold no more than 50 people.. There were fewer than 0 boats in the marina. 5. A number n decreased by is more than A number divided by 5 is at most 8. Graph each inequality. 7. y 8. f 3 9. n Write a compound inequality for each statement. 51. A number m is both less than 8.5 and greater than or equal to A number c is either greater than 1.5 or less than or equal to 1. LESSON 3-6 Solve and graph h q m n q h LESSON 3-7 Solve and graph v 6. 0 q s 65. p w 67. f 68. 5y Reese is running for student council president. In order for a student to be elected president, at least 1 3 of the students must vote for him. If there are 3 students in a class, at least how many students must vote for Reese in order for him to be elected class president? LESSON 3-8 Solve and graph a b z k d p Nikko wants to make flyers promoting a library book sale. The printer charges $0 plus $0.03 per flyer. How many flyers can Nikko make without spending more than the library s $5 budget? Etra Practice EP7

55 Etra Practice Chapter LESSON -1 Write in eponential form a 6a 6a 6a 6a 3. (9) (9). b Simplify (6) 8. (3) 5 Evaluate each epression for the given values of the variables. 9. s y(s 3) for s 1 and y (y ) for 3 and y LESSON - Simplify the powers of Simplify. 15. () (5) (9 3) (3) 19(1 ) (3) 3 LESSON -3 Simplify each epression. Write your answer in eponential form w 7 w c 9. 6 c (3 0 y 3 ) 7. (3 ) 3 8. (a 3 ) LESSON - Multiply or divide. Assume that no denominator equals zero. 9. ( 5 )( ) 30. (7a b )(3b ) 31. (8m 6 n 3 )(5mn 7 ) m y 8 m 1 7 y a 9 b 5 a b Simplify. 35. (3y) (9p 3 r) 37. (a 7 b ) 3 LESSON -5 Write each number in scientific notation ,50,000, Write each number in standard form The population of the United States was approimately people in July 006. In the same month, the population of Canada was approimately people. Which country had the greater population in July 006? EP8 Etra Practice

56 Etra Practice Chapter LESSON -6 Find the two square roots of each number The area of a square garden is 1,681 square feet. What are the dimensions of the garden? Simplify each epression y 6 LESSON m 1 n a 16 b 8 Each square root is between two integers. Name the integers. Eplain your answer Each tile on Michelle s patio is 18 square inches. If her patio is square shaped and consists of 81 tiles, about how big is her patio? Approimate each square root to the nearest hundredth LESSON -8 Write all classifications that apply to each number State if the number is rational, irrational, or not a real number Find a real number between each pair of numbers and and and 36 7 LESSON -9 Use the Pythagorean Theorem to find each missing measure b 78. c y 5 in. 8 km 9 cm 10 cm 5 ft 0 ft 1 km 1 in. Tell whether the given side lengths form a right triangle , 8, , 11, , 10, , 1.5, 1.7 Etra Practice EP9

57 Etra Practice Chapter 5 LESSON 5-1 Write each ratio in simplest form. 1. cups of milk to 8 eggs. 36 inches to feet 3. feet to 0 yards Simplify to tell whether the ratios are equivalent and and and and LESSON 5-8. Nikko jogs 3 miles in 30 minutes. How many miles does she jog per hour? 9. A penny has a mass of.5 g and a volume of approimately 0. cm 3. What is the approimate density of a penny? Estimate the unit rate mg of calcium for 8 oz of yogurt 11. $57.50 for 5 hours 1. Determine which brand of detergent has the lower unit rate. LESSON 5-3 Tell whether the ratios are proportional and and and and Mark is making 35 sandwiches for a luncheon. He made the first 15 sandwiches in 5 minutes. If he continues to work at the same rate, how many more minutes will he take to complete the job? 18. An 18-pound weight is positioned 6 inches from a fulcrum. At what distance from the fulcrum must a -pound weight be positioned to keep the scale balanced? LESSON 5- Detergent Brand Size (oz) Price ($) Pizzazz Spring Clean Bubbling A water fountain dispenses 8 cups of water per minute. Find this rate in pints per minute. 0. Jo s car uses 166 quarts of gas per year. Find this rate in gallons per week. 1. Toby walked 35 feet in one minute. What is his rate in miles per hour?. A three-toed sloth has a top speed of 0. feet per second. A giant tortoise has a top speed of.99 inches per second. Convert both speeds to miles per hour, and determine which animal is faster. 3. There are markers every 1000 feet along the side of a road. While cycling, Ben passes marker number 6 at 3:35 P.M. and marker number at 3:7 P.M. Find Ben s average speed in feet per minute. Use dimensional analysis to check the reasonableness of your answer. EP10 Etra Practice

58 Etra Practice Chapter 5 LESSON 5-5. Which triangles are similar? A A B C G D ft E 11 ft ft 60 C 5 ft B 5 10 ft 1.1 ft 5 I 10 ft H. ft ft Khaled scans a photo that is 5 in. wide by 7 in. long into his computer. If the length of the scanned photo is reduced to 3.5 in., how wide should the scanned photo be for the two photos to be similar? F 6. Mutsuko drew an 8.5-inch-wide by 11-inch-tall picture that will be turned into a 3-inch-wide poster. How tall will the similar poster be? 7. A right triangle has legs that measure 3 cm and cm. The shorter leg of a similar right triangle measures 6 cm. What is the length of the other leg of the similar triangle? LESSON Brian casts a 9 ft shadow at the same time that Carrie casts an 8 ft shadow. If Brian is 6 ft tall, how tall is Carrie? 9. A telephone pole casts an 80 ft shadow, and a child standing nearby who is 3.5 ft tall casts a 6 ft shadow. How tall is the pole? LESSON 5-7 Use the map to answer each question. 30. On the map, the distance from State College to Belmont is cm. What is the actual distance between the two locations? 31. Henderson City is 83 miles from State College. How many centimeters apart should the two locations be placed on the map? State College Scale: 1 cm:5 mi 3. What is the scale of a drawing in which a building that is 95 ft tall is drawn 6 in. tall? 33. A model of a skyscraper was made using a scale of 0.5 in:5 ft. If the actual skyscraper is 570 feet tall, what is the height of the model? 3. Julio uses a scale of 1 8 inch 1 foot when he paints landscapes. In one painting, a giant sequoia tree is inches tall. How tall is the actual tree? 35. On a scale drawing of a house plan, the master bathroom is 1 1 inches wide and 5 8 inches long. If the scale of the drawing is 3 16 inches 1 foot, what are the actual dimensions of the bathroom? Belmont Etra Practice EP11

59 Etra Practice Chapter 6 LESSON 6-1 Compare. Write,,or % % 3. % % Order the numbers from least to greatest , 11.5%, 10%, , 100%, 6 %, , 115%, 83, 83.3% %, 7, 160%, A molecule of ammonia is made up of 3 atoms of hydrogen and 1 atom of nitrogen. What percent of an ammonia molecule is made up of hydrogen atoms? LESSON 6- Estimate % of % of % of % of Approimately 3% of each class walks to school. A student said that in a class of 0 students, approimately students walk to school. Estimate to determine if the student s number is reasonable. Eplain. LESSON What percent of 36 is 9? 16. What percent of 8 is 5? 17. What percent of 16 is? 18. What percent of 50 is? 19. Mt. McKinley in Alaska is 0,30 feet tall. The height of Mt. Everest is about 13% of the height of Mt. McKinley. Estimate the height of Mt. Everest. Round to the nearest thousand. 0. A restaurant bill for $6.5 was split among four people. Dona paid 5% of the bill. Sandy paid 1 5 of the bill. Mara paid $1.5. Greta paid the remainder of the bill. Who paid the most money? LESSON is % of what number?. 6 is 7% of what number? 3. 3 is 8% of what number?. 93 is 6% of what number? is 9% of what number? 6. 5 is 10% of what number? 7. A certain rock is a compound of several minerals. Tests show that the sample contains 17.3 grams of quartz. If 7.5% of the rock is quartz, find the mass in grams of the entire rock. 8. The Alabama River is 79 miles in length, or about 31% of the length of the Mississippi River. Estimate the length of the Mississippi River. Round to the nearest mile. EP1 Etra Practice

60 Etra Practice Chapter 6 LESSON 6-5 Find each percent of increase or decrease to the nearest percent. 9. from 10 to from 38 to from 91 to 3. from 3 to from 86 to 7 3. from 38 to from 19 to from 88 to A stereo that sells for $895 is on sale for 0% off the regular price. What is the discounted price of the stereo? 38. Mr. Schultz s hardware store marks up merchandise 8% over warehouse cost. What is the selling price for a wrench that costs him $1.5? LESSON 6-6 Find each sales ta to the nearest cent. 39. total sales: $ total sales: $ total sales: $ sales ta rate: 8.5% sales ta rate: 6.5% sales ta rate: 7% Find the total sales.. commission: $ commission: $3.5 commission rate: 8% commission rate: 5%. An electronics salesperson sold $15,86 worth of computers last month. She makes 3% commission on all sales and earns a monthly salary of $100. What was her total pay last month? 5. Jon bought a printer for $189 and a set of printer cartridges for $19. Sales ta on these items was 6.5%. How much ta did Jon pay for those items? 6. In her shop, Stephanie earns 16% profit on all of the clothes she sells. If total sales were $390 this month, what was her profit? LESSON 6-7 Find the simple interest and the total amount to the nearest cent. 7. $3000 at 5.5% per year for years 8. $15,599 at 9% per year for 3 years 9. $3,000 at 3.6% per year for 5 years 50. $1,500 at 8% per year for 0 years 51. Rebekah invested $15,000 in a mutual fund at a yearly rate of 8%. She earned $700 in simple interest. How long was the money invested? 5. Shu invested $6000 in a savings account for years at a rate of 5%. a. What would be the value of the investment if the account is compounded semiannually? b. What would be the value of the investment if the account is compounded quarterly? Etra Practice EP13

61 Etra Practice Chapter 7 LESSON 7-1 Identify the quadrant that contains each point. Plot each point on a coordinate plane. A y 1. M( 1, 1). N(, ) 3. Q(3, 1) Give the coordinates of each point.. A 5. B 6. C C B LESSON 7- Determine if each relationship represents a function. y y O 0 0 y O LESSON 7-3 Graph each linear function. 10. y 11. y 3 1. y 13. The outside temperature is 5 F and is increasing at a rate of 6 F per hour. Write a linear function that describes the temperature over time. Then make a graph to show the temperature over the first 3 hours. LESSON 7- Create a table for each quadratic function, and use the table to graph the function. 1. y 15. y y 6 LESSON 7-5 Create a table for each cubic function, and use the table to graph the function. 17. y y y 1 3 Tell whether each function is linear, quadratic, or cubic. 0. y 1. y. y EP1 Etra Practice

62 Etra Practice Chapter 7 LESSON 7-6 Find the slope of each line. 3. y. y 5. 3 y O O 1 O 1 3 LESSON 7-7 Find the slope of the line that passes through each pair of points. 6. (3, ) and (, ) 7. (6, ) and (, 6) 8. (3, 3) and (1, ) 9. (, ) and (1, 1) 30. The table shows how much money Andy and Margie made while working at the concession stand at a baseball game one weekend. Use the data to make a graph. Find the slope of the line, and eplain what the slope means. Time (h) 6 8 Money Earned ($) LESSON Abby rode her bike to the park. She had a picnic there with friends and then rode home. Which graph best shows the situation? Graph A Graph B Graph C Distance from home Distance from home Distance from home Time Time 3. Greg walked to a café for lunch. Then he walked across the street to a store before returning home. Sketch a graph to show Greg s distance compared to time. LESSON Instructions for a chemical-concentrate swimming-pool cleaner state that ounces of concentrate should be added to every 1 1 gallons of water used. How many ounces of concentrate should be added to 18 gallons of water? 3. The distance d that an object falls varies directly with the square of the time t of the fall. This relationship is epressed by the formula d k t. An object falls 90 feet in 3 seconds. How far will the object fall in 15 seconds? Time Etra Practice EP15

63 Etra Practice Chapter 8 LESSON 8-1 Use the diagram to name each figure. 1. a line. three rays A C N 3. a plane. three segments B Use the diagram to name each figure. 5. a right angle 6. two acute angles 7. an obtuse angle 8. a pair of complementary angles LESSON 8- Identify two lines that have the given relationship. 9. perpendicular lines C B C E A A B D D 10. skew lines 11. parallel lines E Identify two planes that appear to have the given relationship. 1. parallel planes H I 13. perpendicular planes 1. neither parallel nor perpendicular D E G F LESSON 8-3 Use the diagram to find each angle measure. 15. If m1 107, find m If m 6, find m. 3 1 In the figure, line d line f. Find the measure of each angle d g 1 10 LESSON 8- Find the missing angle measures in each triangle. f y 3. In the figure, B is the midpoint of AC and BD is perpendicular to AC. Find the length of AD. A 16 m 6 m B C EP16 Etra Practice D

64 Etra Practice Chapter 8 LESSON 8-5 Give all of the names that apply to each figure.. A B 5. cm AB CD cm cm D C cm Find the coordinates of the missing verte. Then tell which lines are parallel and which lines are perpendicular. 6. rhombus ABCD with A(, 3), B(3, 0), and D(1, 0) 7. square JKLM with J(1, 1), K(, 1), and L(, ) 8. rectangle ABCD with A(, 3), B(1, 3), and D(, 1) 9. trapezoid JKLM with J(, 1), K(, 1), and L(1, 1) LESSON 8-6 In the figure, quadrilateral ABCD quadrilateral KLMN. 30. Find. A B Find y. 3. Find z. LESSON 8-7 Graph each transformation. 33. Rotate PQR 90 counter- 3. Reflect the figure across 35. Translate RST clockwise about verte R. the y-ais. 3 units right and 3 units down. P y Q R O D 8y C y E D F G O M 3 N z 10 L 95 K R y S O T LESSON 8-8 Create a tessellation with each figure Etra Practice EP17

65 Etra Practice Chapter 9 LESSON 9-1 Find the perimeter of each figure m 6 m in. 11 m 9 m Graph and find the area of each figure with the given vertices.. (, 1), (5, 1), (, ), (5, ) 5. (1, ), (, 1), (5, ), (6, 1) 6. Find the perimeter and area of the figure in LESSON 9- Find the missing measurement for each figure with the given perimeter. 7. perimeter 7 cm 8. perimeter 9 ft 9. perimeter 16 units 5 cm 10 cm 16 ft 16 ft 3 c d a 3 ft 5 Graph and find the area of each figure with the given vertices. 10. (, 3), (, 3), (, 1) 11. (, 1), (5, 3), (0, 1), (3, 3) 1. The sail of a toy sailboat forms a right triangle with legs that measure 5 inches each. Find the perimeter and area of the sail. LESSON 9-3 Name the parts of circle I. 13. radii 1. diameters J L I M K 15. chords H Find the central angle measure of the sector of a circle that represents the given percent of a whole % % 18. 8% % EP18 Etra Practice

66 Etra Practice Chapter 9 LESSON 9- Find the circumference and area of each circle, both in terms of π and to the nearest hundredth. Use 3.1 for π cm 1 in. 1 ft 3. A wheel has a radius of 1 in. Approimately how far does a point on the wheel travel if it makes 15 complete revolutions? Use 7 for π. LESSON 9-5 Find the shaded area. Round to the nearest tenth, if necessary ft 9 ft 5 m 3 ft 13 m 3 ft 3 ft 6. 8 m 7. 3 yd m 8 m 1 yd 7 yd yd LESSON 9-6 Find the area of each figure Use composite figures to estimate the shaded area Etra Practice EP19

67 Etra Practice Chapter 10 LESSON 10-1 Describe the bases and faces of each figure. Then name the figure Classify each figure as a polyhedron or not a polyhedron. Then name the figure LESSON 10- Find the volume of each figure to the nearest tenth. Use 3.1 for π cm 9. 8 ft ft 5 ft cm 7 in. 10. A can has a diameter of 3 in. and a height of 5 in. Eplain whether doubling only the height of the can would have the same effect on the volume as doubling only the diameter. 15 in. 5 in. 11. A shoe bo is 6.8 in. by 5.9 in. by 16 in. Estimate the volume of the shoe bo. 1. Find the volume of the composite figure LESSON Find the volume of each figure to the nearest tenth. Use 3.1 for π m 1.. yd mm 31 mm 15 m 15 m 8 yd 31 mm 16. A rectangular pyramid has a height of 15 ft and a base that measures 5 ft by 7.5 ft. Find the volume of the pyramid. EP0 Etra Practice

68 Etra Practice Chapter 10 LESSON 10- Find the surface area of each prism to the nearest tenth cm 9 cm 9 cm Find the surface area of each cylinder to the nearest tenth. Use 3.1 for π m. 0 m 7 ft 1 mm 6 m 3 m 3 m 1 ft 0 ft 0 ft 9 ft cm 1 mm LESSON 10-5 Find the surface area of each figure to the nearest tenth. Use 3.1 for π m 15 in. 17 yd 13 in. 1 m 13 in. 10 yd 10 yd 10 yd Find the surface area of each figure with the given dimensions. Use 3.1 for π. 6. cone: 7. regular square pyramid: diameter in. base area 6 ft slant height 3 in. slant height 8 ft LESSON 10-6 Find the volume of each sphere, both in terms of π and to the nearest tenth. Use 3.1 for π. 8. r 5 ft 9. d 0 cm Find the surface area of each sphere, both in terms of π and to the nearest tenth. Use 3.1 for π. 30. r 3.8 mm 31. d 1.5 ft LESSON 10-7 An 8 cm cube and a 5 cm cube are both part of a demonstration kit for architects. Compare the following values of the two cubes. 3. edge length 33. surface area 3. volume Etra Practice EP1

69 Etra Practice Chapter 11 LESSON Use a line plot to organize the data showing the number of miles that students cycled over a weekend. What number of miles did students cycle the most? Number of Miles Cycled by Students Use the given data to make a back-to-back stem-and-leaf plot. World Series Win/Loss Records of Selected Teams (through 001) Team Yankees Pirates Giants Tigers Cardinals Dodgers Orioles Wins Losses LESSON 11- Find the mean, median, mode, and range of each data set , 8, 0, 19, 5, 8. 1, 19, 3, 6, 15, 5, 5 5. The table shows the number of points a player scored in ten games. Find the mean and median of the data. Which measure best describes the typical number of points scored in a game? Justify your answer. Points a Player Scored in Ten Games Game Points LESSON 11-3 Find the lower and upper quartiles for each data set. 6. 7, 31, 6,, 33, 31,, 8, 7. 8, 79, 77, 7, 81, 8, 89, 9, 7, 31,,, 7, 31, 8, 6 80, 76, 80, 83, 86, 73 Use the given data to make a bo-and-whisker plot ,, 9, 17, 16, 1, 5, 16, 9, 11, , 53, 5, 31, 8, 59, 6, 86, 56, 5, 55 LESSON The table shows the relationship between the number of years of post high school education and salary. Use the given data to make a scatter plot. Then describe the relationship between the data sets. Number of Years of Post High School Education and Salary Years Salary ($1000 s) EP Etra Practice

70 Etra Practice Chapter 11 LESSON 11-5 Refer to the spinner at right. Give the probability for each outcome. 11. not red 1. blue 13. not yellow A game consists of randomly selecting four colored marbles from a jar and counting the number of red marbles in the selection. The table gives the eperimental probability of each outcome. Number of Red Marbles Probability What is the probability of selecting or more red marbles? 15. What is the probability of selecting at most 1 red marble? LESSON 11-6 A utensil is drawn from a drawer and replaced. The table shows the results after 100 draws. 16. Estimate the probability of drawing a spoon. 17. Estimate the probability of drawing a fork. A sales assistant tracks the sales of a particular sweater. The table shows the data after 1000 sales. 18. Use the table to compare the probability that the net customer will buy a brown sweater to the probability that the net customer will buy a beige sweater. Outcomes Draws Spoon 33 Knife 36 Fork 31 Outcomes Sales White 361 Beige 07 Brown 189 Black 3 LESSON 11-7 An eperiment consists of rolling a fair number cube. There are si possible outcomes: 1,, 3,, 5, and 6. Find the probability of each event. 19. P(rolling an odd number) 0. P(rolling a ) 1. P(rolling a number greater than 3). P(rolling a 7) An eperiment consists of rolling two fair number cubes. Find each probability. 3. P(rolling a total of ). P(rolling a total less than ) 5. P(rolling a total greater than 1) 6. P(rolling a total of 9) LESSON An eperiment consists of rolling a fair number cube three times. For each toss, all outcomes are equally likely. What is the probability of rolling a three times in a row? 8. A jar contains 3 blue marbles and 9 red marbles. What is the probability of drawing red marbles at the same time? Etra Practice EP3

71 Etra Practice Chapter 1 LESSON 1-1 Determine whether each epression is a monomial r st 5. 6y 3 3. y. 3 3 m 5 n Classify each epression as a monomial, a binomial, a trinomial, or not a polynomial y z 7. 5 m n 3 m 3 8. h h w 7 7wz z a a st 6 Find the degree of each polynomial b 9b 3 b z 5z 6 9z t 17. The trinomial 16t vt 1 describes the height in feet of a baseball thrown straight up from a 1-foot platform with a velocity of v ft/s after t seconds. What is the height of the ball after 3 seconds if v 55 ft/s? 18. The trinomial gives the net profit in dollars that a custom bicycle manufacturer earns by selling bikes in a given month. What is the net profit for a month if 15 bicycles? LESSON 1- Identify the like terms in each polynomial. 19. s 5r 7r 9r 3s y 7 z 7yz 3 y z. 3mn 3p 3p 5p 3mn 3. 8s 6 7s 6s y 10 3y 5y 5 Simplify. 5. 5z z z 11z (a 9) 3a 7 7. y z 8z 6y 10y z y 8. 5c 11cd d 5(c d ) c(c d) 9. 5(a b 3ab) 3(ab 5ab) 30. s t st 5s t 7s t 3st s t 31. A rectangle has a width of 1 cm and a length of ( 6) cm. The area is given by the epression 1( 6) cm. Use the Distributive Property to write an equivalent epression. 3. A parallelogram has a base of (3 ) in. and a height of in. The area is given by the epression (3 ) in. Use the Distributive Property to write an equivalent epression. EP Etra Practice

72 Etra Practice Chapter 1 LESSON 1-3 Add. 33. ( y y y) ( y 3 3 y 3y) 3. (3a ab ) (a b b ) (a b 7ab ) 35. (m 3 3m n ) (6m n 9) 36. (10r 3 s 7r s r) (r 3 s 3r) 37. A rectangle has a width of ( 7) cm and a length of (3 5) cm. An equilateral triangle has sides of length 3. Write an epression for the sum of the perimeters of the rectangle and the triangle. LESSON 1- Find the opposite of each polynomial y y a 3 b 7ab g 5 gh Subtract.. (5 y 3y ) (3 y 8) 3. 1a (5a 3 3a 6). (5r s 9r s rs) (3r s 7rs r ) 5. (1y 3 6y 1) (8y 1) 6. The area of the larger rectangle is (10 15) cm. The area of the smaller rectangle is (5 3) cm. What is the area of the shaded region? LESSON 1-5 Multiply. 7. (5y )(7 3 y ) 8. (a bc )(5a 3 b ) 9. (6m 3 n )(mn) 50. 6t(9s 5t) 51. p(p pq 5) 5. 3y ( 3 y y y 6 11y) 53. A rectangle has a width of 3 y ft and a length of ( y 7) ft. Write and simplify an epression for the area of the rectangle. Then find the area of the rectangle if and y 3. LESSON 1-6 Multiply. 5. (y 5)(y 3) 55. (s 3)(s 5) 56. (3m )(m 3) 57. (y 1) 58. (d 5) 59. (a 9)(a 9) 60. ( 11)( 5) 61. (7b )(7b ) 6. (m n)(6m 8n) Etra Practice EP5

73 Skills Bank Review Skills Place Value to the Billions NS1.1 A place-value chart can help you read and write numbers. The number 35,01,678, (three hundred forty-five billion, twelve million, si hundred seventy-eight thousand, nine hundred twelve and five thousand seven hundred eighty-four ten-thousandths) is shown. Billions Millions Thousands Ones Tenths Hundredths Thousandths Ten-Thousandths 35, 01, 678, EXAMPLE Name the place value of the digit. A the 7 in the thousands column B the 0 in the millions column 7 ten thousands place 0 hundred millions place C the 5 in the billions column D the 8 to the right of the decimal point 5 one billion, or billions, place 8 thousandths PRACTICE Name the place value of the underlined digit ,56,789, ,56,789, ,56,789, ,56,789, ,56,789, ,56,789, Round Whole Numbers and Decimals NS1.3, 5NS1.1 To round to a certain place, follow these steps. 1. Locate the digit in that place, and consider the net digit to the right.. If the digit to the right is 5 or greater, round up. Otherwise, round down. 3. Change each digit to the right of the rounding place to zero. EXAMPLE A Round 15, to the nearest B Round 15, to the nearest thousand. tenth. 15, Locate the digit. 15, Locate the digit. The digit to the right,, is less than 5, The digit to the right, 7, is greater so round down. than 5, so round up. 15, ,000 15, ,539. PRACTICE Round 59,35.78 to the place indicated. 1. hundred thousand. ten thousand 3. thousand. hundredth SB Skills Bank

74 Compare and Order Whole Numbers NS1. You can use place values to compare and order whole numbers. EXAMPLE Order the numbers from least to greatest:,810; 1,997;,79;,638. Start at the left most place value. There is one number with a digit in the greatest place.,810 It is the greatest of the four numbers. Compare the remaining three numbers. All values in 1,997 the net two places, the ten thousands and thousands, are the same.,79 In the hundreds place, the values are different. Use this digit to order the remaining numbers.,638,638;,79;,810; 1,997 PRACTICE Order the numbers in each set from least to greatest. 1.,56;,56;,65;,65. 6,37; 6,37; 6,73; 6, ,957; 3,795; 3,975; 31,999. 9,61; 9,61; 19,16; 19,16 Compare and Order Decimals NS1. You can also use place values to compare and order decimals. EXAMPLE Order the decimals from least to greatest: 1.35, 1.3, Compare two of the numbers at a time Write 1.3 as Start at the left and compare the digits Look for the first place the digits are different Graph the numbers on a number line The numbers are in order from left to right: 1.05, 1.3, and PRACTICE Order the decimals in each set from least to greatest , 9.35, ,.1, , 1.6, , 6.07, 6.3 Skills Bank SB3

75 Divisibility Rules NS.1 A number is divisible by another number if the division results in a remainder of 0. Some divisibility rules are shown below. A number is divisible by... Divisible Not Divisible if the last digit is an even number. 11, if the sum of the digits is divisible by if the last two digits form a number divisible by if the last digit is 0 or 5. 15,195 10,007 6 if the number is even and divisible by if the last three digits form a number divisible by 8. 5,016 1,100 9 if the sum of the digits is divisible by if the last digit is PRACTICE Determine whether each number is divisible by, 3,, 5, 6, 8, 9, or , Factors and Multiples NS.1 When two numbers are multiplied to form a third, the two numbers are said to be factors of the third number. Multiples of a number can be found by multiplying the number by 1,, 3,, and so on. EXAMPLE A List all the factors of 8. B Find the first five multiples of 3. The possible factors are whole numbers from 1 to , 8, , 1 8, and The factors of 8 are 1,, 3,, 6, 8, 1, 16,, and 8. PRACTICE 3 1 3, 3 6, 3 3 9, 3 1, and The first five multiples of 3 are 3, 6, 9, 1, and 15. List all the factors of each number Find the first five multiples of each number SB Skills Bank

76 Prime and Composite Numbers NS. A prime number has eactly two factors, 1 and the number itself. A composite number factors. has more than two Factors: 1 and ; prime 11 Factors: 1 and 11; prime 7 Factors: 1 and 7; prime EXAMPLE Determine whether each number is prime or composite. Factors: 1,, and ; composite 1 Factors: 1,, 3,, 6, and 1; composite 63 Factors: 1, 3, 7, 9, 1, and 63; composite A 17 B 16 C 51 Factors Factors Factors 1, 17 prime 1,,, 8, 16 composite 1, 3, 17, 51 composite PRACTICE Determine whether each number is prime or composite Prime Factorization 5NS1. A composite number can be epressed as a product of prime numbers. This is the prime factorization of the number. To find the prime factorization of a number, you can use a factor tree. EXAMPLE Find the prime factorization of The prime factorization of is 3, or 3 3. PRACTICE Find the prime factorization of each number Skills Bank SB5

77 Greatest Common Divisor (GCD) 6NS. The greatest common divisor (GCD) of two or more whole numbers is the greatest whole number that divides evenly into each number. EXAMPLE Find the greatest common divisor of and 3. Method 1: List all the factors of both numbers. Then find all the common factors. : 1,, 3,, 6, 8, 1, 3: 1,,, 8, 16, 3 The common factors are 1,,, and 8, so the GCD of and 3 is 8. Method : Find the prime factorization. Then find the common prime factors. : 3 3: The common prime factors are,, and. The GCD is the product of the factors, so the GCD of and 3 is 8. PRACTICE Find the GCD of each pair of numbers by either method. 1. 9, 15. 5, , 30., , , , , , , , , 8 Least Common Multiple (LCM) 6NS. The least common multiple (LCM) of two or more numbers is the common multiple with the least value. EXAMPLE Find the least common multiple of 8 and 10. Method 1: List multiples of both numbers. Then find the least value that is in both lists. 8: 8, 16,, 3, 0, 8, 56 10: 10, 0, 30, 0, 50, 60 The least value that is in both lists is 0, so the LCM of 8 and 10 is 0. Method : Find the prime factorization. Then find the most occurrences of each factor. 8: 10: 5 The LCM is the product of the factors, so the LCM of 8 and 10 is 5 0. PRACTICE Find the LCM of each pair of numbers by either method. 1.,. 3, , 5. 10, , , , , 1 9., , , 1. 8, 36 SB6 Skills Bank

78 Multiply and Divide by Powers of Ten NS3., 5NS. When you multiply by powers of ten, move the decimal point one place to the right for each zero in the power of ten. When you divide by powers of ten, move the decimal point one place to the left for each zero in the power of ten. EXAMPLE Find each product or quotient. A B ,000 C D PRACTICE Find each product or quotient Dividing Whole Numbers 5NS. Division is used to separate a quantity into equal groups. The number to be divided is the dividend, and the number you are dividing by is the divisor. The answer to a division problem is known as the quotient. EXAMPLE Divide 808 by Write the dividend under the long division symbol. Subtract. Bring down the net digit. Subtract. Bring down the net digit. Subtract. PRACTICE Divide , , , ,5 Skills Bank SB7

79 Plot Numbers on a Number Line 5NS1.5, 6NS1.1 You can order rational numbers by graphing them on a number line. EXAMPLE Put the numbers 0.5, 3, 0.1, and 5 on a number line. Then order the numbers from least to greatest The values increase from left to right: 0.1, 0.5, 3, 5. PRACTICE Plot each set of numbers on a number line. Then order the numbers from least to greatest. 1..6, 5, , 3 8, ,, , 5 1 3, 5.05, , 3 5, 1, , 9, 0.6, , 1 7, 1 6, , 7, 0., , 5 6,, Simplest Form of Fractions 6NS. A fraction is in simplest form when the greatest common divisor of its numerator and denominator is 1. EXAMPLE Simplify. A : 1,, 3,, 6, 8, 1, Find the greatest 18: 1,, 3, 6, 9, 18 Find the greatest 30: 1,, 3, 5, 6, 10, 15, 30 common divisor 8: 1,,, 7, 1, 8 common divisor of and 30. of 18 and Divide both the numerator and 18 9 Divide both the 8 1 the denominator by 6. numerator and the denominator by. PRACTICE Simplify SB8 Skills Bank

80 Mied Numbers and Improper Fractions 6NS1.0 Mied numbers can be written as fractions greater than 1, and fractions greater than 1 can be written as mied numbers. EXAMPLE A Write 3 as a mied number. B Write 6 as a fraction PRACTICE Divide the numerator Multiply the Add the product to by the denominator. denominator by the numerator Write the remainder as the numerator of a fraction. the whole number Write the sum over 7 the denominator. Write each mied number as a fraction. Write each fraction as a mied number Finding a Common Denominator 6NS. You must often rewrite two or more fractions so that they have the same denominator, or a common denominator. One way to find a common denominator is to multiply the denominators. Or you can use the least common denominator (LCD), which is the LCM of the denominators. EXAMPLE Rewrite 3 and 1 so that they have a common denominator. 6 Method 1: Multiply the denominators: For each fraction, multiply the denominator by a number to get the common denominator. Then multiply the numerator by the same number. Method : Find the LCD. The LCM of the denominators, and 6, is 1. So the LCD is PRACTICE Rewrite each pair of fractions so that they have a common denominator , , , , , 1 5 Skills Bank SB9

81 Adding Fractions 5NS.3 To add fractions, first make sure they have a common denominator. Then add the numerators and keep the common denominator. EXAMPLE Add. Write your answer in simplest form. A Add the numerators. Keep the denominator. B Step 1 Find the LCD. The LCD is 30. Step Rewrite the fractions using the LCD: Step 3 Add: Add the numerators. Keep the denominator. 30 PRACTICE Add. Write your answer in simplest form Subtracting Fractions 5NS.3 To subtract fractions, first make sure they have a common denominator. Then subtract the numerators and keep the common denominator. EXAMPLE Subtract. Write your answer in simplest form. 7 3 A Subtract the numerators. Keep the denominator. B Step 1 Find the LCD. The LCD is. Step Rewrite the fractions using the LCD: Step 3 Subtract: 5 Subtract the numerators. Keep the denominator. PRACTICE Subtract. Write your answer in simplest form SB10 Skills Bank

82 Multiplying Fractions 5NS., 5NS.5 To multiply fractions, you do not need a common denominator. Multiply the numerators, and then multiply the denominators. EXAMPLE Multiply 5 7. Write your answer in simplest form Multiply numerators and denominators Write in simplest form. PRACTICE Multiply. Write your answer in simplest form Dividing Fractions 5NS., 5NS.5 Two numbers are reciprocals if their product is 1. To find the reciprocal of a fraction, switch the numerator and denominator. Dividing by a fraction is the same as multiplying by its reciprocal. So, to divide fractions, multiply the first fraction by the reciprocal of the second fraction. EXAMPLE Divide 5 3. Write your answer in simplest form Change the division to multiplication by the reciprocal Multiply numerators and denominators Write in simplest form. PRACTICE Divide. Write your answer in simplest form Skills Bank SB11

83 Adding Decimals 5NS.1 When adding decimals, first align the numbers at their decimal points. You may need to add zeros to one or more of the numbers so that they all have the same number of decimal places. Then add the same way you would with whole numbers. EXAMPLE Add Align the numbers at their decimal points. Place two zeros after Add and bring the decimal point straight down. You can estimate the sum to check that your answer is reasonable: 1 5 PRACTICE Add Subtracting Decimals 5NS.1 When subtracting decimals, first align the numbers at their decimal points. You may need to add zeros to one or more of the numbers so that they all have the same number of decimal places. Then subtract the same way you would with whole numbers. EXAMPLE Subtract. A Align the numbers at their decimal points Place two zeros after Subtract and bring the decimal point straight down. B Estimate to check that your answer is reasonable: Place two zeros after Align the numbers at their decimal points..997 Subtract and bring the decimal point straight down. PRACTICE Subtract SB1 Skills Bank

84 Multiplying Decimals 5NS.1 When multiplying decimals, multiply as you would with whole numbers. The sum of the number of decimal places in the factors equals the number of decimal places in the product. EXAMPLE Find each product. A B PRACTICE 3 decimal places 1 decimal place decimal places decimal places decimal places 5 decimal places Find each product Dividing Decimals 5NS.1 When dividing with decimals, set up the division as you would with whole numbers. Pay attention to the decimal places, as shown below. EXAMPLE Find each quotient. A B Place decimal point. Insert zeros if necessary. PRACTICE Find each quotient Skills Bank SB13

85 Order of Operations 6AF1.3, 6AF1. When simplifying epressions, follow the order of operations. 1. Simplify within parentheses.. Simplify eponents. 3. Multiply and divide from left to right.. Add and subtract from left to right. EXAMPLE Simplify each epression. A 3 (11 ) 3 (11 ) 3 7 Simplify within parentheses. 9 7 Simplify the eponent. B 63 Multiply ) ( ( 5 3) The fraction bar acts as a grouping symbol. Simplify the numerator and the denominator before dividing. Simplify the power in the numerator. Subtract to simplify the numerator Subtract to simplify the denominator. Divide. PRACTICE Simplify each epression (15 8) (3 6) (6) (50 16) SB1 Skills Bank

86 Measurement 6AF.1 The measurements for time 1 min 60 s 1 wk 7 days 1 leap yr 366 days are the same worldwide. 1 h 60 min 1 yr 1 mo 1 day h 1 yr 365 days The customary system of Length Capacity Weight measurement is used in the 1 in. 1 ft 8 oz 1 c 16 oz 1 lb United States. 3 ft 1 yd c 1 pt 000 lb 1 ton 580 ft 1 mi pt 1 qt The metric system is used Length Capacity Mass elsewhere and in science 1 mm m 1 ml L 1 mg g worldwide. 1 cm 0.01 m 1 kl 1000 L 1 kg 1000 g 1 km 1000 m Use the table below to convert from metric to customary measurements. Length Capacity Mass/Weight Temperature 1 cm 0.39 in. 1 L qt 1 g oz 1 m 3.81 ft 1 L 0.6 gal 1 kg.05 lb 1 m 1.09 yd 1 L.7 c 1 kg ton F 9 5 C 3 1 km 0.61 mi 1 ml fl oz 1 metric T 1.10 ton Use the table below to convert from customary to metric measurements. Length Capacity Weight/Mass Temperature 1 in..50 cm. 1 qt 0.96 L 1 oz g 1 ft m 1 gal L 1 lb 0.5 kg C 5 (F 3) 9 1 yd 0.91 m 1 c 0.37 L 1 ton kg 1 mi km 1 fl oz 9.57 ml 1 ton metric ton EXAMPLE A Write,, or. B Convert 3 km to mi. C Convert 5 C to F. 35 in. 1 yd 1 km 0.61 mi F in. 3 ft 1 yd 3 ft 35 in. 36 in. 3 ft 36 in. 3 km mi F in. 1 yd 3 km mi F 77 F PRACTICE Write,, or lb 0 oz. 00 cm m 3. 6 c qt Convert.. 15 mi to km 5. weeks to hours 6. 3 fl oz to ml F to C 8. 1 tons to kg Skills Bank SB15

87 Polygons A polygon is a closed figure with three or more sides. The name of a polygon is determined by its number of sides. If all the sides are the same length, and all the angles have the same measure, the polygon is a regular polygon. Sides and angles with the same measures are marked with the same symbol. 3MG.1 Number Number of Sides Name of Sides Name 3 Triangle 8 Octagon Quadrilateral 9 Nonagon 5 Pentagon 10 Decagon 6 Heagon 1 Dodecagon 7 Heptagon n n-gon EXAMPLE Identify each polygon. A The mark on each side indicates that the sides are all the same length. The arch inside each angle indicates that the angles all have the same measure. regular heagon B pentagon PRACTICE Identify each polygon Geometric Patterns 3MG.0 Patterns involving polygons may deal with size, color, position, or shape. EXAMPLE Predict the net term:,,,... heagon Each term has one more side than the previous term. The net term will have si sides. PRACTICE 1. Predict the net term.. Describe the missing term.,,,...,,,,... SB16 Skills Bank

88 Classify Triangles and Quadrilaterals MG3.7, MG3.8 A triangle can be classified according to its angle measurements or according to the number of congruent sides it has. Classifying by Angles Classifying by Sides Acute Three acute angles Scalene No sides congruent Right One right angle Isosceles At least sides congruent Obtuse One obtuse angle Equilateral All sides congruent EXAMPLE 1 Classify each triangle according to its angles and sides. A B 1 cm C cm 9 cm acute isosceles obtuse scalene acute equilateral Quadrilaterals can also be classified according to their sides and angles. Parallelogram pairs of parallel, congruent sides Rectangle right angles Rhombus congruent sides Square right angles and congruent sides Parallelograms Other Quadrilaterals Trapezoid eactly 1 pair of parallel sides Isosceles Trapezoid congruent, nonparallel legs Kite pairs of adjacent, congruent sides EXAMPLE Tell whether the following statement is always, sometimes, or never true: A square is a rectangle. always A rectangle must have four right angles, and a square always has four right angles. PRACTICE Classify each triangle according to its angles and sides º 35º 110º in. in. in. Tell whether each statement is always, sometimes, or never true.. A rectangle is a square. 5. A trapezoid is a parallelogram. Name the quadrilaterals that always meet the given conditions. 6. All sides are congruent. 7. Two pairs of sides are congruent. Skills Bank SB17

89 Bar Graphs 5SDAP1. A bar graph displays data using vertical or horizontal bars that do not touch. Bar graphs are often a good way to display and compare data that can be organized into categories. EXAMPLE 1 Use the bar graph to answer each question. A Which language has the most native speakers? The bar for Mandarin is the longest, so Mandarin has the most native speakers. B About how many more people speak Mandarin than speak Hindi? About 500 million more people speak Mandarin than speak Hindi. You can use a double-bar graph to compare two related sets of data. Most Widely Spoken Languages English Hindi Mandarin Spanish ,000 Number of speakers (millions) EXAMPLE The table shows the life epectancies of people in three Central American countries. Make a double-bar graph of the data. Step 1 Choose a scale and interval for the vertical ais. Step Draw a pair of bars for each country s data. Use different colors to show males and females. Step 3 Label the aes and give the graph a title. Step Make a key to show what each bar represents. Age Country Male Female El Salvador 67 7 Honduras Nicaragua Life Epectancies in Central America 0 0 El Salvador Honduras Nicaragua Male Female PRACTICE The bar graph shows the average amount of fresh fruit consumed per person in the United States in Use the graph for Eercises Which fruit was eaten the least?. About how many pounds of apples were eaten per person? 3. About how many more pounds of bananas than pounds of oranges were eaten per person? Fresh Fruit Consumption Average per person (lb) Apples Bananas Grapes Oranges SB18 Skills Bank

90 Line Graphs 5SDAP1. You can use a line graph to show how data changes over a period of time. In a line graph, line segments are used to connect data points on a coordinate grid. The result is a visual record of change. EXAMPLE Make a line graph of the data in the table. Use the graph to determine during which -month period the kitten s weight increased the most. Step 1 Determine the scale and interval for each ais. Place units of time on the horizontal ais. Step Plot a point for each pair of values. Connect the points using line segments. Step 3 Label the aes and give the graph a title. 8 Growth Rate of a Kitten Age (mo) Weight (lb) Weight (lb) Age (mo) The graph shows the steepest line segment between and months. This means the kitten s weight increased most between and months. PRACTICE 1. The table shows average movie theater ticket prices in the United States. Make a line graph of the data. Use the graph to determine during which 5-year period the average ticket price increased the least. Year Price ($) The table shows the number of teams in the National Basketball Association (NBA). Make a line graph of the data. Use the graph to determine during which 5-year period the number of NBA teams increased the most. Year Teams Skills Bank SB19

91 Histograms 5SDAP1. A histogram is a bar graph that shows the frequency of data within equal intervals. The bars must be of equal width and should touch, but not overlap. EXAMPLE The table shows survey results about the number of CDs students own. Make a histogram of the data. Number of CDs 1 lll 5 llll l 9 llll l 13 llll llll 17 llll llll ll 6 lll 10 llll llll 1 llll llll l 18 llll ll 3 llll 7 llll lll 11 llll llll l 15 llll llll l 19 ll llll l 8 llll ll 1 llll llll 16 llll llll l 0 llll l Step 1 Make a frequency table of the data. Be sure to use a scale that includes all of the data values and separate the scale into equal intervals. Use these intervals on the horizontal ais of your histogram. Number of CDs Frequency Step Choose an appropriate scale and interval for the vertical ais. The greatest value on the scale should be at least as great as the greatest frequency. CD Survey Results 60 Step 3 Draw a bar for each interval. The height of the bar is the frequency for that interval. Bars must touch but not overlap. Step Label the aes and give the graph a title. Frequency PRACTICE 1. The list below shows the ages of musicians in a local orchestra. Make a histogram of the data. 1, 35,, 18, 9, 38, 30, 7, 5, 19, 35, 6, 7, 1, 3, 30. The list below shows the results of a typing test in words per minute. Make a histogram of the data. 6, 55, 68, 7, 50, 1, 6, 39, 5, 70, 56, 7, 71, 55, 60, Number of CDs SB0 Skills Bank

92 Circle Graphs 5SDAP1. A circle graph shows parts of a whole. The entire circle represents 100% of the data and each sector represents a percent of the total. EXAMPLE Type of Program Number of Students At Mazel Middle School, students were surveyed about their favorite types of TV programs. Use the given data to make a circle graph. Step 1 Find the total number of students surveyed Step Find the percent of the total students who like each type of program. Step 3 Find the angle measure of each sector of the graph. There are 360 in a circle, so multiply each percent by 360. Science 5 Cooking 15 Sports 50 Sitcoms 150 Movies 60 Cartoons 00 Percent Angle of Sector 5 5 5% % % % % % Step Use a compass to draw a large circle. Use a straightedge to draw a radius. Step 5 Use a protractor to measure the angle of the first sector. Draw the angle. Step 6 Use the protractor to measure and draw each of the other angles. Step 7 Give the graph a title, and label each sector with its name and percent. Color the sectors. Cooking 3% Favorite TV Programs Science 5% Sports 10% Cartoons 0% Sitcoms 30% Movies 1% PRACTICE 1. Use the given data to make a circle graph. Favorite Pets Type of Pet Dog Fish Bird Cat Other Number of People Skills Bank SB1

93 Sampling 6SDAP. A population is a group that someone is gathering information about. A sample is part of a population. For eample, if 5 students are chosen to represent a class of 0 students, the 5 chosen students are a sample of the population of 0 students. The sample is a random sample being chosen. EXAMPLE if every member of the population had an equal chance of Jamal telephoned people on a list of 100 names in the order in which they appeared. He surveyed the first 0 people who answered their phone. Eplain whether the sample is random. Names at the beginning of the list have a greater chance of being selected than those at the end of the list, so the sample is not random. PRACTICE Eplain whether each sample is random. 1. Rebecca surveyed every person in a theater who was sitting in a seat along the aisle.. Inez assigned 50 people a number from 1 to 50. Then she used a calculator to generate 10 random numbers from 1 to 50 and surveyed those with matching numbers. Bias 6SDAP. Bias is error that favors part of a population and/or does not accurately represent the population. Bias can occur from using sampling methods that are not random or from asking confusing or leading questions. EXAMPLE Jenn went to a movie theater and asked people who eited if they agree that the theater should be torn down to build office space. Eplain why the survey is biased. People usually only go to movies if they enjoy them, so those eiting a movie theater would not want it torn down. People who do not use the theater did not have a chance to answer. PRACTICE Eplain why each survey is biased. 1. A surveyor asked, Is it not true that you do not oppose the candidate s views?. Brendan asked everyone on his track team how they thought the money from the athletic department fund-raiser should be spent. SB Skills Bank

94 Compound Events 6SDAP. A compound event consists of two or more single events. EXAMPLE Marilyn randomly draws 1 of 6 cards, numbered from 1 to 6, from a bo and then randomly selects 1 of marbles, 1 red (R) and 1 blue (B), from a jar. Find the probability that the card will show an even number and that the marble will be red R 1, R, R 3, R, R 5, R 6, R B 1, B, B 3, B, B 5, B 6, B 3 ways outcome can occur 3 P(even, red) equally likely outcomes Use a table to list all possible outcomes. Circle or highlight the outcomes with an even number and red. In the Eample, a table was used to list the possible outcomes. Another way to list outcomes of a compound event is to use a tree diagram. Card Number Marble 1 R B R List all possible outcomes for the si cards: 1,, 3,, 5, 6. 3 B R B R B Then, for each outcome of the si cards, list all possible outcomes for the marbles: red and blue for each card. 5 R 6 B R B PRACTICE 1. If you spin the spinner twice, what is the probability that it will land on blue on the first spin and on green on the second spin?. What is the probability that the spinner will land on either red or yellow on the first spin and blue on the second spin? 3. What is the probability that the spinner will land on the same color twice in a row? Skills Bank SB3

95 Inductive and Deductive Reasoning 6AF.0, 7MR. Inductive reasoning involves eamining a set of data to determine a pattern and then making a conjecture about the data. In deductive reasoning, you reach a conclusion by using logical reasoning based on given statements, properties, or premises that you assume to be true. EXAMPLE A Use inductive reasoning to determine the 30th number of the sequence. 3, 5, 7, 9, 11,... Eamine the pattern to determine the relationship between each term in the sequence and its value. Term 1st nd 3rd th 5th Value B To obtain each value, multiply the term by and add 1. So the 30th term is Use deductive reasoning to make a conclusion from the given premises. Premise: Makayla needs at least an 89 on her eam to get a B for the quarter in math class. Premise: Makayla got a B for the quarter in math class. Conclusion: Makayla got at least an 89 on her eam. PRACTICE Use inductive reasoning to determine the 100th number in each pattern. 1. 1, 1, 11,, 1,.... 1,, 9, 16, 5,... 3., 6, 8, 10, 1,.... 0, 3, 6, 9, 1, 15,... Use deductive reasoning to make a conclusion from the given premises. 5. Premise: If it is raining, then there must be a cloud in the sky. Premise: It is raining. 6. Premise: A quadrilateral with four congruent sides and four right angles is a square. Premise: Quadrilateral ABCD has four right angles. Premise: Quadrilateral ABCD has four congruent sides. 7. Premise: Darnell is 3 years younger than half his father s age. Premise: Darnell s father is 0 years old. SB Skills Bank

96 Selected Answers Chapter Eercises c 9. 1 c pt pt $ B 9. yes 51. A , 1, 61, , Eercises 1. 3p d plus the product of 3 and s plus the quotient of y and n; $75; $15; $175; $ n j q more than the product of 16 and g less than the quotient of w 1 and y g 7. 13y 6 9. m times the sum of m and times the quotient of 16 and w ( 7) or 7 1. C 3. 9n; $ Eercises , 8, , 0, ,, , 7, , 1, 37. 5, 5, Antarctica, Asia, North America, Europe, South America, Africa, Australia 57. 7, 6, A t 8 1- Eercises () a. $1,16,137,000,000 b. $1,763,863,000,000 c. about $618,000,000,000 or $618 billion 9. C Eercises () ft above the starting point 33. Great Pyramid to Cleopatra; about 500 years 35. Cleopatra takes the throne and Napoleon invades Egypt Eercises gains $ $ , 5; 6, ; , 3; 15 3, D 7. j y Eercises ,635 ft t ; 7 C B Eercises people n 3; n servings h; $ n 15; n q (8); q mi 53. $195 $156 m; m $ C Eercises DVDs 17. z h 39. Nine less than times a number is 3; ; m ; m m,000; m 65 miles per year m ; m 13 miles A Chapter 1 Study Guide: Review 1. equation. opposite 3. absolute value (k ) 8. t less than the product of 5 and b plus the product of 3 and s less than the quotient of 10 and r more than the quotient of y and z 3 1. t 8. k lb mi 6. g 8 7. k 9 8. p w y z mi 53. months y n n 59. y hours Selected Answers SA1

97 Chapter -1 Eercises yes no 57. yes 59. yes a. 9 ; 1 6 ; 1 ; 7 9 ; 15 1 ; 1 ; ; 3 8 b. 3 3; 3; ; 3 5; ; 5 5; c. 0., repeating; 0.16, repeating; 0.5, terminating; 0.6, repeating; 0.565, terminating; 0.8, terminating; 0.65, terminating; 0.375, terminating 65. GCD ; C ; Eercises in., 7.5 in., in., 8.5 in a. apricot, sulphur, large orange sulphur, white-angled sulphur, great white b. between the apricot sulphur and the large orange sulphur , 3, 0.75, D Eercises s s in quadrillion Btu 3. D b 1 9. a Eercises miles boys a. 11 tsp b. 1 1 tsp c. tsp 7. A 9. C Eercises serving glasses in about B Eercises yd miles in cups 9a m b mi c. 71 mi meter meters 55. The company did not find a common denominator when adding 1 and Eercises 1. y m s w y days m k c d r d carats Cullinan III 33. z j t d 1 1. v y. 5. c 0 7. y m carats 55. 3v 6 1 ; 1 1 minutes 56. p (m 19) Eercises 1. 7 hours 3. y a 9. y m r n 7 13; , in. 39. B y m 5.6 Chapter Study Guide: Review 1. rational number. terminating decimal 3. reciprocal or multiplicative inverse , 3, 0.5, , 0, , $ m y 8 5. c r t w r 59. h d a c SA Selected Answers

98 Chapter Eercises 1. Comm. Prop. of Add Comm. Prop. of Mult Distrib. Prop. 31. Assoc. Prop. of Add. 33. Comm. Prop. of Add $ ; Distrib. Prop. 5. y; Assoc. Prop. of Add (Comm. Prop. of Add.) ( 6) (19 1) (Assoc. Prop. of Add.) in. 9. The sentence should read, You can use the Commutative Property of Addition (Distrib. Prop.) 3 (Mult.) ( ) 3 (Assoc. Prop. of Add.) 6 3 (Add) C Eercises f p y 9. 9 y 11. 7g 5h r t y y 1. 6a z b y d 3e y (5 ); no; 6r 1m 5m 15 5r 7, Distrib. Prop.; 6r 5r 1m 5m 15 7, Comm. Prop.; 6r 5r 1m 5m 15 7; 11r 17m d r 11r 5. k g 53s b 9. y ( y ); y a ; Distrib. Prop ; Assoc. Prop. of Mult. 3-3 Eercises 1. d 3 3. e 6 5. h p hours 13. k w y h 6 1. m n 7. b y $11.80 per hour and F 1. C 3. n t 3k Eercises d min; $ all real numbers 17. y a y 5. n , ; units 35a. 17 protons b C g Eercises 1. p m s 5 or s s y c 1 or c w m d 89, B 1. 5, 19, , 9, 7, Eercises f 5. k ; c ; z y k 1 3. { : 0} 5. {b : b 3.5} 7a. 98,00 s 01,5; s 103,3 9. The solution is. 33. B t Eercises 1. r j, or j a, or a 0 7. r sandwiches , or p, or p h q r, or r 6 1. w 3 3. t a A lb, 135 lb 39. at least $13.3 per 5 week Eercises 1. k 3. y 8 5. y h d at least 1 caps q a 3 3. k 3 5. r 3 7. p 3 9. w a q b f at least 31 beads 3a. $158 b. 17 mo 7. B 9. Comm. Prop. of Mult. 51. Comm. Prop. of Add r 60 Chapter 3 Study Guide: Review 1. inequality. Comm. Prop. 3. terms. Comm. Prop. of Add. 5. Assoc. Prop. of Add. 6. Dist. Prop. 7. Assoc. Prop. of Add m w y 11. t t 3t 3 1. y h 1. t r z 17. a s c y. no solution 3 3. z 5. Let d distance; d 1 mi 5. Let c cost; c Let s number of students; s Selected Answers SA3

99 r 31. n y 5 3. n ; n m n t p b 7 0. a 8 1. z 1. h 6 3. a k 3 6. y 1 8 Chapter -1 Eercises b d 19. () c , ,1 bacteria 3. (3d) 5. (7) cm B Eercises ,, or , meter 5. 38,30 lb, C y Eercises m or r 17. ( 1 3 ) 19. y t 13 1 r (1) 9 or t a cannot combine 7. y , or ; a b B Eercises 1. 56y a 5 b 5 5. y 7. 3n ab c a y m 15 n z a b q y y b a 15 b m a3 b r 5. 16m n y 9a. The degree of a monomial is the sum of the eponents of the variables in the monomial. b D 55. 0y k 59. g or 7-5 Eercises 1. 15, , ,000, no , , ,500,000, , ,000, , , ,113, a g b g , ,000, feet per second , ,.3 10, , C 73. number of students t 3-6 Eercises ft 7. y a s ft y a b p 15 q ; ; 6 3 ; 8 ; 10 5 ; C Eercises 1. 6 and and and and and and B 35. E 37. F in ft 3. 5, 5 3, 7.15, 9, km 7. 9a. about 610 mi/h b. about 7.8 h 51. B Eercises 1. irrational, real 3. rational, real 5. rational 7. irrational 9. rational 11. rational 17. rational, real 19. integer, rational, real 1. rational 3. irrational 5. irrational 7. not real 31. whole, integer, rational, real 33. irrational, real 35. rational, real 37. rational, real 39. rational, real 1. integer, rational, real 3. 3 is undefined so it is not a 0 real number. 0 3 is 0 so it is a rational number. 55. irrational 57. rational 59. irrational 63. C 65. C 67. Dist. Prop , Eercises 1. 0 m 3. cm 5. yes 7. yes ft 11. about 1. mi 13. no SA Selected Answers

100 Yes ft 5a. 110 m b m m 31. C and and 8 Chapter Study Guide: Review 1. irrational number. scientific notation 3. Pythagorean theorem; legs; hypotenuse. real numbers 5. (3) 6. k 7. (9) , p m , or y (10) m 10 n z 11. a 7 b 3. 0r 6 s 6. 9p 5. 6t 6. 3 y m9 n t p 10 q y ,000m 8 n , , , , and and and m 65. a and and and and and and rational 7. irrational 75. rational 76. irrational 77. rational 78. not a real number 79. Possible answer: no 83. yes 8. no Chapter Eercises yes no ; 5 ; ; yes 9. no 31. yes 33. no C 1. yes Eercises 1. 3 mi 3. approimately 0 students per bus 5. approimately 500 Calories per serving oz bo g/cm approimately cups per batch 13. approimately $ per lb oz package points per game beats per measure 1. approimately 50 beats per minute 3. approimately apples per pound 5. $3.75/lb; $.50/lb; lb 3 7. approimately $110 per day 31. width: 0 in.; height: 15 in. 33. The bunch of has the lower unit price. 35. w t no 1. no 5-3 Eercises 1. yes 3. no 5. no in. 9. no 11. no 13. yes m 17. 8, , , $ minutes 7. 1 computers 9. 1 molecules 31a. about 3: b. about 68 mm Hg and ounce can 5- Eercises km/s mi/h page/min km/h cereal boes fish mi g tons m/s gal 3. C 7. B m $0.175 per oz 1. $9 per monitor 5-5 Eercises 1. triangle A and triangle B cm gal 7. similar 9. similar 11. yes ft in ft cm quarts 5-6 Eercises yd ft 5. ft ft ft ft 15. C Eercises ft 3. 1 in mi ft ft ft in in ; 6.6 ft 3. D 5. 5 and and and $0.17 per apple Chapter 5 Study Guide: Review 1. ratio; proportion. rate; unit rate 3. similar; scale factor yes 9. no yes 11. no disks 13. unit prices are the same 1. 8-pack h w y min 0. 90,000 m/h ft/min m/min mi/min ( 8 mi/h). 1.5 in in ft ft miles 9. 3 in mi mi mi Chapter Eercises % , %, 36%, % % ,, %, 70% 3. 0%, 5 30%, 0%, 10% 5. 0%, 30%, 5%, 5% 33. B z 5 Selected Answers SA5

101 6- Eercises B 3. B 5. C cars , hours 3a. no b. yes c. 1 per mi ; 1000 per mi 7. B 9. B Eercises % 3. 75% 5. 3% mi 9. 00% 11. 1% % ft above sea level a. 10 b. 0 c % 31. Lena: $11.87, Ana: $1.36, Joseph: $1.50, George: $ B g/1 kg mi/580 ft oz/1 lb Eercises oz cards 13a. 50 b. 15 c a. 30 b. 0 c , % 1. 98, C 5. 5 and and and and and $81, Deborah should choose the salary option that pays $100 plus % of sales. 17a. $6,08 b. $1,717 c. 17.8% d. 19.8% 19. $ y % decrease 6-7 Eercises 1. $3.38; $ $ about $ years % 11. $9.50, $ $6.5, $ $9.6, $ years 1. How long did Alice keep her money in the savings account? 5. B 7. 1 gal/ qt Chapter 6 Study Guide: Review 1. percent. percent of change 3. commission % % $ $ % ft mi lb 7 oz 0. 7,750% 1. 3.%. $1 3. $16,830. $ $ $ $ % yr 30. $1000 at 3.75% for 3 years; $ about $57. Chapter 7 17, (, ) 3. (5, ) 5. (5, 6) 7. y (8, 1) 6 (1, 1) (5, 5) (3, 6) O 9. triangle; Quadrants I and II 31. III 33. (1, 7) 35. a. (68, 6 ) b. (80, 6 ) c. (91, 3 ) 39. B 1. about $ per hour 3. about 16 students per teacher , 1 7, 15%, Eercises 5. yes 7. no 13. no 15. no 17. yes 19. a. yes b. input: {0, 0, 0, 60, 80, 100}; output: {0, 150, 300, 50, 600, 750} 1. a. $0.0 b. any nonnegative number of hours ( 0) c. 550 hours 5. All real numbers 7. D $3 O 6 y (, 3) 6-5 Eercises 1. 8% increase % increase 5. $ % increase % % decrease % decrease 15. % decrease 17. $ a. $78 b. $117 c. $39 d. 80% 5.,900% 7. decrease; 13% 9. C 31. 5% 33. $7.9; $ % Eercises 1. II 3. III 5, 7. (1, ) (3, ) y O 7-3 Eercises 1. 6 (, 1) O 3. a. y 750 y (, 5) (0, 3) 6-6 Eercises 1. $ % 5. $ % 9. $ $ (6, 3) 11. (, 0) 13. I 15. IV SA6 Selected Answers

102 b. 5. Amount of water (gal) 5,000,000 3,000,000 1, Time (hr) y 1. Simon calculated the y-coordinates incorrectly Eercises 6 y O b. 3 s 1. a. $860, $90, $5000, $500, $5060 b B 5. It has no -intercepts ft ft 33. 1,. 7-5 Eercises 1. y O 7. O 6 6 y (, 7) 3. O y 3. 8 y O 8 (, 1) 9. $550; $975; $100; $185; $ y 70 O (0, 3) y 5. linear 7. 1 y O Distance (mi) Distance (ft) y 1 Time (h) 1 Time (s) 15. a. 5 ppm b. about 38 ppm 19. It is not linear , 6, , 0, , 7, Graph C 17. Graph B 19. a. h O t y O 16 y 1 8 O Selected Answers SA7

103 13. quadratic 15. quadratic 17. y O 19. y O 7-6 Eercises 1. constant variable constant 15. variable a. $0.11/yr; $0.3/yr; $0.19/yr b to D Eercises The slope of the line is The slope of the line 5 is. 19. y The 5 roof is flat. 5. z 7. 3 w 9. miles Eercises y y 1. y O 3. The sign determines whether the curve rises or falls from left to right. 5. a. y y = +3 3 O b. 1; 3;, c B % increase 33. 1% increase 35. y O 6 3 y = +1 y = 3 3 y = 1. Graph A 3. Graph B 9. Graph A 10. Graph B 13. B inches Eercises 1. yes 3. no direct variation 5. y 1 ; about 968 kg 7. yes 6 9. no 11. A direct variation is a linear relationship in which the y-intercept is always y 15. y y y Each watermelon would need to be eactly the same weight $38.75; $ Chapter 7 Study Guide: Review 1. direct variation. function 3. linear function. J(, 1), IV 5. K(, 3), II 6. L(1, 0), -ais 7. M(, ), III 8. Possible answer: y Possible answer: y yes O (, 1) (0, 3) (, 5) 6 O (, 8) 6 8 y y O y (0, 6) (, ) 8 SA8 Selected Answers

104 16.. y 31. y O O quadratic. linear 5. constant 6. constant Distance (mi) O y y 5; $.50 Time 8- Eercises y O y y O Chapter Eercises 1. XY 3. XY, YZ, ZX 5. AEB or DEB 7. AEC 9. AEB and BED, AEC and CED 11. plane N or plane JKL 13. KJ, KL, KM, LK, MK 15. VWZ, YWX 17. VWZ, YWX 19. false 1. false 3. false 5. false 7. 30, YV, VX, XY, YZ 33. A 35. m ft 8- Eercises 13. none of these 15. skew 17. BC, FG, and EH 1. plane ABF, plane FBC, plane DAE, and plane DCG 3. yes 7. B 9. 36m y AEC 35. BEC, CED 37. AEC, CED 8-3 Eercises , 5, and The measures of the remaining angles are q s c , 30, r t m , 135, y w C 5. 30, y 100, z and and AB CD 8-5 Eercises 1. AN CD 3. Parallelogram, rhombus, rectangle, square 5. C(, 1) 7. CD AB 9. Parallelogram, rhombus, rectangle, square 11. C(, 1) true 3. false 5. true 7. The slope of CD is also undefined because parallel lines have the same slope. 9. D 31. B Eercises 1. triangle ABC triangle FED 3. q 5 5. s 7 7. quadrilateral PQRS quadrilateral ZYXW 9. n , y 7, z r, s 10, t C P(, 1) Selected Answers SA9

105 8-7 Eercises 1. rotation 3. y Aʹ Cʹ Bʹ O 5. L(, 3) M(, 6), N(7, 3), O(3, 1) 7. y N M M L O N 9. translation 11. y J H J H F G O F G 17. y C B D A C O B D A 19. (3, ) 1. (m, n) 3. (5, ) 9. A(0, ), B(0, 1), C(5, 1) 31. constant in. 8-8 Eercises Chapter 8 Study Guide: Review 1. parallel lines; perpendicular lines. rectangle; square; rhombus; square 3. KM. LKM 5. LKM and JKM 6. PQ and SV 7. plane SVR plane RVT 8. plane PQR plane STV m cm 16. trapezoid 17. y 18. Z Y N L O O y K M W X 13. A(1, 3), B(5, 1), C(7, 5), D(3, 7) 8 y D C A B O B 8 A C 8 D 15. y C B C B D A D A O yes 15. heagon 17. D O y t. 1. q 7. y B 3. B A C A O A C B y B C C A O SA10 Selected Answers

106 . C 5. Possible answer: 6. Possible answer: Chapter Eercises 1. 8 cm ft units 7. 1 units 9. cm m 13. units units ft; 5 ft ft; 10.5 ft 1. $ ,000 mi 7. B a rational 35. rational 37. not a real number 9- Eercises 1. 9 units 3. 3 units 5. 1 units units 9. 5 units units units units m cm m units 5. 5 units y B C A A O B ft 9. When the dimensions are multiplied by, the area will be times as great and the perimeter will be times as great cm ft ft ft ; 160. ft 39. C mi 3. 1 units 9-3 Eercises 1. OQ, OR, OS, OT 3. RT, RS, ST, TQ 5. CA, CB, CD, CE, CF 7. GB, BF, DE, FE, AE cm Eercises 1. 6π cm; 18.8 cm π ft ; 5.8 ft 5. A π units ; 1.6 units ; C π units; 1.6 units 7. 18π in.; 56.5 in π cm ; cm 11. A 16π units ; 50. units ; C 8π units; 5.1 units 13. C 10.7 m; A 9.1 m 15. C 56.5 in.; A 5.3 in cm cm m m 5. C 30π ft 9. ft; A 5π ft ft 7.a. 9.6 in. b. 8.3 in. c. three regular pancakes 31. C 33. m units 9-5 Eercises 1. 8 m cm in ft 9. 5 cm in ,800 mi in 19. C 1. y π in.; 31. in π cm; 5.7 cm 9-6 Eercises 13. no 17. Approimate the area of the glacier with a trapezoid (b 1, b 3, h 1) that has area 5 and a triangle (b 3, h 1) that has area D 1. rational 3. rational Chapter 9 Study Guide: Review 1. perimeter, area. chord 3. about 7 9 in, 1 in m, 80 m ft; 55 8 ft 6. 0 yd; 11 yd 7. 9 cm, 1. cm in, 6.3 in ft 10. HF, FI, FG 11. GI 1. HI, GI, GJ, JI 13. A 1π 5. in ; C π 75. in 1. A 17.6π 55. cm ; C 8.π 6. cm 15. A 9π 8.3 m ; C 6π 18.8 m 16. A 0.36π 1.1 ft ; C 1.π 3.8 ft m ft cm 0. 1 units units. 1 units units Chapter Eercises 1. pentagon; triangles; pentagonal pyramid 3. triangles; rectangles; triangular prism 5. polyhedron; heagonal pyramid 7. triangle; triangles; triangular pyramid 9. heagon; triangles; heagonal pyramid 11. not a polyhedron; cylinder 13. square prism 15. triangular pyramid 19. rectangular pyramid 1. cylinder 3. A oz for $ Eercises cm m ft in m cm a. 800 in a in 3 b. about 18.8 ft in 3 1. D 3. (5, 9) 5. in.; 1 in 10-3 Eercises 1. 0 cm ft cm ,55,000 ft m ft units in ft cm 3 Selected Answers SA11

107 in ,056 ft B π ft ; 176 ft 10- Eercises 1. 8 cm 3. 5 cm m in cm cm cm mm cm yd π mm 3. m 5. $ C units 10-5 Eercises m 3. 1 m ft mm 9. no km ,1,850π mi 15. a. 81; 77 b. Menkaure; 191,68 ft c. Khufu; 91,636,7 ft B ft Eercises 1. 36π cm 3 ; cm π m 3 ; 0.7 m 3 5. π in ; 1.6 in 7. 56π cm ; cm 9. The volume of the sphere and the cube are about equal ( 68 in 3 ) π cm 3 ; cm π in 3 ;. in π m ; 651. m π cm ; 156 cm π in 3 ; in 3 1. V 5.1π yd 3 ; S 6.π yd cm in m 10-7 Eercises 1. :1 3. 6: cm 3 7. :1 9. 8: ,750 in cm; 1 cube cm; 79 cubes cm; 33 cubes 19. 1,000,000 cm 3 1a in 3 b. about 10.9 gal 3. No; the surface area increases by times; the volume increases by 8 times. 7. D w mm in Chapter 10 Study Guide: Review 1. cylinder. surface area 3. cone. cylinder 5. rectangular pyramid cm 3 7. mm mm ft in ft cm m mm in in cm cm in 0. 88π 90.3 in π,16.6 m 3. 3:1 3. 9:1. 7:1 Chapter Eercises Democrats ; B line plot units 11- Eercises 1. 0; 0; 5 and 0; Mean: 35.5; median: ; 88; 88; ;.;. and 6.;. 9. mean 6.; median ; 8; 1 1. D 3. Stems Leaves 11-3 Eercises 1. 5; Republicans Key: 1 means 1 6 means The medians are equal, but data set B has a much greater range ; Data set Y has a greater median. Data set Y has a greater range ; ; B 9. and and ; 5; ; 63; 8 and Eercises 1. Population (millions) 3. positive correlation Price ($1000) Miles peer gallon ,000 30,000 50,000 Area (mi ) 7. positive correlation F 11. positive correlation 13. negative correlation 17. A cm 1. 9 to Eercises Hurricanes Tropical storms , or 60%; 0., or 0% , or 70.9% , or 9% SA1 Selected Answers

108 sample space: blue, green, red, yellow; outcome shown: yellow 13. sample space: 1,, 3,, 5, 6; outcome shown: Eercises , or 3% ; , or 31.9% ; Eercises red yes 33. no 11-8 Eercises dependent independent D 3. 11; Chapter 11 Study Guide: Review 1. median; mode. probablilty 3. line of best fit; scatter plot; correlation ; 311.5; 33 and 3; ; 6; none; no correlation 11. positive correlation , or 85%; 0.15, or 15% , or 15% Chapter Eercises 1. yes 3. no 5. binomial 7. not a polynomial yes 15. no 17. yes 19. monomial 1. trinomial 3. not a polynomial in monomial; binomial; 37. trinomial; not a polynomial 1. trinomial; 3 3. not a polynomial Eercises 1. 3b and b, 5b and b a 1a 9. t and 5t, t and 5t 11. 9p 7p y s s m 0m 3. 17mn d 7. 8y 8y in 9. C % y 5 5 O 1-3 Eercises r s 9rs 5. 15ab 3ab a b w in. 9. 7g g h 6 1h h t t w w 17. 7w y wy wy r 3 r 5r 5 7. C or ft 35. ft 1- Eercises 1. y b 3 5b b 9. 8m n 3mn mn 11. y 5y in 3 ; 30 in v 5v 17. y y 19. 9b b a p 3 5p p t 10pt 7. b ab 9. 6y 1 y in ; m r 10 s zy 3 5zy 1-5 Eercises 1. 15s 3 t h 6 j p r hm 8h A 1 b 1 h 1 b h 13. g 3 h s 5 t h 5 j z 3 1z 1. 6c d 3 1c d s t 3 15s 3 t 3 6s t 5. b a 3 b m 5 15m y f g f 3 g f g m p 8 1m 3 p 7 m p V πr 3 πr y 3 ; 63π 3. 15c 3 d 0c d 5. m 3n in 1-6 Eercises 1. y 5y m 7m 5 5. m 9m ft 9. b v v b 11bc 5c 19. 1r 11rs 5s yd 3. b 6b a 1a 9 9. b 7b 60 Selected Answers SA13

109 31. t 13t b 5b m 11mn 3n 37. r r rs 8s 1. PV bp av ab c 5. B m 1m y y 16y Chapter 1 Study Guide: Review 1. polynomial; degree. FOIL; binomials 3. binomial; trinomial. trinomial 5. not a polynomial 6. not a polynomial 7. monomial 8. not a polynomial 9. binomial t 3t gh 9g h 17. 0mn 1m 18. 8a 10b st 3t h 8h 7 3. y y y. 13n w 1w ab 11ab a b 9. p 3 q p q pq 30. 1s t s t 3 3st a b 3 30a 3 b 3 36a 3 b a b 3. m 3 16m 3 m g 3 h 3 15gh 5 0gh 30h 3. j 5 k 3 3 j k j 6 k y y y 7 3 y p 8p b 10b 38. 3r 11r 39. 3a 11ab 0b 0. m 1m t 36. 6b bt 8t y y 11 SA1 Selected Answers

110 Glossary/Glosario KEYWORD: MT8CA Glossary ENGLISH SPANISH EXAMPLES absolute value The distance of a number from zero on a number line; shown by. (p. 15) valor absoluto Distancia a la que está un número de 0 en una recta numérica. El símbolo del valor absoluto es acute angle An angle that measures less than 90. (p. 379) ángulo agudo Ángulo que mide menos de 90. acute triangle A triangle with all angles measuring less than 90. (p. 39) triángulo acutángulo Triángulo en el que todos los ángulos miden menos de 90. Addition Property of Equality The property that states that if you add the same number to both sides of an equation, the new equation will have the same solution. (p. 33) Addition Property of Opposites The property that states that the sum of a number and its opposite equals zero. (p. 18) additive inverse The opposite of a number. (p. 8) Propiedad de igualdad de la suma Propiedad que establece que puedes sumar el mismo número a ambos lados de una ecuación y la nueva ecuación tendrá la misma solución. Propiedad de la suma de los opuestos Propiedad que establece que la suma de un número y su opuesto es cero. inverso aditivo El opuesto de un número (1) 0 The additive inverse of 5 is 5. adjacent angles Angles in the same plane that are side by side and have a common verte and a common side. (p. 388) ángulos adyacentes Ángulos en el mismo plano que comparten un vértice y un lado. a b algebraic epression An epression that contains at least one variable. (p. 6) algebraic inequality An inequality that contains at least one variable. (p. 136) alternate eterior angles A pair of angles on the outer sides of two lines cut by a transversal that are on opposite sides of the transversal. (p. 389) epresión algebraica Epresión que contiene al menos una variable. desigualdad algebraica Desigualdad que contiene al menos una variable. ángulos alternos eternos Par de ángulos en los lados eternos de dos líneas intersecadas por una transversal, que están en lados opuestos de la transversal. 8 (m b) a b 3 c d a b a and d are alternate eterior angles. Glossary/Glosario G1

111 ENGLISH SPANISH EXAMPLES alternate interior angles A pair of angles on the inner sides of two lines cut by a transversal that are on opposite sides of the transversal. (p. 389) ángulos alternos internos Par de ángulos en los lados internos de dos líneas intersecadas por una transversal, que están en lados opuestos de la transversal. t v r and v are alternate interior angles. r s altitude (of a triangle) A perpendicular segment from a verte to the line containing the opposite side. (p. 393) altura (de un triángulo) Segmento perpendicular que se etiende desde un vértice hasta la recta que forma el lado opuesto. angle A figure formed by two rays with a common endpoint called the verte. (p. 379) ángulo Figura formada por dos rayos con un etremo común llamado vértice. angle bisector A line, segment, or ray that divides an angle into two congruent angles. (p. 38) bisectriz de un ángulo Línea, segmento o rayo que divide un ángulo en dos ángulos congruentes. M N P O arc An unbroken part of a circle. (p. 6) arco Parte continua de un círculo. area The number of nonoverlapping unit squares needed to cover a given surface. (p. 35) área El número de unidades cuadradas que se necesitan para cubrir una superficie dada. The area is 10 square units. Associative Property of Addition The property that states that for all real numbers a, b, and c, the sum is always the same, regardless of their grouping. (p. 116) Associative Property of Multiplication The property that states that for all real numbers a, b, and c, their product is always the same, regardless of their grouping. (p. 116) average The sum of a set of data divided by the number of items in the data set; also called mean. (p. 537) Propiedad asociativa de la suma Propiedad que establece que para todos los números reales a, b y c, la suma siempre es la misma sin importar cómo se agrupen. Propiedad asociativa de la multiplicación Propiedad que establece que para todos los números reales a, b y c, el producto siempre es el mismo, sin importar cómo se agrupen. promedio La suma de los elementos de un conjunto de datos dividida entre el número de elementos del conjunto. También se llama media. a b c (a b) c a (b c) a b c (a b) c a (b c) Data set:, 6, 7, 8, 10 Average: G Glossary/Glosario

112 ENGLISH SPANISH EXAMPLES back-to-back stem-and-leaf plot A stem-and-leaf plot that compares two sets of data by displaying one set of data to the left of the stem and the other to the right. (p. 533) bar graph A graph that uses vertical or horizontal bars to display data. (p. SB17) diagrama doble de tallo y hojas Diagrama de tallo y hojas que compara dos conjuntos de datos presentando uno de ellos a la izquierda del tallo y el otro a la derecha. gráfica de barras Gráfica en la que se usan barras verticales u horizontales para presentar datos. Data set A: 9, 1, 1, 16, 3, 7 Data set B: 6, 8, 10, 13, 15, 16, 1 Set A Set B Key: 1 means 1 3 means 3 Time (s) Sunlight s Travel Time to Planets Earth Mars Jupiter Planet Saturn base (in numeration) When a number is raised to a power, the number that is used as a factor is the base. (p. 166) base Cuando un número es elevado a una potencia, el número que se usa como factor es la base ; 3 is the base. base (of a polygon) A side of a polygon, or the length of that side. (p. 35) base (de un polígono) Lado de un polígono; cara de una figura tridimensional según la cual se mide o se clasifica la figura. base (of a three-dimensional figure) A face of a threedimensional figure by which the figure is measured or classified. (p. 80) base (de una figura tridimensional) Cara de una figura tridimensional a partir de la cual se mide o se clasifica la figura. Bases of a cylinder Bases of a prism Base of a cone Base of a pyramid base (of a trapezoid) One of the two parallel sides of a trapezoid. (p. 0) base (de un trapecio) Uno de los dos lados paralelos del trapecio. binomial A polynomial with two terms. (p. 590) binomio Polinomio con dos términos. y a 3 m 3 n 6mn Glossary/Glosario G3

113 ENGLISH SPANISH EXAMPLES bisect To divide into two trazar una bisectriz Dividir en dos congruent parts. (p. 38) partes congruentes. JK bisects LJM bo-and-whisker plot A graph that displays the highest and lowest quarters of data as whiskers, the middle two quarters of the data as a bo, and the median. (p. 53) gráfica de mediana y rango Gráfica que muestra los valores máimo y mínimo, los cuartiles superior e inferior, así como la mediana de los datos. Lower quartile Minimum Upper quartile Median Maimum capacity The amount a container can hold when filled. (p. 51) Celsius A metric scale for measuring temperature in which 0 C is the freezing point of water and 100 C is the boiling point of water; also called centigrade. (p. SB15) center (of a circle) The point inside a circle that is the same distance from all the points on the circle. (p. 6) capacidad Cantidad que cabe en un recipiente cuando se llena. Celsius Escala métrica para medir la temperatura, en la que 0 C es el punto de congelación del agua y 100 C es el punto de ebullición. También se llama centígrado. centro (de un círculo) Punto interior de un círculo que se encuentra a la misma distancia de todos los puntos de la circunferencia. A large milk container has a capacity of 1 gallon. center of rotation The point about which a figure is rotated. (p. 10) centro de una rotación Punto alrededor del cual se hace girar una figura Center central angle An angle formed by two radii with its verte at the center of a circle. (p. 7) ángulo central de un círculo Ángulo formado por dos radios cuyo vértice se encuentra en el centro de un círculo. certain (probability) Sure to happen; an event that is certain has a probability of 1. (p. 556) seguro (probabilidad) Que con seguridad sucederá. Representa una probabilidad de 1. When rolling a number cube, it is certain that you will roll a number less than 7. chord A segment with its endpoints on a circle. (p. 6) cuerda Segmento de recta cuyos etremos forman parte de un círculo. G Glossary/Glosario

114 ENGLISH SPANISH EXAMPLES circle The set of all points in a plane that are the same distance from a given point called the center. (p. 6) círculo Conjunto de todos los puntos en un plano que se encuentran a la misma distancia de un punto dado llamado centro. circle graph A graph that uses sectors of a circle to compare parts to the whole and parts to other parts. (p. SB1) gráfica circular Gráfica que usa secciones de un círculo para comparar partes con el todo y con otras partes. Residents of Mesa, AZ % 13% 7% 30% Under 18 11% 18 circumference The distance around a circle. (p. 50) circunferencia Distancia alrededor de un círculo. Circumference clockwise A circular movement to the right in the direction shown. (p. 1) en el sentido de las manecillas del reloj Movimiento circular en la dirección que se indica. coefficient The number that is multiplied by a variable in an algebraic epression. (p. 10) commission A fee paid to a person for making a sale. (p. 98) commission rate The fee paid to a person who makes a sale epressed as a percent of the selling price. (p. 98) common denominator A denominator that is the same in two or more fractions. (p. 70) common factor A number that is a factor of two or more numbers. (p. SB6) common multiple A number that is a multiple of each of two or more numbers. (p. SB6) Commutative Property of Addition The property that states that two or more numbers can be added in any order without changing the sum. (p. 116) coeficiente Número que se multiplica por una variable en una epresión algebraica. comisión Pago que recibe una persona por realizar una venta. tasa de comisión Pago que recibe una persona por hacer una venta, epresado como un porcentaje del precio de venta. común denominador Denominador que es común a dos o más fracciones. factor común Número que es factor de dos o más números. común múltiplo Número que es múltiplo de dos o más números. Propiedad conmutativa de la suma Propiedad que establece que sumar dos o más números en cualquier orden no altera la suma. 5 is the coefficient in 5b. A commission rate of 5% and a sale of $10,000 results in a commission of $500. The common denominator of 5 8 and is is a common factor of 16 and is a common multiple of 3 and ; a b b a Glossary/Glosario G5

115 ENGLISH SPANISH EXAMPLES ; a b b a Commutative Property of Multiplication The property that states that two or more numbers can be multiplied in any order without changing the product. (p. 116) Propiedad conmutativa de la multiplicación Propiedad que establece que multiplicar dos o más números en cualquier orden no altera el producto. compatible numbers Numbers that are close to the given numbers that make estimation or mental calculation easier. (p. 78) números compatibles Números que están cerca de los números dados y hacen más fácil la estimación o el cálculo mental. To estimate , use the compatible numbers 8000 and 5000: ,000. complementary angles Two angles whose measures add to 90. (p. 379) ángulos complementarios Dos ángulos cuyas medidas suman A 53 B The complement of a 53 angle is a 37 angle. composite figure A figure made up of simple geometric shapes. (p. 36) figura compuesta Figura formada por figuras geométricas simples. cm 3 cm cm cm 5 cm 5 cm cm composite number A whole number greater than 1 that has more than two positive factors. (p. SB5) compound event An event made up of two or more simple events. (p. 569) compound inequality A combination of more than one inequality. (p. 137) compound interest Interest earned or paid on principal and previously earned or paid interest. (p. 30) cone A three-dimensional figure with a circular base lying in one plane plus a verte not lying on that plane. The remaining surface of the cone is formed by joining the verte to points on the circle by line segments. (p. 81) número compuesto Número mayor que 1 que tiene más de dos factores que son números cabales. suceso compuesto Suceso formado por dos o más sucesos simples. desigualdad compuesta Combinación de dos o más desigualdades. interés compuesto Interés que se gana o se paga sobre el capital y los intereses previamente ganados o pagados. cono Figura tridimensional con una base circular que está en un plano más un vértice que no está en ese plano. El resto de la superficie del cono se forma uniendo el vértice con puntos del círculo por medio de segmentos de recta., 6, 8, and 9 are composite numbers. Rolling a 3 on a number cube and spinning a on a spinner is a compound event. or 10; 10 If $100 is put into an account with an interest rate of 5% compounded monthly, then after years, the account will have $ G6 Glossary/Glosario

116 ENGLISH SPANISH EXAMPLES Q R congruent Having the same size and shape. (p. 06) congruentes Que tienen la misma forma y el mismo tamaño. P S PQ RS congruent angles Angles that have the same measure. (p. 38) ángulos congruentes Ángulos que tienen la misma medida. A C E B D F ABC DEF congruent segments Segments that have the same length. (p. 38) segmentos congruentes Segmentos que tienen la misma longitud. P Q R S PQ SR constant A value that does not change. (p. 10) constant of variation The constant k in direct and inverse variation equations. (p. 357) conversion factor A fraction whose numerator and denominator represent the same quantity but use different units; the fraction is equal to 1 because the numerator and denominator are equal. (p. 37) coordinate One of the numbers of an ordered pair that locate a point on a coordinate graph. (p. 3) constante Valor que no cambia. constante de variación La constante k en ecuaciones de variación directa e inversa. factor de conversión Fracción cuyo numerador y denominador representan la misma cantidad pero con unidades distintas; la fracción es igual a 1 porque el numerador y el denominador son iguales. coordenada Uno de los números de un par ordenado que ubica un punto en una gráfica de coordenadas. 3, 0, π y 5 constant of variation hours 1 day and 1 day hours y B O The coordinates of B are (, 3) coordinate plane (coordinate grid) A plane formed by the intersection of a horizontal number line called the -ais and a vertical number line called the y-ais. (p. 3) plano cartesiano (cuadrícula de coordenadas) Plano formado por la intersección de una recta numérica horizontal llamada eje y otra vertical llamada eje y. O y-ais -ais Glossary/Glosario G7

117 ENGLISH SPANISH EXAMPLES correlation The description of the relationship between two data sets. (p. 58) correlación Descripción de la relación entre dos conjuntos de datos. correspondence The relationship between two or more objects that are matched. (p. 06) correspondencia La relación entre dos o más objetos que coinciden. A and D are corresponding angles. A B C AB and DE are corresponding sides. E D F corresponding angles (for lines) For two lines intersected by a transversal, a pair of angles that lie on the same side of the transversal and on the same sides of the other two lines. (p. 389) corresponding angles (in polygons) Matching angles of two or more polygons. (p. ) ángulos correspondientes (en líneas) Dadas dos líneas cortadas por una transversal, el par de ángulos ubicados en el mismo lado de la transversal y en los mismos lados de las otras dos líneas. ángulos correspondientes (en polígonos) Ángulos que están en la misma posición relativa en dos o más polígonos. m n o p q r s t m and q are corresponding angles. A and D are corresponding angles. corresponding sides Matching sides of two or more polygons. (p. ) lados correspondientes Lados que se ubican en la misma posición relativa en dos o más polígonos. AB and DE are corresponding sides. counterclockwise A circular movement to the left in the direction shown. (p. 1) en sentido contrario a las manecillas del reloj Movimiento circular en la dirección que se indica. cross products In the statement a b c d, bc and ad are the cross products. (p. 3) productos cruzados En el enunciado a b c d, bc y ad son productos cruzados. 3 6 For the proportion 3 6, the cross products are 6 1 and 3 1. G8 Glossary/Glosario

118 ENGLISH SPANISH EXAMPLES cube (geometric figure) A rectangular prism with si congruent square faces. (p. 77) cubo (figura geométrica) Prisma rectangular con seis caras cuadradas congruentes. cube (in numeration) A number raised to the third power. (p. 168) cubic function A polynomial function of degree 3. (p. 338) cubo (en numeración) Número elevado a la tercera potencia. función cúbica Función polinomial de grado is the cube of. y = 3 customary system of measurement The measurement system often used in the United States. (p. SB15) cylinder A three-dimensional figure with two parallel congruent circular bases. The third surface of the cylinder consists of all parallel circles of the same radius whose centers lie on the segment joining the centers of the bases. (p. 81) sistema usual de medidas El sistema de medidas que se usa comúnmente en Estados Unidos. cilindro Figura tridimensional con dos bases circulares paralelas y congruentes. La tercera superficie del cilindro consiste en todos los círculos paralelos del mismo radio cuyo centro está en el segmento que une los centros de las bases. inches, feet, miles, ounces, pounds, tons, cups, quarts, gallons decagon A polygon with ten sides. (p. SB16) decágono Polígono de diez lados. deductive reasoning The process of using logic to draw conclusions. (p. SB) degree The unit of measure for angles or temperature. (p. 379) degree of a polynomial The highest power of the variable in a polynomial. (p. 591) denominator The bottom number of a fraction that tells how many equal parts are in the whole. (p. 66) Density Property The property that states that between any two real numbers, there is always another real number. (p. 199) razonamiento deuctivo Proceso en el que se utiliza la lógica para sacar conclusions. grado Unidad de medida para ángulos y temperaturas. grado de un polinomio La potencia más alta de la variable en un polinomio. denominador Número que está abajo en una fracción y que indica en cuántas partes iguales se divide el entero. Propiedad de densidad Propiedad según la cual entre dos números reales cualesquiera siempre hay otro número real. The polynomial has degree 5. In the fraction, 5 is the 5 denominator. Glossary/Glosario G9

119 ENGLISH SPANISH EXAMPLES dependent events Events for sucesos dependientes Dos A bag contains 3 red marbles and which the outcome of one event sucesos son dependientes si el blue marbles. Drawing a red marble and then drawing a blue affects the probability of the resultado de uno afecta la marble without replacing the first other. (p. 569) probabilidad del otro. marble is an eample of dependent events. diagonal A line segment that connects two non-adjacent vertices of a polygon. (p. 03) diagonal Segmento de recta que une dos vértices no adyacentes de un polígono. E A B D C Diagonal diameter A line segment that passes through the center of a circle and has endpoints on the circle, or the length of that segment. (p. 6) diámetro Segmento de recta que pasa por el centro de un círculo y tiene sus etremos en la circunferencia, o bien la longitud de ese segmento. difference The result when one number is subtracted from another. (p. 10) dimensions (geometry) The length, width, or height of a figure. (p. 80) diferencia El resultado de restar un número de otro. dimensiones (geometría) Longitud, ancho o altura de una figura. In , 11 is the difference. direct variation A relationship between two variables in which the data increase or decrease together at a constant rate. (p. 357) variación directa Relación entre dos variables en la que los datos aumentan o disminuyen juntos a una tasa constante. y y discount The amount by which the original price is reduced. (p. 95) descuento Cantidad que se resta del precio original de un artículo. disjoint events Two events are disjoint if they cannot occur in the same trial of an eperiment. (p. 566) Distributive Property The property that states if you multiply a sum by a number, you will get the same result if you multiply each addend by that number and then add the products. (p. 117) dividend The number to be divided in a division problem. (p. SB7) divisible Can be divided by a number without leaving a remainder. (p. SB) sucesos desunidos Dos sucesos son desunidos si no pueden ocurrir en la misma prueba de un eperimento. Propiedad distributiva Propiedad que establece que, si multiplicas una suma por un número, obtienes el mismo resultado que si multiplicas cada sumando por ese número y luego sumas los productos. dividendo Número que se divide en un problema de división. divisible Que se puede dividir entre un número sin dejar residuo. When rolling a number cube, rolling a 3 and rolling an even number are disjoint events (0 1) (5 0) (5 1) In 8, 8 is the dividend. 18 is divisible by 3. G10 Glossary/Glosario

120 ENGLISH SPANISH EXAMPLES Division Property of Equality The property that states that if you divide both sides of an equation by the same nonzero number, the new equation will have the same solution. (p. 37) Propiedad de igualdad de la división Propiedad que establece que puedes dividir ambos lados de una ecuación entre el mismo número distinto de cero, y la nueva ecuación tendrá la misma solución divisor The number you are dividing by in a division problem. (p. SB7) domain The set of all possible input values of a function. (p. 36) double-bar graph A bar graph that compares two related sets of data. (p. SB17) divisor El número entre el que se divide en un problema de división. dominio Conjunto de todos los posibles valores de entrada de una función. gráfica de doble barra Gráfica de barras que compara dos conjuntos de datos relacionados. In 8, is the divisor. The domain of the function y 1 is all real numbers. Number of students Students at Hill Middle School Grade 6 Grade 7 Grade 8 Boys Girls edge The line segment along which two faces of a polyhedron intersect. (p. 80) arista Segmento de recta donde se intersecan dos caras de un poliedro. Edge endpoint A point at the end of a line segment or ray. (p. 378) etremo Un punto ubicado al final de un segmento de recta o rayo. equally likely Outcomes that have the same probability. (p. 56) equation A mathematical sentence that shows that two epressions are equivalent. (p. 3) equilateral triangle A triangle with three congruent sides. (p. 393) igualmente probables Resultados que tienen la misma probabilidad de ocurrir. ecuación Enunciado matemático que indica que dos epresiones son equivalentes. triángulo equilátero Triángulo con tres lados congruentes. When tossing a coin, the outcomes heads and tails are equally likely equivalent epressions Equivalent epressions have the same value for all values of the variables. (p. 10) epresión equivalente Las epresiones equivalentes tienen el mismo valor para todos los valores de las variables. 5 and 9 are equivalent epressions. Glossary/Glosario G11

121 ENGLISH SPANISH EXAMPLES equivalent ratios Ratios that name the same comparison. (p. ) razones equivalentes Razones que representan la misma comparación. 1 and are equivalent ratios. estimate (n) An answer that is close to the eact answer and is found by rounding or other methods. (v) To find such an answer. (p. 78) evaluate To find the value of a numerical or algebraic epression. (p. 6) even number A whole number that is divisible by two. (p. SB) event An outcome or set of outcomes of an eperiment or situation. (p. 556) eperiment (probability) In probability, any activity based on chance (such as tossing a coin). (p. 556) eperimental probability The ratio of the number of times an event occurs to the total number of trials, or times that the activity is performed. (p. 560) eponent The number that indicates how many times the base is used as a factor. (p. 166) eponential form A number is in eponential form when it is written with a base and an eponent. (p. 166) epression A mathematical phrase that contains operations, numbers, and/or variables. (p. 6) estimación (s) Una solución aproimada a la respuesta eacta que se halla mediante el redondeo u otros métodos. estimar (v) Hallar una solución aproimada a la respuesta eacta. evaluar Hallar el valor de una epresión numérica o algebraica. número par Número cabal divisible entre. suceso Un resultado o una serie de resultados de un eperimento o una situación. eperimento (probabilidad) En probabilidad, cualquier actividad basada en la posibilidad, como lanzar una moneda. probabilidad eperimental Razón del número de veces que ocurre un suceso al número total de pruebas o al número de veces que se realiza el eperimento. eponente Número que indica cuántas veces se usa la base como factor. forma eponencial Se dice que un número está en forma eponencial cuando se escribe con una base y un eponente. epresión Enunciado matemático que contiene operaciones, números y/o variables. 500 is an estimate for the sum Evaluate 7 for 3. 7 (3) ,, 6 When rolling a number cube, the event an odd number consists of the outcomes 1, 3, and 5. Tossing a coin 10 times and noting the number of heads. Kendra attempted 7 free throws and made 16 of them. Her eperimental probability of making a free throw is number made number attempted 3 8; 3 is the eponent is the eponential form for. face A flat surface of a polyhedron. (p. 80) cara Superficie plana de un poliedro. Face G1 Glossary/Glosario

122 ENGLISH SPANISH EXAMPLES factor A number that is multiplied by another number to get a product. (p. SB) factor Número que se multiplica por otro para hallar un producto. 7 is a factor of 1 since Fahrenheit A temperature scale in which 3 F is the freezing point of water and 1 F is the boiling point of water. (p. SB15) fair When all outcomes of an eperiment are equally likely, the eperiment is said to be fair. (p. 56) first quartile The median of the lower half of a set of data; also called lower quartile. (p. 5) FOIL An acronym for the terms used when multiplying two binomials: the First, Inner, Outer, and Last terms. (p. 618) formula A rule showing relationships among quantities. (p. 3) fraction A number in the form a b, where b 0. (p. 66) frequency table A table that lists items together according to the number of times, or frequency, that the items occur. (p. SB19) Fahrenheit Escala de temperatura en la que 3 F es el punto de congelación del agua y 1 F es el punto de ebullición. justo Se dice de un eperimento donde todos los resultados posibles son igualmente probables. primer cuartil La mediana de la mitad inferior de un conjunto de datos. También se llama cuartil inferior. FOIL Sigla en inglés de los términos que se usan al multiplicar dos binomios: los primeros, los eternos, los internos y los últimos (First, Outer, Inner, Last). fórmula Regla que muestra relaciones entre cantidades. fracción Número escrito en la forma a, b donde b 0. tabla de frecuencia Una tabla en la que se organizan los datos de acuerdo con el número de veces que aparece cada valor (o la frecuencia). When tossing a coin, heads and tails are equally likely, so it is a fair eperiment. Lower quartile Minimum F L ( )( 3) 3 6 I 6 O A w is the formula for the area of a rectangle. 3 Data set: 1, 1,,, 3,, 5, 5, 5, 6, 6 Frequency table: Data Upper quartile Median Maimum Frequency function An input-output relationship that has eactly one output for each input. (p. 36) función Relación de entrada-salida en la que a cada valor de entrada corresponde eactamente un valor de salida Glossary/Glosario G13

123 ENGLISH SPANISH EXAMPLES graph of an equation A graph of the set of ordered pairs that are solutions of the equation. (p. 13) gráfica de una ecuación Gráfica del conjunto de pares ordenados que son soluciones de la ecuación. y 1 O y great circle A circle on a sphere such that the plane containing the circle passes through the center of the sphere. (p. 508) círculo máimo Círculo de una esfera tal que el plano que contiene el círculo pasa por el centro de la esfera. Great circle greatest common divisor (GCD) The largest whole number that divides evenly into two or more given numbers. (p. SB6) máimo común divisor (MCD) El mayor de los factores comunes compartidos por dos o más números dados. The GCD of 7 and 5 is 9. height In a triangle or quadrilateral, the perpendicular distance from the base to the opposite verte or side. (p. 35) In a trapezoid, the perpendicular distance between the bases. (p. 0) In a prism or cylinder, the perpendicular distance between the bases. (p. 13) In a pyramid or cone, the perpendicular distance from the base to the opposite verte. (p. 0) altura En un triángulo o cuadrilátero, la distancia perpendicular desde la base de la figura al vértice o lado opuesto. En un trapecio, la distancia perpendicular entre las bases. En un prisma o cilindro, la distancia perpendicular entre las bases. En una pirámide o cono, la distancia perpendicular desde la base al vértice opuesto. b h b 1 h Height hemisphere A half of a sphere. (p. 508) hemisferio La mitad de una esfera. heptagon A seven-sided polygon. (p. SB16) heptágono Polígono de siete lados. heagon A si-sided polygon. (p. SB16) heágono Polígono de seis lados. G1 Glossary/Glosario

124 ENGLISH SPANISH EXAMPLES histogram A bar graph that shows the frequency of data within equal intervals. (p. SB19) hypotenuse In a right triangle, the side opposite the right angle. (p. 03) histograma Gráfica de barras que muestra la frecuencia de los datos en intervalos iguales. hipotenusa En un triángulo rectángulo, el lado opuesto al ángulo recto. Frequency Starting Salaries Salary range (thousand $) hypotenuse Identity Property of Multiplication The property that states that the product of 1 and any number is that number. (p. 37) Identity Property of Addition The property that states the sum of zero and any number is that number. (p. 3) Propiedad de identidad del uno Propiedad que establece que el producto de 1 y cualquier número es ese número. Propiedad de identidad del cero Propiedad que establece que la suma de cero y cualquier número es ese número image A figure resulting from a transformation. (p. 10) imagen Figura que resulta de una transformación. B B A C A C impossible (probability) Can never happen; an event that is impossible has a probability of 0. (p. 556) improper fraction A fraction in which the numerator is greater than or equal to the denominator. (p. SB9) independent events Events for which the outcome of one event does not affect the probability of the other. (p. 569) indirect measurement The technique of using similar figures and proportions to find a measure. (p. 8) imposible (en probabilidad) Que no puede ocurrir. Suceso cuya probabilidad de ocurrir es 0. fracción impropia Fracción cuyo numerador es mayor que o igual al denominador. sucesos independientes Dos sucesos son independientes si el resultado de uno no afecta la probabilidad del otro. medición indirecta La técnica de usar figuras semejantes y proporciones para hallar una medida. When rolling a standard number cube, rolling a 7 is an impossible event , 3 3 A bag contains 3 red marbles and blue marbles. Drawing a red marble, replacing it, and then drawing a blue marble is an eample of independent events. Glossary/Glosario G15

125 ENGLISH SPANISH EXAMPLES inductive reasoning The process of conjecturing that a general rule or statement is true because specific cases are true. (p. SB) razonamiento inductivo Proceso de razonamiento por el que se determina que una regal o enunciado son verdaderos porque ciertos casos específicos son verdaderos. inequality A mathematical statement that compares two epressions by using one of the following symbols:,,,, or. (p. 136) input The value substituted into an epression or function. (p. 36) integers The set of whole numbers and their opposites. (p. 1) interest The amount of money charged for borrowing or using money. (p. 303) desigualdad Enunciado matemático que compara dos epresiones por medio de uno de los siguientes símbolos:,,,, ó. valor de entrada Valor que se usa para sustituir una variable en una epresión o función. enteros Conjunto de todos los números cabales y sus opuestos. interés Cantidad de dinero que se cobra por el préstamo o uso del dinero For the function y 6, the input produces an output of.... 3,, 1, 0, 1,, 3,... interior angles Angles on the inner sides of two lines cut by a transversal. (p. 389) ángulos internos Ángulos en los lados internos de dos líneas intersecadas por una transversal. t v r s r, s, t, and v are interior angles. intersecting lines Lines that cross at eactly one point. (p. 388) interval The space between marked values on a number line or the scale of a graph. (p. SB18) inverse operations Operations that undo each other: addition and subtraction, or multiplication and division. (p. 3) irrational number A real number that cannot be epressed as a ratio of two integers. (p. 198) líneas secantes Líneas que se cruzan en un solo punto. intervalo El espacio entre los valores marcados en una recta numérica o en la escala de una gráfica. operaciones inversas Operaciones que se cancelan mutuamente: suma y resta, o multiplicación y división. número irracional Número real que no se puede epresar como una razón de dos enteros. Adding 3 and subtracting 3 are inverse operations: 5 3 8; Multiplying by 3 and dividing by 3 are inverse operations: 3 6; 6 3, π m n isolate the variable To get a variable alone on one side of an equation or inequality in order to solve the equation or inequality. (p. 3) despejar la variable Dejar sola la variable en un lado de una ecuación o desigualdad para resolverla G16 Glossary/Glosario

126 ENGLISH SPANISH EXAMPLES isosceles triangle A triangle with at least two congruent sides. (p. 393) triángulo isósceles Triángulo que tiene al menos dos lados congruentes. lateral area The sum of the areas of the lateral faces of a prism or pyramid, or the area of the lateral surface of a cylinder or cone. (p. 98) área lateral Suma de las áreas de las caras laterales de un prisma o pirámide, o área de la superficie lateral de un cilindro o cono. Lateral area (8)(1) (6)(1) 336 cm lateral face In a prism or a pyramid, a face that is not a base. (p. 98) cara lateral En un prisma o pirámide, una cara que no es la base. Bases Lateral face Right prism lateral surface In a cylinder, the curved surface connecting the circular bases; in a cone, the curved surface that is not a base. (p. 99) superficie lateral En un cilindro, superficie curva que une las bases circulares; en un cono, la superficie curva que no es la base. Lateral surface Right cylinder least common denominator (LCD) The least common multiple of two or more denominators. (p. 70) mínimo común denominador (mcd) El mínimo común múltiplo de dos o más denominadores. The LCD of 3 and 5 is 1. 6 least common multiple (LCM) The least number, other than zero, that is a multiple of two or more given numbers. (p. SB6) mínimo común múltiplo (mcm) El menor de los números cabales, distinto de cero, que es múltiplo de dos o más números dados. The LCM of 6 and 10 is 30. legs In a right triangle, the sides that include the right angle; in an isosceles triangle, the pair of congruent sides. (p. 03) catetos En un triángulo rectángulo, los lados adyacentes al ángulo recto. En un triángulo isósceles, el par de lados congruentes. leg leg like terms Two or more terms that have the same variable raised to the same power. (p. 10) line A straight path that etends without end in opposite directions. (p. 378) términos semejantes Dos o más términos que contienen la misma variable elevada a la misma potencia. línea Trayectoria recta que se etiende de manera indefinida en direcciones opuestas. In the epression 3a 5b 1a, 3a and 1a are like terms. Glossary/Glosario G17

127 ENGLISH SPANISH EXAMPLES line graph A graph that uses line segments to show how data changes. (p. SB18) gráfica lineal Gráfica que muestra cómo cambian los datos mediante segmentos de recta. Score Marlon s Video Game Scores Game number line of best fit A straight line that comes closest to the points on a scatter plot. (p. 59) línea de mejor ajuste La línea recta que más se aproima a los puntos de un diagrama de dispersión line of reflection A line that a figure is flipped across to create a mirror image of the original figure. (p. 10) ínea de refleión Línea sobre la cual se invierte una figura para crear una imagen reflejada de la figura original. Q R S T S T R Q line plot A number line with marks or dots that show frequency. (p. 53) diagrama de acumulación Recta numérica con marcas o puntos que indican la frecuencia. X X X X X X X X X Number of pets line segment A part of a line between two endpoints. (p. 378) segmento de recta Parte de una línea con dos etremos. G H GH linear equation An equation whose solutions form a straight line on a coordinate plane. (p. 330) ecuación lineal Ecuación cuyas soluciones forman una línea recta en un plano cartesiano. y 1 linear function A function whose graph is a straight line. (p. 330) función lineal Función cuya gráfica es una línea recta. y 1 y O lower quartile The median of the lower half of a set of data; also called first quartile. (p. 5) cuartil inferior La mediana de la mitad inferior de un conjunto de datos; también se llama primer cuartil. Lower quartile Minimum Upper quartile Median Maimum G18 Glossary/Glosario

128 ENGLISH SPANISH EXAMPLES markup The amount by which a wholesale cost is increased. (p. 95) maimum The greatest value in a data set. (p. 53) mean The sum of a set of data divided by the number of items in the data set; also called average. (p. 537) measure of central tendency A measure used to describe the middle of a data set. (p. 538) median The middle number, or the mean (average) of the two middle numbers, in an ordered set of data. (p. 537) metric system of measurement A decimal system of weights and measures that is used universally in science and commonly throughout the world. (p. SB15) midpoint The point that divides a line segment into two congruent line segments. (p. 393) minimum The least value in a data set. (p. 53) mied number A number made up of a whole number that is not zero and a fraction. (p. SB9) mode The number or numbers that occur most frequently in a set of data; when all numbers occur with the same frequency, we say there is no mode. (p. 537) monomial A number or a product of numbers and variables with eponents that are whole numbers. (p. 178) margen de beneficio Cantidad que se agrega a un costo mayorista. máimo El valor mayor de un conjunto de datos. media La suma de todos los elementos de un conjunto de datos dividida entre el número de elementos del conjunto. También se llama promedio. medida de tendencia dominante Medida que describe la parte media de un conjunto de datos. mediana El número intermedio o la media (el promedio) de los dos números intermedios en un conjunto ordenado de datos. sistema métrico de medición Sistema decimal de pesos y medidas empleado universalmente en las ciencias y de uso común en todo el mundo. punto medio El punto que divide un segmento de recta en dos segmentos de recta congruentes. mínimo El valor meno de un conjunto datos. número mito Número compuesto por un número cabal distinto de cero y una fracción. moda Número o números más frecuentes en un conjunto de datos; si todos los números aparecen con la misma frecuencia, no hay moda. monomio Un número o un producto de números y variables con eponentes que son números cabales. Data set:, 6, 7, 8, 10 Maimum: 10 Data set:, 6, 7, 8, 10 Mean: mean or median Data set:, 6, 7, 8, 10 Median: 7 centimeters, meters, kilometers, gram, kilograms, milliliters, liters B is the midpoint of AC. Data set:, 6, 7, 8, 10 Minimum: 1 8 Data set: 3, 5, 8, 8, 10 Mode: 8 3 y Glossary/Glosario G19

129 ENGLISH SPANISH EXAMPLES multiple The product of any number and a non-zero whole number is a multiple of that number. (p. SB) múltiplo El producto de cualquier número y un número cabal distinto de cero es un múltiplo de ese número. 30, 0, and 90 are all multiplies of 10. Multiplication Property of Equality The property that states that if you multiply both sides of an equation by the same number, the new equation will have the same solution. (p. 38) multiplicative inverse One of two numbers whose product is 1; also called reciprocal. (p. 8) mutually eclusive Two events are mutually eclusive if they cannot occur in the same trial of an eperiment. (p. 566) Propiedad de igualdad de la multiplicación Propiedad que establece que puedes multiplicar ambos lados de una ecuación por el mismo número y la nueva ecuación tendrá la misma solución. inverso multiplicativo Uno de dos números cuyo producto es 1; también llamado recíproco. mutuamente ecluyentes Dos sucesos son mutuamente ecluyentes cuando no pueden ocurrir en la misma prueba de un eperimento (3) 1 3 (3)(7) 1 The multiplicative inverse of 3 is 3. When rolling a number cube, rolling a 3 and rolling an even number are mutually eclusive events. negative correlation Two data sets have a negative correlation if one set of data values increases while the other decreases. (p. 59) correlación negativa Dos conjuntos de datos tienen correlación negativa si los valores de un conjunto aumentan a medida que los valores del otro conjunto disminuyen. y negative integer An integer less than zero. (p. 1) entero negativo Entero menor que cero. is a negative integer net An arrangement of twodimensional figures that can be folded to form a polyhedron. (p. 96) plantilla Arreglo de figuras bidimensionales que se doblan para formar un poliedro. 6 m 10 m 10 m 6 m no correlation Two data sets have no correlation when there is no relationship between their data values. (p. 59) sin correlación Caso en que los valores de dos conjuntos no muestran ninguna relación. y numerator The top number of a fraction that tells how many parts of a whole are being considered. (p. 66) numerador El número de arriba de una fracción; indica cuántas partes de un entero se consideran. 5 numerator numerical epression An epression that contains only numbers and operations. (p. 6) epresión numérica Epresión que incluye sólo números y operaciones. ( 3) 1 G0 Glossary/Glosario

130 ENGLISH SPANISH EXAMPLES obtuse angle An angle whose measure is greater than 90 but less than 180. (p. 379) obtuse triangle A triangle containing one obtuse angle. (p. 39) octagon An eight-sided polygon. (p. SB16) ánlgulo obtuso Ángulo que mide más de 90 y menos de 180. triángulo obtusángulo Triángulo que tiene un ángulo obtuso. octágono Polígono de ocho lados. odd number A whole number that is not divisible by two. (p. SB) opposites Two numbers that are an equal distance from zero on a number line; also called additive inverse. (p. 1) order of operations A rule for evaluating epressions: First perform the operations in parentheses, then compute powers and roots, then perform all multiplication and division from left to right, and then perform all addition and subtraction from left to right. (p. SB1) número impar Número cabal que no es divisible entre. opuestos Dos números que están a la misma distancia de cero en una recta numérica. También se llaman inversos aditivos. orden de las operaciones Regla para evaluar epresiones: primero se hacen las operaciones entre paréntesis, luego se hallan las potencias y raíces, después todas las multiplicaciones y divisiones de izquierda a derecha, y por último, todas las sumas y restas de izquierda a derecha. 1, 3, 5 5 and 5 are opposites Simplify the power Divide. 16 Add. 0 5 units 5 units ordered pair A pair of numbers that can be used to locate a point on a coordinate plane. (p. 3) par ordenado Par de números que sirven para ubicar un punto en un plano cartesiano. B y O The coordinates of B are (, 3). origin The point where the -ais and y-ais intersect on the coordinate plane; (0, 0). (p. 3) origen Punto de intersección entre el eje y el eje y en un plano cartesiano: (0, 0). O origin outcome (probability) A possible result of a probability eperiment. (p. 556) resultado (en probabilidad) Posible resultado de un eperimento de probabilidad. When rolling a number cube, the possible outcomes are 1,, 3,, 5, and 6. Glossary/Glosario G1

131 ENGLISH SPANISH EXAMPLES outlier A value much greater or much less than the others in a data set. (p. 538) valor etremo Un valor mucho mayor o menor que los demás valores de un conjunto de datos. Most of data Mean Outlier output The value that results from the substitution of a given input into an epression or function. (p. 36) valor de salida Valor que resulta después de sustituir una variable por un valor de entrada determinado en una epresión o función. For the function y 6, the input produces an output of. parabola The graph of a quadratic function. (p. 33) parábola Gráfica de una función cuadrática. parallel lines Lines in a plane that do not intersect. (p. 38) líneas paralelas Líneas que se encuentran en el mismo plano pero que nunca se intersecan. r s parallel planes Planes that do not intersect. (p. 385) planos paralelos Planos que no se cruzan. Plane AEF and plane CGH are parallel planes. parallelogram A quadrilateral with two pairs of parallel sides. (p. 399) paralelogramo Cuadrilátero con dos pares de lados paralelos. pentagon A five-sided polygon. (p. SB16) pentágono Polígono de cinco lados. percent A ratio comparing a number to 100. (p. 7) percent of change The amount stated as a percent that a number increases or decreases. (p. 9) percent of decrease A percent change describing a decrease in a quantity. (p. 9) porcentaje Razón que compara un número con el número 100. porcentaje de cambio Cantidad en que un número aumenta o disminuye, epresada como un porcentaje. porcentaje de disminución Porcentaje de cambio en que una cantidad disminuye. 5 5% 1 00 An item that costs $8 is marked down to $6. The amount of the decrease is $, and the percent of decrease is 0.5 5%. 8 G Glossary/Glosario

132 ENGLISH SPANISH EXAMPLES percent of increase A percent change describing an increase in a quantity. (p. 9) porcentaje de incremento Porcentaje de cambio en que una cantidad aumenta. The price of an item increases from $8 to $1. The amount of the increase is $ and the percent of increase is % 8 perfect square A square of a whole number. (p. 190) cuadrado perfecto El cuadrado de un número cabal. 5 5, so 5 is a perfect square. perimeter The sum of the lengths of the sides of a polygon. (p. 3) perímetro La suma de las longitudes de los lados de un polígono. 18 ft 6ft perimeter ft perpendicular bisector A line that intersects a segment at its midpoint and is perpendicular to the segment. (p. 38) mediatriz Línea que cruza un segmento en su punto medio y es perpendicular al segmento. perpendicular lines Lines that intersect to form right angles. (p. 38) líneas perpendiculares Líneas que al intersecarse forman ángulos rectos. n m perpendicular planes Planes that intersect at 90 angles. (p. 385) planos perpendiculares Planos que se cruzan en ángulos de 90. pi (π) The ratio of the circumference of a circle to the length of its diameter; π 3.1 or 7. (p. 50) pi (π ) Razón de la circunferencia de un círculo a la longitud de su diámetro; π 3.1 ó 7. plane A flat surface that etends forever. (p. 378) plano Superficie plana que se etiende de manera indefinida en todas direcciones. R A B C point An eact location in space. (p. 378) polygon A closed plane figure formed by three or more line segments that intersect only at their endpoints (vertices). (p. 399) punto Ubicación eacta en el espacio. polígono Figura plana cerrada, formada por tres o más segmentos de recta que se intersecan sólo en sus etremos (vértices). P polyhedron A three-dimensional figure in which all the surfaces or faces are polygons. (p. 80) polynomial One monomial or the sum or difference of monomials. (p. 590) population The entire group of objects or individuals considered for a survey. (p. SB) poliedro Figura tridimensional cuyas superficies o caras tiene forma de polígonos. polinomio Un monomio o la suma o la diferencia de monomios. población Grupo completo de objetos o individuos que se desea estudiar. 3y 7y In a survey about study habits of middle school students, the population is all middle school students. Glossary/Glosario G3

133 ENGLISH SPANISH EXAMPLES positive correlation Two data sets have a positive correlation when their data values increase or decrease together. (p. 59) correlación positiva Dos conjuntos de datos tienen una correlación positiva cuando los valores de ambos conjuntos aumentan o disminuyen al mismo tiempo. y positive integer An integer greater than zero. (p. 1) power A number produced by raising a base to an eponent. (p. 166) entero positivo Entero mayor que cero. potencia Número que resulta al elevar una base a un eponente. is a positive integer. 3 8, so to the 3rd power is 8. prime factorization A number written as the product of its prime factors. (p. SB5) prime number A whole number greater than 1 that has eactly two factors, itself and 1. (p. SB5) principal The initial amount of money borrowed or saved. (p. 30) principal square root The nonnegative square root of a number. (p. 190) factorización prima Un número escrito como el producto de sus factores primos. número primo Número cabal mayor que 1 que sólo es divisible entre 1 y él mismo. capital Cantidad inicial de dinero depositada o recibida en préstamo. raíz cuadrada principal Raíz cuadrada no negativa de un número. 10 5, is prime because its only factors are 5 and ; the principal square root of 5 is 5. prism A three-dimensional figure with two congruent parallel polygonal bases. The remaining edges join corresponding vertices of the bases so that the remaining faces are rectangles. (p. 80) probability A number from 0 to 1 (or 0% to 100%) that describes how likely an event is to occur. (p. 556) prisma Figura tridimensional con dos bases poligonales congruentes y paralelas. El resto de las aristas se unen a los vértices correspondientes de las bases de manera que el resto de las caras sean rectángulos. probabilidad Un número entre 0 y 1 (ó 0% y 100%) que describe qué tan probable es un suceso. A bag contains 3 red marbles and blue marbles. The probability of randomly choosing a red marble is 3 7. product The result when two or more numbers are multiplied. (p. 6) producto Resultado de multiplicar dos o más números. The product of and 8 is 3. profit The difference between total income and total epenses. (p. 99) ganancia Diferencia entre el total de ingresos y de gastos. If total income is $,00, and total epenses are $,100, the profit is $,00 $,100 $300. proportion An equation that states that two ratios are equivalent. (p. 3) proporción Ecuación que establece que dos razones son equivalentes. 3 6 protractor A tool for measuring angles. (p. 78) transportador Instrumento para medir ángulos. G Glossary/Glosario

134 ENGLISH SPANISH EXAMPLES pyramid A three-dimensional figure with a polygonal base lying in one plane plus one additional verte not lying on that plane. The remaining edges of the pyramid join the additional verte to the vertices of the base. (p. 80) pirámide Figura tridimensional con una base poligonal en un plano más un vértice adicional que no está en ese plano. El resto de las aristas de la pirámide unen el vértice adicional con los vértices de la base. Pythagorean Theorem In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. (p. 03) Teorema de Pitágoras En un triángulo rectángulo, la suma de los cuadrados de los catetos es igual al cuadrado de la hipotenusa. 13 cm 1 cm cm quadrant The - and y-aes divide the coordinate plane into four regions. Each region is called a quadrant. (p. 3) cuadrante El eje y el eje y dividen el plano cartesiano en cuatro regiones. Cada región recibe el nombre de cuadrante. Quadrant II O Quadrant I Quadrant III Quadrant IV quadratic function A function of the form y a b c, where a 0. (p. 33) función cuadrática Función del tipo y a b c, donde a 0. y 6 8 quadrilateral A four-sided polygon. (p. 399) cuadrilátero Polígono de cuatro lados. quarterly Four times a year. (p. 305) trimestral Cuatro veces al año. quartile Three values, one of which is the median, that divide a data set into fourths. (p. 5) quotient The result when one number is divided by another. (p. SB7) cuartil Cada uno de tres valores, uno de los cuales es la mediana, que dividen en cuartos un conjunto de datos. cociente Resultado de dividir un número entre otro. Lower quartile Minimum Upper quartile Median Maimum In 8, is the quotient. radical symbol The symbol used to represent the nonnegative square root of a number. (p. 19) símbolo de radical El símbolo con que se representa la raíz cuadrada no negativa de un número Glossary/Glosario G5

135 ENGLISH SPANISH EXAMPLES radius A line segment with one endpoint at the center of the circle and the other endpoint on the circle, or the length of that segment. (p. 6) radio Segmento de recta con un etremo en el centro de un círculo y el otro en la circunferencia, o bien la longitud de ese segmento. Radius random sample A sample in which each individual or object in the entire population has an equal chance of being selected. (p. SB1) range (in statistics) The difference between the greatest and least values in a data set. (p. 537) range (of a function) The set of all possible output values of a function. (p. 36) rate A ratio that compares two quantities measured in different units. (p. 8) rate of change A ratio that compares the amount of change in a dependent variable to the amount of change in an independent variable. (p. 3) rate of interest The percent charged or earned on an amount of money; see simple interest. (p. 30) ratio A comparison of two numbers or quantities. (p. ) rational number A number that can be written in the form a b, where a and b are integers and b 0. (p. 66) ray A part of a line that starts at one endpoint and etends forever. (p. 378) muestra aleatoria Muestra en la que cada individuo u objeto de la población tiene la misma posibilidad de ser elegido. rango (en estadística) Diferencia entre los valores máimo y mínimo de un conjunto de datos. rango (en una función) El conjunto de todos los valores de salida posibles de una función. tasa Una razón que compara dos cantidades medidas en diferentes unidades. tasa de cambio Razón que compara la cantidad de cambio de la variable dependiente con la cantidad de cambio de la variable independiente. tasa de interés Porcentaje que se cobra por una cantidad de dinero prestada o que se gana por una cantidad de dinero ahorrada; ver interés simple. razón Comparación de dos números o cantidades. número racional Número que se puede epresar como a, b donde a y b son números enteros y b 0. rayo Parte de una línea que comienza en un etremo y se etiende de manera indefinida. Mr. Henson chose a random sample of the class by writing each student s name on a slip of paper, miing up the slips, and drawing five slips without looking. Data set: 3, 5, 7, 7, 1 Range: The range of y is y 0. The speed limit is 55 miles per hour or 55 mi/h. The cost of mailing a letter increased from cents in 1985 to 5 cents in During this period, the rate of change was change in cost 5 1 c hange in years cent per year. 1 to 5, 1:5, can be epressed as can be epressed as 1. D real number A rational or irrational number. (p. 198) número real Número racional o irracional Rational Numbers () Integers () -3 Whole Numbers () Natural Numbers () 1 Real Numbers Irrational Numbers 17 π - 11 e G6 Glossary/Glosario

136 ENGLISH SPANISH EXAMPLES reciprocal One of two numbers whose product is 1; also called multiplicative inverse. (p. 8) recíproco Uno de dos números cuyo producto es igual a 1. También se llama inverso multiplicativo. The reciprocal of 3 is 3. rectangle A parallelogram with four right angles. (p. 399) rectángulo Paralelogramo con cuatro ángulos rectos. rectangular prism A threedimensional figure that has three pairs of opposite parallel congruent faces that are rectangles. (p. 80) prisma rectangular Figura tridimensional que tiene tres pares de caras opuestas, paralelas y congruentes que son rectángulos. reflection A transformation of a figure that flips the figure across a line. (p. 10) refleión Transformación que ocurre cuando se invierte una figura sobre una línea. B B A C C A regular polygon A polygon in which all angles are congruent and all sides are congruent. (p. SB16) polígono regular Polígono en el que todos los ángulos y todos los lados son congruentes. regular pyramid A pyramid whose base is a regular polygon and whose lateral faces are all congruent. (p. 50) pirámide regular Pirámide que tiene un polígono regular como base y caras laterales congruentes. regular tessellation A repeating pattern of congruent regular polygons that completely covers a plane with no gaps or overlaps. (p. 16) teselado regular Patrón que se repite formado por polígonos regulares congruentes que cubren completamente un plano sin dejar espacios y sin superponerse. repeating decimal A rational number in decimal form in which a group of one or more digits (where all digits are not zero) repeat infinitely. (pp. 66, 191) rhombus A parallelogram with all sides congruent. (p. 399) decimal periódico Número racional en forma decimal en el que un grupo de uno o más dígitos (donde todos los dígitos son distintos de cero) se repiten infinitamente. rombo Paralelogramo en el que todos los lados son congruentes right angle An angle that measures 90. (p. 379) ángulo recto Ángulo que mide eactamente 90. Glossary/Glosario G7

137 ENGLISH SPANISH EXAMPLES right cone A cone in which a perpendicular line drawn from the base to the tip (verte) passes through the center of the base. (p. 50) cono recto Cono en el que una línea perpendicular trazada de la base a la punta (vértice) pasa por el centro de la base. Ais Right cone right triangle A triangle containing a right angle. (p. 39) triángulo rectángulo Triángulo que tiene un ángulo recto. rise The vertical change when the slope of a line is epressed as the ratio r ise r u, n or rise over run. (p. 35) distancia vertical El cambio vertical cuando la pendiente de una línea se epresa como la razón distancia vertical distancia horizontal, o "distancia vertical sobre distancia horizontal". For the points (3, 1) and (6, 5), the rise is 5 (1) 6. rotation A transformation in which a figure is turned around a point. (p. 10) rotación Transformación que ocurre cuando una figura gira alrededor de un punto. F E G D G F D E run The horizontal change when the slope of a line is epressed as the ratio r ise r u, n or rise over run. (p. 35) distancia horizontal El cambio horizontal cuando la pendiente de una línea se epresa como la razón distancia vertical distancia horizontal, o "distancia vertical sobre distancia horizontal". For the points (3, 1) and (6, 5), the run is sales ta A percent of the cost of an item, which is charged by governments to raise money. (p. 98) sample A part of the population. (p. SB1) impuesto sobre la venta Porcentaje del costo de un artículo que los gobiernos cobran para recaudar fondos. muestra Una parte de la población. In a survey about the study habits of middle school students, a sample is a group of 100 randomly chosen middle school students. sample space All possible outcomes of an eperiment. (p. 556) scale The ratio between two sets of measurements. (p. 5) espacio muestral Conjunto de todos los resultados posibles de un eperimento. escala La razón entre dos conjuntos de medidas. When rolling a number cube, the sample space is 1,, 3,, 5, 6. 1 cm : 5 mi G8 Glossary/Glosario

138 ENGLISH SPANISH EXAMPLES scale drawing A drawing that uses a scale to make an object smaller than (a reduction) or larger than (an enlargement) the real object. (p. 5) dibujo a escala Dibujo en el que se usa una escala para que un objeto se vea menor (reducción) o mayor (agrandamiento) que el objeto real al que representa. E A D B C H G A blueprint is an eample of a scale drawing. F scale factor The ratio used to enlarge or reduce similar figures. (p. 53) factor de escala Razón empleada para agrandar o reducir figuras semejantes. scale model A proportional model of a three-dimensional object. (p. 5) modelo a escala Modelo proporcional de un objeto tridimensional. scalene triangle A triangle with no congruent sides. (p. 393) triángulo escaleno Triángulo que no tiene lados congruentes. scatter plot A graph with points plotted to show a possible relationship between two sets of data. (p. 58) diagrama de dispersión Gráfica de puntos que muestra una posible relación entre dos conjuntos de datos. 8 6 y scientific notation A method of writing very large or very small numbers by using powers of 10. (p. 18) second quartile The median of a set of data. (p. 76) notación científica Método que se usa para escribir números muy grandes o muy pequeños mediante potencias de 10. segundo cuartil Mediana de un conjunto de datos. 1,560,000,000, Data set:, 6, 7, 8, 10 Second quartile: 7 sector A region enclosed by two radii and the arc joining their endpoints. (p. 7) sector Región encerrada por dos radios y el arco que une sus etremos. segment A part of a line between two endpoints. (p. 378) segmento Parte de una línea entre dos etremos. G H GH side One of the segments that form a polygon. (p. 399) lado Uno de los segmentos que forman un polígono. similar Figures with the same shape but not necessarily the same size are similar. (p. ) semejantes Figuras que tienen la misma forma, pero no necesariamente el mismo tamaño. Glossary/Glosario G9

139 ENGLISH SPANISH EXAMPLES simple interest A fied percent of the principal. It is found using the formula I Prt, where P represents the principal, r the rate of interest, and t the time. (p. 30) interés simple Un porcentaje fijo del capital. Se calcula con la fórmula I Cit, donde C representa el capital, i, la tasa de interés y t, el tiempo. $100 is put into an account with a simple interest rate of 5%. After years, the account will have earned I $10. simplest form A fraction is in simplest form when the numerator and denominator have no common factors other than 1. (p. SB8) simplify To write a fraction or epression in simplest form. (p. SB8) mínima epresión Una fracción está en su mínima epresión cuando el numerador y el denominador no tienen más factor común que 1. simplificar Escribir una fracción o epresión numérica en su mínima epresión. Fraction: 1 8 Simplest form: 3 skew lines Lines that lie in different planes that are neither parallel nor intersecting. (p. 38) líneas oblicuas Líneas que se encuentran en planos distintos, pore so no se intersecan ni son paralelas. E A F B slant height The distance from the base of a cone to its verte, measured along the lateral surface. (p. 50) altura inclinada Distancia de la base de un cono a su vértice, medida a lo largo de la superficie lateral. C Slant height D G H AE and CD are skew lines. slope A measure of the steepness of a line on a graph; the rise divided by the run. (p. 35) pendiente Medida de la inclinación de una línea en una gráfica. Razón de la distancia vertical a la distancia horizontal. Slope r ise 3 run y (, 1) (, ) O solution of an equation A value or values that make an equation true. (p. 3) solution of an inequality A value or values that make an inequality true. (p. 10) solution set The set of values that make a statement true. (p. 136) solución de una ecuación Valor o valores que hacen verdadera una ecuación. solución de una desigualdad Valor o valores que hacen verdadera una desigualdad. conjunto solución Conjunto de valores que hacen verdadero un enunciado. Equation: 6 Solution: Inequality: 3 10 Solution: 7 Inequality: 3 5 Solution set: solve To find an answer or a solution. (p. 3) resolver Hallar una respuesta o solución. G30 Glossary/Glosario

140 ENGLISH SPANISH EXAMPLES sphere A three-dimensional figure with all points the same distance from the center. (p. 508) esfera Figura tridimensional en la que todos los puntos están a la misma distancia del centro. square A rectangle with four congruent sides. (p. 399) cuadrado Rectángulo con cuatro lados congruentes. square (numeration) A number raised to the second power. (p. 19) square root One of the two equal factors of a number. (p. 190) stem-and-leaf plot A graph used to organize and display data so that the frequencies can be compared. (p. 533) straight angle An angle that measures 180. (p. 379) substitute To replace a variable with a number or another epression in an algebraic epression. (p. 6) Subtraction Property of Equality The property that states that if you subtract the same number from both sides of an equation, the new equation will have the same solution. (p. 33) sum The result when two or more numbers are added. (p. 18) supplementary angles Two angles whose measures have a sum of 180. (p. 379) surface area The sum of the areas of the faces, or surfaces, of a three-dimensional figure. (p. 98) cuadrado (en numeración) Número elevado a la segunda potencia. raíz cuadrada Uno de los dos factores iguales de un número. diagrama de tallo y hojas Gráfica que muestra y ordena los datos, y que sirve para comparar las frecuencias. ángulo llano Ángulo que mide eactamente 180. sustituir Reemplazar una variable por un número u otra epresión en una epresión algebraica. Propiedad de igualdad de la resta Propiedad que establece que puedes restar el mismo número de ambos lados de una ecuación y la nueva ecuación tendrá la misma solución. suma Resultado de sumar dos o más números. ángulos suplementarios Dos ángulos cuyas medidas suman 180. área total Suma de las áreas de las caras, o superficies, de una figura tridimensional. In 5, the number 5 is squared. 16, or 16, so and are square roots of 16. Stem Leaves Substituting 3 for m in the epression 5m gives 5(3) Key: 3 means 3. The sum of is cm 8 cm 6 cm Surface area (8)(1) (8)(6) (1)(6) 3 cm Glossary/Glosario G31

141 ENGLISH SPANISH EXAMPLES system of equations A set of two or more equations that contain two or more variables. (p. 131) sistema de ecuaciones Conjunto de dos o más ecuaciones que contienen dos o más variables. y 1 y 3 term (in an epression) The parts of an epression that are added or subtracted. (p. 10) terminating decimal A decimal number that ends or terminates. (p. 66) tessellation A repeating pattern of plane figures that completely cover a plane with no gaps or overlaps. (p. 16) término (en una epresión) Las partes de una epresión que se suman o se restan. decimal finito Decimal con un número determinado de posiciones decimales. teselado Patrón repetido de figuras planas que cubren totalmente un plano sin superponerse ni dejar huecos Term Term Term theoretical probability The ratio of the number of equally likely outcomes in an event to the total number of possible outcomes. (p. 56) third quartile The median of the upper half of a set of data; also called upper quartile. (p. 5) probabilidad teórica Razón del número de resultados igualmente probables en un suceso al número total de resultados posibles. tercer cuartil La mediana de la mitad superior de un conjunto de datos. También se llama cuartil superior. When rolling a number cube, the theoretical probability of rolling a is 1 6. Lower quartile Minimum Upper quartile Median Maimum transformation A change in the size or position of a figure. (p. 10) transformación Cambio en el tamaño o la posición de una figura. B B A ABC C A A B C C translation A movement (slide) of a figure along a straight line. (p. 10) traslación Desplazamiento de una figura a lo largo de una línea recta. J M J M K L K L transversal A line that intersects two or more lines. (p. 389) transversal Línea que cruza dos o más líneas Transversal trapezoid A quadrilateral with eactly one pair of parallel sides. (p. 399) trapecio Cuadrilátero con un par de lados paralelos. A B C D G3 Glossary/Glosario

142 ENGLISH SPANISH EXAMPLES tree diagram A branching diagram that shows all possible combinations or outcomes of an event. (p. SB3) diagrama de árbol Diagrama ramificado que muestra todas las posibles combinaciones o resultados de un suceso. H T trial In probability, a single repetition or observation of an eperiment. (p. 556) triangle A three-sided polygon (p. 39) prueba En probabilidad, una sola repetición u observación de un eperimento. triángulo Polígono de tres lados. When rolling a number cube, each roll is one trial. Triangle Sum Theorem The theorem that states that the measures of the angles in a triangle add up to 180. (p. 39) triangular prism A threedimensional figure with two congruent parallel triangular bases and whose other faces are rectangles. (p. 85) trinomial A polynomial with three terms. (p. 590) Teorema de la suma del triángulo Teorema que establece que las medidas de los ángulos de un triángulo suman 180. prisma triangular Figura tridimensional con dos bases triangulares congruentes y paralelas cuyas otras caras son rectángulos. trinomio Polinomio con tres términos. 3y 5y unit analysis The process of changing one unit of measure to another. (p. 37) unit conversion factor A fraction used in unit conversion in which the numerator and denominator represent the same amount but are in different units. (p. 37) unit price A unit rate used to compare prices. (p. 9) unit rate A rate in which the second quantity in the comparison is one unit. (p. 8) upper quartile The median of the upper half of a set of data; also called third quartile. (p. 5) conversión de unidades Proceso que consiste en cambiar una unidad de medida por otra. factor de conversión de unidades Fracción que se usa para la conversión de unidades, donde el numerador y el denominador representan la misma cantidad pero están en unidades distintas. precio unitario Tasa unitaria que sirve para comparar precios. tasa unitaria Una tasa en la que la segunda cantidad de la comparación es la unidad. cuartil superior La mediana de la mitad superior de un conjunto de datos; también se llama tercer cuartil. 60 min 1 h or 1 h 60 min Cereal costs $0.3 per ounce. 10 cm per minute Lower quartile Minimum Upper quartile Median Maimum Glossary/Glosario G33

143 ENGLISH SPANISH EXAMPLES variable A symbol used to represent a quantity that can change. (p. 6) verte (of an angle) The common endpoint of the sides of the angle. (p. 379) variable Símbolo que representa una cantidad que puede cambiar. vértice de un ángulo Etremo común de los lados del ángulo. In the epression 3, is the variable. A is the verte of CAB. verte (of a polygon) The intersection of two sides of the polygon. (p. 399) vértice (de un polígono) La intersección de dos lados del polígono. verte (of a polyhedron) A point at which three or more edges of a polyhedron intersect. (p. 80) vértice (de un poliedro) Un punto en el que se intersecan tres o más aristas de un poliedro. A, B, C, D, and E are vertices of the polygon. vertical angles A pair of opposite congruent angles formed by intersecting lines. (p. 388) ángulos opuestos por el vértice Par de ángulos opuestos congruentes formados por líneas secantes and 3 are vertical angles. vertical line test A test used to determine whether a relation is a function. If any vertical line crosses the graph of a relation more than once, the relation is not a function. (p. 37) prueba de linea vertical Prueba utilizada para determinar si una relación es una función. Si una línea vertical corta la gráfica de una relación más de una vez, la relación no es una función. y volume The number of cubic units needed to fill a given space. (p. 85) volumen Número de unidades cúbicas que se necesitan para llenar un espacio. ft 3 ft 1 ft Volume ft 3 -ais The horizontal ais on a coordinate plane. (p. 3) eje El eje horizontal del plano cartesiano. -ais O G3 Glossary/Glosario

144 ENGLISH SPANISH EXAMPLES -coordinate The first number in an ordered pair; it tells the distance to move right or left from the origin (0, 0). (p. 3) coordenada El primer número de un par ordenado; indica la distancia que debes moverte hacia la izquierda o la derecha desde el 5 is the -coordinate in (5, 3). origen, (0, 0). y-ais The vertical ais on a coordinate plane. (p. 3) eje y El eje vertical del plano cartesiano. y-ais O y-coordinate The second number in an ordered pair; it tells the distance to move up or down from the origin (0, 0). (p. 3) coordenada y El segundo número de un par ordenado; indica la distancia que debes avanzar hacia arriba o hacia abajo desde el origen, (0, 0). 3 is the y-coordinate in (5, 3). zero pair A number and its opposite, which add to 0. (p. ) par nulo Un número y su opuesto, cuya suma es and 18 Glossary/Glosario G35

145 Inde Absolute value, 15 Abstract art, 599 Academic Vocabulary,, 6, 11, 166,, 7, 30, 376, 3, 76, 58, 588 Acute angles, 379 Acute triangles, 39, SB17 Addition Associative Property of, of decimals, 7, SB1 of fractions, 75, SB10 with unlike denominators, 87 89, SB10 of integers, of mied numbers, of polynomials, modeling, 60 of rational numbers, 7 75 properties, 3, 33, 116 solving equations by, 3 3 solving inequalities by, Addition Property of Equality, 33 Additive inverse, 18 Adjacent angles, 388 Alaska, 8 Algebra The development of algebra skills and concepts is a central focus of this course and is found throughout this book. absolute value, 15 combining like terms, 10 11, 1, equations, 3 addition, 3 33 checking solutions of, 3, 33, decimal, solving, 9, 98 division, linear, 330, 331 multi-step, see Multi-step equations multiplication, solutions of, 3 subtraction, 3 33 systems of, 131 two-step, see Two-step equations epressions, 6 7, 10 11, algebraic, 6 7 numerical, 6 7 variables and, 6 7 functions, 36 cubic, graphing, 36 37, , linear, see Linear functions quadratic, tables and, 36 inequalities, see Inequalities linear functions, multi-step equations, 1 15 properties Addition, of Equality, 33 Associative, 116 of circles, 6 7 Commutative, 116 Distributive, 117 Division, of Equality, 37 Identity, 3, 37 Multiplication, of Equality, 38 Subtraction, of Equality, 33 proportions, and indirect measurement, 8 9 in scale drawings, models, and maps, 5 53, solving, 3 3 solving equations by adding or subtracting, 3 3 modeling, 1 by multiplying or dividing, 37, 38 two-step, 3 5, with variables on both sides, solving inequalities by adding or subtracting, by multiplying or dividing, 1 15 two-step, tiles, 1, 18, , 60, 607, translating between words and math, 63 translating words into math, variables, 6 7 on both sides, solving equations with, dependent, 3 independent, 3 isolating, 3 solving for, 3 Algebra tiles, 1, 18, , 60, 607, Algebraic epressions, 6, evaluating, 6 7 simplifying, writing, Algebraic inequalities, 136 Alternate eterior angles, 389 Alternate interior angles, 389 American Samoa, 396 Analysis dimensional, unit, 37 Anamorphic images, 98 Angles, 379 acute, 379 adjacent, 388 alternate eterior, 389 alternate interior, 389 bisector, 38 central, of a circle, 7 classifying, 379 complementary, 379 congruent, 06 corresponding, 389 in polygons, 03 obtuse, 379 of quadrilaterals, 03 of triangles, points and lines and planes and, relationships of, right, 379 straight, 379 supplementary, 379 vertical, 388 Animals, 81 Answer choices, eliminating, Answering contet based test items, Ant lions, 505 Applications Animals, 81 Architecture, 3, 195, 5, 55, 35, 93 Art, 19, 7, 500, 51, 60 Astronomy, 35, 139, 178, 187, 335 Banking, 8 Business, 8, 39, 13, 131, 13, 139, 13, 178, 6, 81, 337, 513, 597, 606, 609, 611 Chemistry, 17 Computer, 193 Construction, 35, 60 Consumer Economics, 80, 300 Consumer Math, 5, 6, 100, 118, 1, 559 Cooking, 6 Economics, 1, 151 Energy, 77 Entertainment, 9, 150, 6, 31, 53 Environment, 5, 333 Finance, 9, 16, 81 Food, 0, 53 Games, 195, 573 Geography, 8, 5, 77, 85 Geometry, 1, 17, 169, 18, 183, 606 Health, 19, 81, 50, 615 History, 187, 08, 09 Hobbies, 6, 1, 183, 195, 7, 336 Home Economics, 39 Language Arts, 13, 87 Life Science, 73, 101, 171, 17, 175, 187, 0, 1, 53, 8, 89, 90, 95, 361, 89, 505, 511, 568, 598 Literature, 97 Manufacturing, 80, 35 Measurement, 69, 90 Meteorology, 73 Money, 307 Multi-Step, 39, 80, 90, 91, 97, 199, 09, 31, 77, 87, 97,, 50 Music, 0, 9, 87 Nutrition, 39, 96, 11 Patterns, 17, 86 Recreation, 0, 79, 88, 16, 196, 8, 515 Safety, 35, 561 School, 7, 80, 19, 573 Science, 7, 17, 8, 9, 36, 91, 96, 17, 133, 187, 199, 6, 8, 81, 88, 97, 336, 507, 55 I Inde

146 Social Studies, 5, 35, 71, 86, 16, 188, 8, 86, 396, 38, 89, 91, 507, 55 Sports, 1, 7, 38, 68, 7, 7, 76, 13, 17, 151, 19, 0, 81, 38, 336, 53, 50, 51 Transportation, 0, 1, 593 Travel, 15, 16 Weather, 119, 35 Approimating square roots, 197 Arc, of a circle, 6 Architecture, 3, 195, 5, 55, 35, 93 Are You Ready?, 3, 61, 113, 165, 1, 71, 375, 31, 75, 57, 587 Area, 35 of circles, 51 of irregular figures, lateral, 98 of parallelograms, of rectangles, of squares, 19 surface, 98 of cones, of cylinders, of prisms, of pyramids, of spheres, 509 of trapezoids, 0 1 of triangles, 0 1 Arguments, writing convincing, 3 Art, 19, 7, 500, 51, 60 Ashurbanipal, King, 6 Aspect ratio, 31 Assessment Chapter Test, 55, 109, 159, 17, 65, 315, 369, 7, 69, 53, 581, 69 Cumulative Assessment, 58 59, , , 18 19, 68 69, , , 8 9, 7 73, 5 55, , Mastering the Standards, 58 59, , , 18 19, 68 69, , , 8 9, 7 73, 5 55, , Ready to Go On?, 30, 8, 9, 10, 13, 15, 190, 10,, 58, 9, 308, 3, 0, 0,, 6, 9, 516, 55, 57, 600, 6 Strategies for Success Any Type: Using a Graphic, Etended Response: Write Etended Responses, Gridded Response: Write Gridded Responses, Multiple Choice Answering Contet-Based Test Items, Eliminate Answer Choices, Short Response: Write Short Responses, Study Guide: Review, 5 5, , , 1 16, 6 6, 31 31, , 6, 66 68, 50 5, , Associative Property of Addition, of Multiplication, Astronomy, 35, 139, 178, 187, 335 Aes, 3 Back-to-back stem-and-leaf plot, Bacteria, 171, 11 Balance of trade, 1 Balance scale, 3 Banking, 8 Bar graphs, 531, SB18 histograms, SB0 Base, of polyhedrons, 80 Bases, 168 Benchmarks, 78 Berkeley, 119 Best fit, lines of, 59 Biased samples, SB Binary fission, 171 Binomials, 590 multiplication of, , special products of, 619 Bisecting figures, 38 Bisectors constructing, perpendicular, 38 Blood pressure, 36 Board foot, 597 Boeing 77, 3 Book, using your, for success, 5 Bo-and-whisker plots, 5 5, creating, 53, 57 British thermal units (Btu), 77 Buffon, Comte de, 576 Business, 8, 39, 13, 131, 13, 139, 13, 178, 6, 81, 337, 513, 597, 606, 609, 611 Calculator approimating square roots on a, 197 graphing, see Graphing calculator California locations Berkeley, 119 Carlsbad, 515 Joe Matos Cheese Factory, 0 Legoland, 515 Mammoth Lakes, 37 Menlo Park, 16 Monterey Bay Aquarium, 0 Rincon Park, 0 San Diego, 70 San Francisco, 0 Santa Monica International Chess Park, 195 Santa Rosa, 0 Stanford Linear Accelerator Center, 16 Yosemite National Park, 5 California Link, 9, 77, 13, 195, 0, 515 Capacity, 51 customary units of, SB15 metric units of, SB15 Carlsbad, CA, 515 Caution! 10, 6, 169, 00, 36 Celsius temperature scale, 103, 331 Center of a circle, 6 of rotation, 10 Central angles, 7 Central tendency, measures of, 538 Certain event, 556 Challenge Challenge eercises are found in every lesson. Some eamples: 9, 13, 17, 1, 5 Change percents of, 9 rates of, 3 35, see also Rates of change Chapter Project Online,, 60, 11, 16, 0, 70, 318, 37, 7, 56, 586 Chapter Test, 55, 109, 159, 17, 65, 315, 369, 7, 69, 53, 581, 69, see also Assessment Chemistry, 17 Chess, 195 Choose a Strategy, 9, 9, 86, 133, 171, 1, 87, 97, 337, 396, 50, 515, 606, 611 Chord, of a circle, 6 Circle(s), 6 7, arcs of, 6 area of, 51 central angles, 7 chords of, 6 circumference, 50 diameter, 6, 50 graphs, 7, SB1 great, 508 properties of, 6 7 radius, 6, 50 Circle graphs, 7, SB1 interpreting, 7 making, SB1 reading, 7 Circumference, Classifying angles, 379 polygons, 399, SB16 SB17 polynomials, quadrilaterals, 399 real numbers, three-dimensional figures, 81 triangles, , SB17 Closed circle, 137 Coefficients, 10 Inde I3

147 Combining like terms, Combining transformations, 15 Commission, 98 Commission rate, 98 Common denominator, 70, 87 Common multiple, SB6 least (LCM), SB6 Communicating Math apply, 87 choose, 9 compare, 19, 7, 137, 19, 169, 89, 335, 36, 505, 509, 5, 561, 60, 609, 613 compare and contrast, 81 decide, 193 demonstrate, 85 describe, 19, 3, 3, 71, 99, 117, 11, 11, 19, 186, 193, 5, 3, 53, 80, 331, 335, 359, 1, 17, 1, 87, 91, 513, 539, 550, 566, 591 determine, 79, 186, 197, 80 discuss, 197 draw, 7 eplain, 7, 15, 19, 3, 3, 67, 71, 75, 8, 89, 95, 99, 117, 131, 137, 11, 15, 169, 177, 181, 186, 193, 01, 07, 5, 3, 39, 9, 53, 75, 89, 33, 331, 351, 389, 39, 00, 07, 17, 7, 81, 500, 505, 509, 513, 539, 5, 591, 60, 609 epress, 11, 173, 36 give, 11, 67, 131, 15, 5, 9, 39, 561 give an eample, 7, 75, 79, 89, 5, 75, 351, 539, 566, 571, 597, 619 identify, 37 list, 7, 15, 177 model, 87, 91 name, 85, 33 show, 169, 75, 85 suppose, 7, 33 tell, 7, 8, 89, 11, 15, 173, 181, 01, 3, 389, 07, 571, 597 Think and Discuss Think and Discuss is found in every lesson. Some eamples: 7, 11, 15, 19, 3 use, 01 Write About It Write About It eercises are found in every lesson. Some eamples: 9, 13, 17, 1, 5 Commutative Property of Addition, of Multiplication, Comparing customary units and metric units, SB15 data sets, 5 numbers in scientific notation, 186 rational numbers, ratios, 5, 3 volumes and surface areas, 509 Comparing and ordering whole numbers, SB3 Compass, Compatible numbers, 117, 78 Complementary angles, 379 Composite figures area of, 36 perimeter of, 36 volume of, 87 Composite numbers, SB5 Compound events, Compound inequalities, 137 Compound interest, 30, 30 computing, eploring, 30 Computer graphics, 398 Computer spreadsheets, Computer, 193 Computing compound interest, 30, Concept Connection, 9, 103, 153, 11, 59, 309, 363, 1, 63, 517, 575, 63 Concept maps, 33 Conclusions, see Reasoning Concorde, 3 Cones, 81, 90 nets of, 503 right, 50 surface area of, volume of, Congruence, Congruent angles, constructing, Congruent figures, 38 Congruent triangles, 06 Constant of variation, 357 Constant rate of change, 3 35 Constants, 10 Constructing bisectors and congruent angles, graphs, using spreadsheets for, nets, 96 97, 503 scale drawings and scale models, Construction, 35, 60 Consumer application, 559 Consumer Economics, 80, 300 Consumer Math, 5, 6, 100, 118, 1, 559 Contet-based test items, answering, Converse of the Pythagorean Theorem, Conversion factors, 37, SB15 units of measure, Conversions, metric, SB15 Converting, customary units to metric units, SB15 metric units to customary units, SB15 Convincing arguments, writing, 3 Cooking, 6 Coordinate geometry, Coordinate plane, 3 33 graphing on a, 330, 33, 338 Coordinates, 3 33 Cornell system of note taking, 167 Correlation, Correlation types, 59 Correspondence, 06 Corresponding angles, 389 Corresponding sides, Countdown to Mastery, CA CA7 Creating bo-and-whisker plots, 57 graphs, using spreadsheets for, histograms, SB0 scatter plots, 553 tessellations, Cross products, 3 Cubic functions, Cubic units, 85 Cullinan diamond, 96 Cumulative Assessment, 58 59, , , 18 19, 68 69, , , 8 9, 7 73, 5 55, , , see also Assessment Cupid s Span, 0 Customary system of measurement, 37 39, SB15 converting between metric and, SB15 Cylinders, 81, 85 nets of 97 surface area of, eploring, volume of, da Vinci, Leonardo, 506 Data, see also Displaying and organizing data bar graphs, 531, SB18 bo-and-whisker plots, 53 5 circle graphs, 77, SB1 collecting, 531 displaying, 7, , 53 5, SB18 SB1 double-bar graphs, SB18 histograms, SB0 line graphs, SB19 line plots, 53 organizing, stem-and-leaf plots, 533 back-to-back, Decagon, SB16 Decimals addition of, 7, 75, 9 comparing, 71 converting between percents and fractions and, 7 75 division of, 83 equivalent fractions and, 67 I Inde

148 fractions and, 66 multiplication of, 79, 9 by powers of ten, SB7 ordering, 71 repeating, 6 65, rounding, SB solving equations with, 9 subtraction of, 7, 75, 9 terminating, 6 65, writing as percents, 7 75 Decrease, percent of, 9 95 Deductive reasoning, SB Degrees of polynomials, 591 Denominator(s), 66 like, adding and subtracting with, 75 unlike, adding and subtracting with, Density, 8 Density Property of real numbers, 01 Dependent events, finding probability of, Dependent variable, 3 Devils Postpile National Monument, 37 Diagonals, 169 Diagram tree, SB3 Diameter, 6, 50 Diastolic blood pressure, 36 Dimensional analysis, Dimensions changing, eploring effects of, 86, 505, Direct variation, Discounts, 95 Disjoint events, 566 Displaying and organizing data, 7, , 53 5, SB18 SB1 bar graphs, 531, SB18 bo-and-whisker plots, 53 5 circle graphs, 7, SB1 double-bar graphs, SB18 histograms, SB0 line graphs, SB19 line plot, 53 stem-and-leaf plots, 533 back-to-back, Distracter, 56 Distributive Property, 117, 11, 597 Divisibility rules, SB Division of decimals, 83, SB13 and mied numbers, 8 by powers of ten, SB7 of fractions, 8 8 of integers, 6 7 long, SB7 of monomials, of numbers in scientific notation, 189 of powers, by powers of ten, SB7 of rational numbers, 8 8, SB11, SB13 solving equations by, solving inequalities by, 1 15 of whole numbers, SB7 Division Property of Equality, 37 DNA model, 53 Double-bar graphs, SB18 Draw three-dimensional figures, 77 Drawings, scale, 5 53 Duckweed plants, 187 Earth, 186, 187, 508 Earthquakes, 563 Economics, 1, 151, 301 Edge, of a three-dimensional figure, 80 Edison, Thomas, 39 Effective notes, taking, 167 Eggs, 511 Eliminating answer choices, Energy, 77 Enlargement, 53 Entertainment, 9, 150, 6, 31, 53 Environment, 5, 333 Equality Addition Property of, 3 Division Property of, 37 Multiplication Property of, 38 Subtraction Property of, 33 Equally likely outcomes, 56 Equations, 3 graphs of, , , linear, see Linear equations multi-step, see Multi-step equations with no solutions, 130 one-step, see One-step equations solutions of, 3 solving, see Solving equations systems of, see Systems of equations and tables and graphs, 36, 330, 331, 33, 335, 338, 339 two-step, see Two-step equations with variables on both sides, modeling, 18 Equilateral triangles, 393, SB17 Equivalent epressions, 10 Equivalent fractions decimals and, 7 Equivalent ratios, 5, 3 Escher, M. C., 19 Estimate, 78 Estimating square roots, with percents, Estimation,, 86, 90, 171, 179, 19, 31, 81, 93, 51 Evaluating algebraic epressions, 6 7 epressions using the order of operations, 169 epressions with rational numbers, 75, 83, 89 negative eponents, Events, 556 disjoint, 566 independent, see Independent events mutually eclusive, 566 Eam, preparing for your final, 589 Eperiment, 556 Eperimental probability, Eploring compound interest, 30 effects of changing dimensions, 86, 505, Pythagorean Theorem, 0 rational numbers, 6 65 three-dimensional figures, volume of prisms, 8 Eponential form, 168 Eponents, integer, negative, properties of, Epressions algebraic, 6 7, simplifying, writing, equivalent, 10 evaluating, with rational numbers, 75, 83, 89 numerical, 6 7 variables and, 6 7 Etended Response, 91, 175, 31, 97, , 391, 515, 536, 56, 611 Write Etended Responses, Etra Practice, EP EP5 Face lateral, 98 of a three-dimensional figure, 80 Factor(s), SB common, SB6 conversion, 37 scale, 53 Factorization, prime, SB5 Fahrenheit scale, 331 Fahrenheit temperature converting between Celsius and, 103, 331 scale, 103 Fair objects, 56 Ferris wheel, 30, 53 Figures bisecting, 38 built of cubes, 98 composite, 36, 87 congruent, 38 geometric, irregular, area of, similar, see Similar figures three-dimensional, Inde I5

149 see Three-dimensional figures two-dimensional, see Two-dimensional figures Final Eam, study for a, 589 Finance, 9, 16, 81 Finding numbers when percents are known, percents, probability of dependent events, probability of independent events, surface area of prisms and cylinders, surface area of pyramids, 50 surface area of similar solids, 513 unit prices to compare costs, 9 volume of prisms and cylinders, volume of pyramids and cones, volume of similar solids, 513 Fireworks, 591 Flip, see Reflection Fluid ounce, SB15 Focus on Problem Solving Look Back, 93, 601 Make a Plan, 135, 93, 95, 555 Solve, 31, 191, 3, 33 Understand the Problem, 05 FOIL mnemonic, 618 Food, 0, 53 Foot, SB15 Formulas, learning and using, 77, see also inside back cover Fraction(s) addition of, 75 with unlike denominators, decimals and percents and, 7 75 division of and mied numbers, 8 8 equivalent, see Equivalent fractions improper, SB9 multiplication of, and mied numbers, relating, to decimals and percents, 7 75 simplest form, SB8 solving equations with, 9 95, 1 15 subtraction of, 75 with unlike denominators, unit, 10 writing as mied numbers, SB9 writing as terminating and repeating decimals, 66 Fraction form, dividing rational numbers in, 8 Frequency tables, SB0 Fulcrum, 3 Functions, cubic, linear, quadratic, tables and, 36, 330, 331, 33, 335, 338, 339 graphs and, 330, 331, 33, 335, 338, 339 Gallon, SB15 Game Time Points, 15 Buffon s Needle, 576 Circles and Squares, 6 Coloring Tessellations, Copy-Cat, 60 Crazy Cubes, 50 Egg Fractions, 10 Egyptian Fractions, 10 Equation Bingo, 1 Magic Cubes, 518 Magic Squares, 1 Math Magic, 50 Percent Puzzlers, 310 Percent Tiles, 310 Planes in Space, 518 Polygon Rummy, Rolling for Tiles, 6 Shape Up, 6 Short Cuts, 6 Squared Away, 36 Tic-Frac-Toe, 60 Trans-Plants, 15 What s Your Function?, 36 Game Time Etra, 10, 15, 1, 60, 310, 36,, 6, 518, 576, 6 Games, 195, 573 Gas mileage, 593 GCD (greatest common divisor), SB6 Geography, 8, 5, 77, 85 Geometric patterns, SB16 Geometry angles, , , 39 39, area, 35 36, 0 1, 51 building blocks of, circles, 6 7, area of, 51 circumference of, 50 circumference, 50 cones, 81 volume of, 90 9 surface area of, constructing bisectors and congruent angles, congruent figures, coordinate, cylinders, 81 volume of, surface area of, 96 97, lines, parallel, , perpendicular, , 388 of reflection, 10 skew, 38 transversal, nets, 96 97, 503 parallel line relationships, 389 parallelograms, 399 area of, 35 perimeter of, 3 planes, 378 polygons, 399 finding angle measures in, 03 regular, SB16 polyhedrons, 80 prisms, 8, volumes of, 8, surface area of, 96 97, pyramids, 80, volume of, surface area of, quadrilaterals, 399, 03, SB16, SB17 rays, 378 rectangles, 3 36 area of, perimeter of, 3 36 rhombuses, 399, SB17 rhombuses, 399, SB17 scale drawings and scale models, 5 53, 56 57, 59 similar figures, 5 surface area and volume, sphere, squares, 399, SB17 surface area, , 503, , 509 tessellations, three-dimensional figures, 7 55 introduction to, modeling, trapezoids area of, 0 1 perimeter of, 39 triangles, 39 39, SB16 SB17 area of, 0 1 perimeter of, 39 two-dimensional figures, volume, 8 87, Giant Ocean Tank, 89 Giant shark, 88, 89 Gigabyte, 179 Global temperature, 73 go.hrw.com, see Online Resources Googol, 179 Gram, SB15 Graph(s) bar, 531, SB18 circle, 7, SB1, see also Circle graphs constructing, using spreadsheets for, creating, using technology for, 530 double-bar, SB18 of equations, , , interpreting, line, , SB19 tables and, 36, 330, 33, 338 I6 Inde

150 Graphing on a coordinate plane, 3 33 inequalities, 137, 10 11, 1, integers on a number line, 1 linear equations, 330 linear functions, points, 1, 3 33 Technology Labs, see Technology Lab transformations, 10 1, 15 Graphing calculator creating bo-and-whisker plots, 57 creating scatter plots, 553 multiplying and dividing numbers in scientific notation, 189 Great circle, 508 Great Lakes, 31 Great Pyramid of Giza, 91 Greatest common divisor (GCD), SB6 Gridded Response, 9, 1, 5, 36, 0, 69, 77, 86, 101, 13, 17, 17, , 171, 09, 36, 1, 7, 87, 91, 301, 337, 35, 361, 381, 0, 09, 3, 9, 53, 71, 50, 507, 511, 559, 568, 573, 593, 606, 61 Write Gridded Responses, Hands-On Lab Angles in Polygons, 03 Combine Transformations, 15 Construct Bisectors and Congruent Angles, Construct Scale Drawings and Scale Models, Eplore Compound Interest, 30 Eplore Rational Numbers, 6 65 Eplore the Pythagorean Theorem, 0 Eplore Three-Dimensional Figures, Eplore Volume of Prisms, 8 Find Surface Areas of Prisms and Cylinders, Find Volumes of Prisms and Cylinders, 8 Identify and Construct Altitudes, 397 Make a Scale Model, Model Equations with Variables on Both Sides, 18 Model Polynomial Addition, 60 Model Polynomial Subtraction, 607 Model Polynomials, Model Two-Step Equations, 1 Multiply Binomials, Nets of Cones, 503 Nets of Prisms and Cylinders, 96 Hawaiian alphabet, 87 Health, 19, 81, 50, 615 Heart rate maimum, 615 target, 615 Height of parallelograms, slant, 50 using indirect measurement to find, 8 9 using scales and scale drawings to find, Helpful Hint, 11, 18, 3, 3, 38,, 67, 117, 10, 19, 130, 137, 10, 180, 193, 05, 07, 3, 85, 06, 10, 35, 80, 508, 618 Hemispheres, 508 Heptagons, SB16 Heagons, 03, SB16 Hill, A. V., 61 Histograms, SB0 History, 187, 08, 09, 83 Hobbies, 6, 1, 183, 195, 7, 336 Home Economics, 39 Homework Help Online Homework Help Online is available for every lesson. Refer to the go.hrw.com bo at the beginning of each eercise set. Some eamples: 8, 1, 16, 0, Hot Tip!, 57, 59, 111, 161, 163, 19, 67, 69, 317, 371, 71, 55, 583, 585, 631 Hurricanes, 35, 55 Hypotenuse, 05 Ice Hotel, 17 Identifying irrational numbers, proportions, 3 33 right triangles, Identity Property of Addition, 3 Identity Property of Multiplication, 37 Image(s), 10 anamorphic, 98 Impossible event, 556 Improper fractions, SB9 Inch, SB15 Increase, percent of, 9 Independent events, finding probability of, Independent variable, 3 Indirect measurement, 8 9 Inductive reasoning, SB Industrial supplies, 1 Inequalities, algebraic, 136 compound, 137 graphing, 137, 10 11, 1 solving, by adding or subtracting, by multiplying or dividing, 1 15 translating word phrases into, 136 two-step, solving, writing, 136, 11 compound, 137 Input, 36 Integer eponents, Integers, 1 absolute value, 15 addition of, comparing, 1 division of, 6 7 multiplication of, 6 7 and order of operations, 7 ordering, 1 15 subtraction of, 3 Interest, 303 compound, see Compound interest rate of, 303 simple, Interpreting circle graphs, 7 graphics, 59 graphs, Interstate highway system, 7 Inverse operations, 3 Inverse Property of Multiplication, 8 Inverse additive, 18 multiplicative, 8 Investment time, 303 Ions, 36 Irrational numbers, 00 Irregular figures, area of, Isolating the variable, 3 Isosceles triangles, 393, SB17 It s in the Bag! A Worthwhile Wallet, 61 Canister Carry-All, 105 Graphing Tri-Fold, 365 It s a Wrap, 13 Note-Taking Taking Shape, 51 Origami Percents, 311 Perfectly Packaged Perimeters, 65 Picture Envelopes, 155 Polynomial Petals, 65 Probability Post-Up, 577 Project CD Geometry, 3 The Tube Journal, 519 Journal, math, keeping a, 31 Jupiter, 186 Kasparov, Garry, 195 Kente cloth, 1 Kilobyte, 179 Kilogram, SB15 Kiloliter, SB15 Kilometer, SB15 Kilowatt-hour, 39 Kite(s), SB17 Krill, 175 Kwan, Michelle, 10 Inde I7

151 Lab Resources Online, 1, 6, 18, 189, 0, 38, 78, 8, 96, 503, 530, 57, 553, 59, 60, 607, 616 Landscaping, 55 Language Arts, 13, 87 Lateral area, 98 Lateral faces, 98 Lateral surface, 99 LCD (least common denominator), 70 LCM (least common multiple), 70 Leaf, 533 Least common denominator (LCD), 70, Least common multiple (LCM), 70, SB6 Lee, Harper, 97 Leg, of a triangle, 05 LEGOLAND, 515 Length customary units of, SB15 metric units of, SB15 Lessons, reading, for understanding, 115 Life Science, 73, 101, 171, 17, 175, 187, 0, 1, 53, 89, 90, 95, 361, 89, 505, 511, 568, 598, 61 Lift, 3 Light bulb filament, 39 Light sticks, 81 Like denominators, adding and subtracting with, 7 75 Like terms, 10, 596 solving equations with, 1 15 Lincoln, Abraham, 88 Line graphs, SB19 Line plots, 53 Line segments, 378 Line(s), 378 of best fit, 59 graphing, parallel, perpendicular, points and planes and angles and, of reflection, 10 segments, 378 skew, slope of a, transversals to, 389 Linear equations, 330 graphing, Linear functions, 330 graphing, Link Animals, 81 Architecture, 55, 93 Art, 7, 19, 599 Business, 606 Economics, 1, 301 Energy, 77 Entertainment, 9 Environment, 333 Games, 195 Health, 36 History, 09, 83 Home Economics, 39 Language Arts, 13 Life Science, 101, 171, 175, 187, 89, 361, 89, 505, 511, 568, 61 Literature, 97 Meteorology, 73 Money, 307 Recreation, 88, 515 Science, 17, 9, 91, 133, 175, 81 Social Studies, 5, 7, 91, 1, 591 Sports, 17, 51 Weather, 35 Liquid mirror, 335 Liter, SB15 Literature, 97 Long division, 83, SB7 Louvre Pyramid, 5, 93 Lower quartile, 5 53 Luor Hotel, 35 Magic squares, 1 Making circle graphs, SB1 conjectures, SB scale models, Mammoth Lakes, CA, 37 Manufacturing, 80, 35 Map, concept, 33 Mars, 187 Mass, metric units of, SB16 Mastering the Standards, 58 59, , , 18 19, 68 69, , , 8 9, 7 73, 5 55, , , see also Assessment Math translating between words and, 63 translating words into, Math epressions translating, into word phrases, 11 translating word phrases into, 10 Math journals, keeping, 31 Matrushka dolls, 86 Maimum, 53 Mean, Measurement, 69, 90 conversion tables, SB15 customary system of, indirect, 8 9 metric system of, 37 39, SB15 Measures of central tendency and range, Median, Menkaure Pyramid, 09 Merced River, 11 Mercury (planet), 35, 186 Metamorphoses, 19 Meteorites, 535 Meteorology, 73 Meter, SB15 Methane, 333 Metric conversions, 37, SB15 Metric system of measurement, SB15 converting between customary and, SB15 Midpoint, 393 Mile, SB15 Milligram, SB15 Milliliter, SB15 Millimeter, SB15 Minimum, 53 Mirror, liquid, 335 Mied numbers, addition of, dividing fractions and, 8 8 equivalent fractions and, SB9 multiplying fractions and, subtraction of, 87 Mode, 537 Modeling equations with variables on both sides, 18 polynomial addition, 60 polynomial subtraction, 607 polynomials, two-step equations, 1 Models scale, 5 53, 59, see also Scale models Mona Lisa, 7 Money, 38, 307 Monomials, 180 division of, multiplication of, 180 multiplication of polynomials by, raising, to powers, 181 square roots of, 193 Monterey Bay Aquarium, 0 Mountain bikes, 51 Multiple, least common (LCM), 70, SB6 Multiple Choice Multiple Choice test items are found in every lesson. Some eamples: 9, 13, 17, 1, 5 Answering Contet-Based Test Items, Eliminate Answer Choices, Multiplication Associative Property of, of binomials, , of decimals, 79, 9 of fractions and mied numbers, of integers, 6 7 of monomials, 180 of numbers in scientific notation, 189 I8 Inde

152 of polynomials, by monomials, of powers, 176 by powers of ten, 18, SB7 properties, 38 of rational numbers, solving equations by, solving inequalities by, 1 15 Multiplication Property of Equality, 38 Multiplicative inverse, 8 Multi-Step, 39, 80, 90, 91, 97, 199, 09, 31, 87, 96, 38, 0, 50 Multi-Step Application, 39, 619 Multi-step equations solving, 1 15, Muscle contractions, 61 Music, 0, 9, 87 Mutually eclusive events, 566 Negative correlation, 59 Negative eponents, Negative slope, 39 Neptune, 187 Nets of cones, 503 of prisms and cylinders, Newborns, 7 Newtons (N), 3 n-gons, SB16 Niagara Falls, 91 Nickels, 75 Nielsen Television Ratings, 83 No correlation, 59 Nonagons, SB16 Notation scientific, see Scientific notation set-builder, 1 Note-Taking Strategies, see Reading and Writing Math Notes, taking effective, 167 Number line, 18 Numbers compatible, 78 composite, SB5 division of, in scientific notation, 189 finding, when percents are known, irrational, 00 mied, SB9, see also Mied numbers multiplication of, in scientific notation, 189 percents of, 83 8 prime, SB5 rational, , 00 01, see also Rational numbers real, Numerator, 66 Numerical epressions, 6 7 Nutrition, 39, 96, 11, 356 Obtuse angles, 379 Obtuse triangles, 39, SB17 Ocean trenches, 9 Octagons, SB16 Of Mice and Men (Steinbeck), 13 One-step equations solving, with decimals, 9 solving, with fractions, 9 95 solving, with integers, 3 3, solving, with rational numbers, 9 95 Online Resources Chapter Project Online,, 60, 11, 16, 0, 70, 318, 37, 7, 56, 586 Game Time Etra, 10, 15, 1, 60, 310, 36,, 6, 518, 576, 6 Homework Help Online Homework Help Online is available for every lesson. Refer to the go.hrw.com bo at the beginning of each eercise set. Some eamples: 8, 1, 16, 0, Lab Resources Online, 1, 6, 18, 189, 0, 38, 78, 8, 96, 530, 57, 553, 59, 60, 607, 616 Parent Resources Online Parent Resources Online is available for every lesson. Refer to the go.hrw.com bo at the beginning of each eercise set. Some eamples: 8, 1, 16, 0, Standards Practice Online, 58, 110, 16, 18, 68, 316, 37, 8, 7, 5, 58, 630 Web Etra!, 5, 101, 195, 09, 36, 55, 91, 19, 3, 83, 563, 599, 606 Open circle, 137 Operations inverse, 3 order of, 6, 3, 7 Opposites, 1 Order of operations, 6, SB1 using, 169, 173 Ordered pairs, 3 Ordering measurements, customary and metric, 37 rational numbers, 71 Organizing data, 53 53, SB18 1 Origami, 311 Origin, 3 Ounce, fluid, SB15 Outcomes, 556 equally likely, 56 Outlier, Output, 36 Pacific Wheel, 30, 53 Pairs, ordered, 3 Pandas, 6 Parabola, 33 Parallel lines, properties of transversals to, 389 and skew lines, Parallelograms, 399, SB17 area of, perimeter of, 3 36 Parent Resources Online Parent Resources Online are available for every lesson. Refer to the go.hrw.com bo at the beginning of each eercise set. Some eamples: 8, 1, 16, 0, Parentheses, 6 Parthenon, 83 Patterns, 17, 86 in integer eponents, looking for, Pediment, 5 Pei, I. M., 93 Peirsol, Aaron, 7 PEMDAS mnemonic, 6 Pentagons, 03, SB16 Percent problems, solving, 83 85, Percent(s) applications of, of change, 9 of decrease, 9 95 defined, 7 estimating with, finding, using an equation, 83, 8 using a proportion, 83, 85 fractions and decimals and, 7 75 of increase, 9 95 known, finding numbers for, of numbers, 83 8 Perfect squares, 19 Perimeter, 196, 3 of parallelograms, 3 36 of rectangles, 3 36 of trapezoids, 39 1 of triangles, 39 1 Periscopes, 391 Perpendicular bisectors, 38 Perpendicular lines, , Person-day, 39 Person-hour, 38 Physics, 591 Pi (), 03, 50 Pint, SB15 Piels, 193 Place value, SB Planes, 378 points and lines and angles and, Pluto, 187 Points, 378 on the coordinate plane, 3 33 graphing, 1, 3 33 Inde I9

153 lines and planes and angles and, plotting, 33 Polygons, 399 angles in, , 03 classifying, 399, SB16 17 regular, SB16 Polyhedrons, Polynomials classifying, addition of, modeling, 60 defined, degrees of, 591 modeling, multiplication of, by monomials, simplifying, subtraction of, modeling, 607 Population(s), SB samples and, SB Positive correlation, 59 Positive slope, 39 Pound, SB15 Powers, 168 division of, multiplication of, 176 of products, 181 raising monomials to, 181 raising powers to, 177 and roots, 19 simplifying, of ten, 18 zero, 173 Preparing for your final eam, 589 Price, unit, 9 Prime factorization, SB5 Prime numbers, SB5 Principal, 303 Principal square root, 19 Prisms, 80, 85 lateral faces, 98 naming, 80 nets of, 96 rectangular, 85, see also Rectangular prism surface area of, triangular, 85 volume of, eploring, 8 Probability defined, of dependent events, finding, of disjoint events, 566 eperimental, of independent events, finding, theoretical, Problem Solving Problem solving is a central focus of this course and is found throughout this book. Problem Solving Application, 3, 8, 98 99, 15, 06, 38, 9, 613 Problems, reading, for understanding, 73 Production costs, 586 Profit, Properties Addition, of Equality, 33 Associative, 603 of Addition, of Multiplication, Commutative of Addition, of Multiplication, Density, of real numbers, 01 Distributive, 117 Division, of Equality, 37 Identity of Addition, 3 of Multiplication, 37 Inverse of Multiplication, 8 Multiplication, of Equality, 38 of circles, 6 7, of eponents, Subtraction, of Equality, 33 Proportions, 3 3 identifying, 3 and indirect measurement, 8 and percent, 83 ratios and, 3 similar figures and, solving, 33 3 using, to find scales, 5 writing, 33 3 Protractors, Punnett squares, 568 Pyramid of Khafre, 09 Pyramids, 80, 90 naming, 80 regular, 50 stone, 83 surface area of, volume of, Pythagorean Theorem, and area, 39 converse of the, eploring the, 0 Quadrants, 3 Quadratic functions, Quadrilaterals angles of, 03, SB16 classifying, 399 Quart, SB15 Quartiles, 5 53 Radical symbol, 19 Radius, 6, 50 Raising monomials to powers, 181 powers to powers, 177 Random samples, SB Range, 537 Rate of change, 3 35 slope and, 3 35 Rate of interest, 303 Rates, 8 9 commission, 98 of interest, 303 unit, 8 9, see also Unit rates Rational numbers, , addition of, 7 75 comparing, decimal epansion of, 6 65 defined, 66 division of, 8 8 eploring, 6 65 multiplication of, ordering, 71 solving equations with, 9 95, subtraction of, 7 75 Ratios, 5 comparing, 5, 3 equivalent, 5, 3 and proportions, 3 writing, in simplest form, Rays, 378 Reading circle graphs, 77 graphics, 59 lessons for understanding, 115 numbers in scientific notation, 185 problems for understanding, 73 Reading and Writing Math, 5, 63, 115, 167, 3, 73, 31, 377, 33, 77, 59, 589 Reading Math, 8, 137, 168, 177, 5, 7, 39, 379, 11, 0, 6, 86, 513 Reading Strategies, see also Reading and Writing Math Interpret Graphics, 59 Read a Lesson for Understanding, 115 Read Problems for Understanding, 73 Use Your Book for Success, 5 Ready to Go On?, 30, 8, 9, 10, 13, 15, 190, 10,, 58, 9, 308, 3, 36, 0, 0,, 6, 9, 516, 55, 57, 600, 6, see also Assessment Real numbers, Density Property of, 01 Reasoning Reasoning is a central focus of this course and is found throughout this book. Some eamples: 13, 16, 17, 9, 39, 0, 5, 69, 71, 7, 76, 83, 90, 95, 98, 119, 1, 17, 1, 13, 150, 171, 17, 183, 195, 199, 08, 6, SB deductive, SB inductive, SB proportional, 0 69 Reciprocals, 8 Recreation, 0, 79, 88, 16, 196, 8, 515 I10 Inde

154 Rectangles, 399, SB17 area of, perimeter of, 3 36 Rectangular prism, 85 volume of, eploring, 8 Rectangular pyramid, 90 Recycling, 5 Reduction, 53 Reflection(s), 10 line of, 10 translations and rotations and, 10 1 Regular polygons, SB16 Regular pyramids, 50 Regular tessellations, 16 Relating decimals, fractions, and percents, 7 75 Relationships, angle, Remember!, 6, 1, 67, 70, 75, 9, 11, 15, 1, 18, 19, 181, 75, 35, 50, 80 Repeating decimals defined, 66 eploring, 6 65 period of, 65 writing, as fractions, 67 Representations of data, see also Displaying and organizing data multiple, using, 377 Reptiles, 361 Reptiles, (M.C. Escher), 19 Reticulated python, 89 Rhombuses, SB17 Right angles, 379 Right cones, 50 Right triangles, 39, SB17 finding angles in, 39 finding lengths of sides in, identifying, Rincon Park, 0 Rise, Roots square, square, estimating, Rotation(s), 10 center of, 10, 1 translations and reflections and, 10 1 Rounding decimals, SB whole numbers, SB Rules, divisibility, SB Run, Safety, 35, 561 Sales ta, Sample(s), SB biased, SB populations and, SB random, SB surveys and, SB Sample spaces, 556 San Diego, 70 San Francisco, CA, 0 Santa Rosa, CA, 0 Scale, 5 Scale drawings, 5 constructing, 56 Scale factors, 53 Scale models, 5 53, 59 constructing, Scalene triangles, 393, SB17 Scaling three-dimensional figures, Scatter plots, creating, 553 School, 7, 80, 19, 3 Science, 7, 17, 8, 9, 36, 91, 96, 17, 133, 187, 199, 6, 8, 81, 89, 97, 336, 507 Scientific notation, comparing numbers in, 186 division of numbers in, 189 multiplication of numbers in, 189 reading numbers in, 185 writing numbers in, Sections, 63 Sector, 7 Segments, line, 378 Selected Answers, SA1 SA1 Semiregular tessellations, 18 Set-builder notation, 1 Short Response, 13, 9, 97, 151, 179, 188, 195, 7, 51, 55, 66 67, 333, 356, 396, 1, 19, 38, 70, 71, 563, 599, 615 Write Short Responses, Sides, corresponding, Silos, 88 Similar figures, finding missing measures in, 5 and indirect measurement, 8 9 and scale drawings and models, 5 53 proportions and, three-dimensional surface area of, 513 volume of, 513 using, 8 9 Similar polygons, 5 Simple interest, Simplest form, 67 writing ratios in, Simplifying algebraic epressions, negative eponents, polynomials, powers, , Skew lines, 38 Skills Bank, SB SB Slant height, 50 Slide, see Translations Slope, 35 36, 398 of a line, rates of change and, 3 35 Snakes, 101 Snowboard half-pipe, 50 Social Studies, 5, 35, 7, 71, 86, 16, 188, 8, 86, 91, 396, 38, 89, 91, 507 Solid figures, see Three-dimensional figures Solution set, 136 Solutions, 3 of equations, 3 Solving equations, see Solving equations inequalities, see Solving inequalities multi-step equations, 1 15, percent problems, 83 85, proportions, 3 3 two-step equations, 3 5, Solving equations by addition, 3 3 with decimals, 9, by division, with fractions, 9 95, 99 linear, by multiplication, multi-step, 1 15, with rational numbers, 9 95, by subtraction, 3 3 two-step, 3 5, using addition and subtraction properties, 3 3 using multiplication and division properties, with variables on both sides, Solving inequalities, by adding or subtracting, by multiplying or dividing, 1 15 two-step, Special products, 619 Speed, 8 9, 3, 38, 39 Spheres, surface area of, 509 volume of, 508 Spiral Standards Review Spiral Standards Review questions are found in every lesson. Some eamples: 9, 13, 17, 1, 5 Sports, 1, 7, 38, 68, 7, 7, 76, 13, 17, 151, 19, 0, 81, 38, 336, 53, 51 Spreadsheets using, to construct graphs, Square roots approimating, to the nearest hundredth, 197 using a calculator, 197 estimating, of monomials, 193 principal, 19 squares and, Square units, 85 Square(s), 19, 399, SB17 area of, 35 Inde I11

155 magic, 1 perfect, 19 square roots and, Standard form, 185 Standards Practice Online, 58, 110, 16, 18, 68, 316, 37, 8, 7, 5, 58, 630 Stanford Linear Accelerator Center, 16 Statisticians, 70 Steinbeck, John, 13 Stem, 533 Stem-and-leaf plots, 533 back-to-back, Step Pyramid of King Zoser, 507 Straight angles, 379 Strategies for Success, see also Assessment Any Type: Using a Graphic, Etended Response: Write Etended Responses, Gridded Response: Write Gridded Responses, Multiple Choice Answering Contet-Based Test Items, Eliminate Answer Choices, Short Responses, Study for a Final Eam, 589 Study Guide: Review, 5 5, , , 1 16, 6 6, 31 31, , 6, 66 68, 50 5, , 66 68, see also Assessment Study Strategies, see also Reading and Writing Math Concept Map, 33 Study for a Final Eam, 589 Take Effective Notes, 167 Subscripts, 0 Substitute, 6 Subtraction of decimals, 7 of fractions, 75 with unlike denominators, of integers, 3 of mied numbers, of polynomials, modeling, 607 of rational numbers, 7 75 solving equations by, 3 3 solving inequalities by, Subtraction Property of Equality, 33 Supplementary angles, 379 Surface area, 98 of cones, eploring, 503 of cylinders, eploring, of figures built of cubes, 98 of prisms, eploring, of pyramids, of similar three-dimensional figures, of spheres, 509 Surface, lateral, 99 Surveys, samples and, SB Systems of equations, 131 solving, 131 writing, 131 Systolic blood pressure, 36 Tables frequency, SB0 functions and, 36, 37, 330, 331, 33, 335, 338, 339 graphs and, 330, 331, 33, 335, 338, 339 Taiwan, 188 Taking effective notes, 167 Target heart rate, 615 Ta, sales, 98 Ta brackets, 301 Technology Lab Make a Bo-and-Whisker Plot, 57 Make a Scatter Plot, 553 Multiply and Divide Numbers in Scientific Notation, 189 Use a Spreadsheet to Make Graphs, Television Ratings, Nielsen, 83 Temperature conversions, 103 global, 73 scales, 103, 331 Terabyte, 179 Terminating decimals defined, 66 eploring, 6 65 writing, as fractions, 67 Terms, 10 like, 10 not like, 596 Tessellations, regular, 16 semiregular, 18 Test, cumulative, studying for a, 589 Test items, contet-based, answering, The Grapes of Wrath (Steinbeck), 13 Theorem, Pythagorean, see Pythagorean Theorem Theoretical probability, Think and Discuss Think and Discuss is found in every lesson. Some eamples: 7, 11, 15, 19, 3 Three-dimensional figures classifying, 81 drawing, 77 eploring, introduction to, scaling, surface area of, 96, 509 volume of, 8 87, 508 Tides, 8 Tiles, algebra, 1, 18, , 60, 607, Time, investment, 303 Timeline, 5 Tips, 79 To Kill a Mockingbird (Lee), 97 Ton, SB15 Torus, 518 Toys, 606 Transamerica Pyramid, 9 Transformations, 10 combining, 15 graphing, 10 1 Translating math epressions into word phrases, 11 sentences into two-step equations, 3 word phrases into inequalities, 136 word phrases into math epressions, 10 between words and math, 63 Translations, 10 rotations and reflections and, 10 1 Transportation, 0, 1, 593 Transversals, 389 to parallel lines, properties of, 389 Trapezoids, 399, SB17 area of, 0 1 isosceles, SB17 perimeter of, 39 Travel, 15, 16 Tree diagrams, SB3 Trenches, ocean, 9 Trial, 556 Triangle Sum Theorem, 39 Triangles, 39 39, SB16 SB17 acute, 39, SB17 angles in, area of, 0 1 classifying, congruent, 06 equilateral, 393, SB17 isosceles, 393, SB17 obtuse, 39, SB17 perimeter of, 39 right, 39, SB17, see also Right triangles scalene, 393, SB17 similar, 5 Triangular prism, 85 Triangular pyramid, 90 Trinomials, 590 Trump Tower, 57 Turns, see Rotation(s) Twins, 06 Two-dimensional figures, Two-step equations modeling, 1 solving, 3 5 I1 Inde

156 solving, with rational numbers, Two-step inequalities, solving, Umbra, 507 Undefined slope, 350 Understanding reading lessons for, 115 reading problems for, 73 Unisphere, 83 Unit(s) conversion factors, 37 customary, SB15 metric, SB15 Unit analysis, 37 Unit conversion factor, 37 Unit fractions, 10 Unit price, 9 Unit rates, 8 9 estimating, 9 rates and, 8 9 United States census, 91 Unlike denominators addition of fractions with, subtraction of fractions with, Unpacking the Standards,, 6, 11, 166,, 7, 30, 376, 3, 76, 58, 588 Upper quartile, 5 53 Use your book for success, 5 Use your own words, 377 Using formulas, 77 graphics, nets to build prisms and cylinders, similar figures, 8 9 slopes, 350 spreadsheets to construct graphs, technology to make graphs, your book for success, 5 your own words, 377 Value, absolute, 15 Variable(s) on both sides modeling equations with, 18 solving equations with, epressions and, 6 7 Variable rate of change, 3 Variation, direct, Venn diagrams, 00 Venus, 187 Verte of an angle, 379 of a cone, 81 of a polygon, of a polyhedron, 80 of a three-dimensional figure, 80 Vertical angles, 388 Vertical line test, 37 Volume, 85 of cones, of cylinders, of prisms, eploring, 8 of pyramids, of similar three-dimensional figures, of spheres, 508 Weather, 119, 35 Web Etra!, 5, 101, 195, 09, 36, 55, 91, 19, 3, 83, 93, 563, 599, 606, Weight, customary units of, SB15 Whales, 175 What s the Error?, 13, 1, 36, 69, 73, 81, 97, 119, 13, 17, 139, 17, 179, 183, 195, 03, 7, 31, 1, 77, 35, 35, 391, 53, 89, 93, 56, 559, 593 What s the Question?, 307, 39, 333, 0, 51, 615 Wheel, 6 Whole numbers comparing and ordering, SB3 dividing, SB7 long division, SB7 rounding, SB Word phrases translating, into inequalities, 136 translating, into math epressions, 10 translating math epressions into, 11 Words into math, translating, 136 and math, translating between, 63 use your own, 377 Write a Problem, 0, 77, 13, 151, 188, 08, 7, 51, 8, 361, 09, 507, 573, 606 Write About It Write About It eercises are found in every lesson. Some eamples: 9, 13, 17, 1, 5 Writing convincing arguments, 3 etended responses, gridded responses, inequalities, 136, 11 compound, 137 numbers in scientific notation, numbers in standard form, 185 proportions, 3 short responses, Writing Math, 66, 19, 388 Writing Strategies, see also Reading and Writing Math Draw Three-Dimensional Figures, 77 Keep a Math Journal, 31 Translate Between Words and Math, 63 Use Your Own Words, 377 Write a Convincing Argument, 3 -ais, 3 -coordinate, 3 Yard, SB15 y-ais, 3 y-coordinate, 3 Yosemite National Park, 88, 11, 5 Zero power, 173 Zero slope, 39 Inde I13

157 Credits Staff Credits Bruce Albrecht, Margaret Chalmers, Tica Chitrarachis, Lorraine Cooper, Marc Cooper, Jennifer Craycraft, Martize Cross, Nina Degollado, Julie Dervin, Michelle Dike, Lydia Doty, Sam Dudgeon, Kelli R. Flanagan, Stephanie Friedman, Jeff Galvez, Pam Garner, Diannia Green, Jennifer Gribble, Liz Huckestein, Jevara Jackson, Simon Key, Jane A. Kirschman, Kadonna Knape, Cathy Kuhles, Jill M. Lawson, Liann Lech, Virginia Messler, Susan Mussey, Kim Nguyen, Nathan O Neal, Manda Reid, Michael Rinella, Annette Saunders, Kay Selke, Robyn Setzen, Patricia Sinnott, Victoria Smith, Dawn Marie Spinozza, Jeannie Taylor, Karen Vigil, Kira J. Watkins, Sherri Whitmarsh, David W. Wynn Photo Credits Frontmatter: viii Gary Crabbe/Enlightened Images; i Ed Young/CORBIS; Dr. Eric Chalker/Inde Stock Imagery, Inc.; i Peter Ginter/Bilderberg; ii Jenny Thomas/HRW; iii Ron Vesely/MLB Photos via Getty Images; iv John Kelly/Getty Images; v VEER/Christopher Talbot Frank/Getty Images; vi Richard Cummins/CORBIS; vii Robert Landau/CORBIS; viii Court Mast/Marling Mast/Getty Images; i Armando Arorizo/epa/Corbis Chapter One: -3 (bkgd), Gary Crabbe/Enlightened Images; 9 (l), The Granger Collection, New York; 9 (r), The Kobal Collection; 10 Robert Landau/CORBIS; 1 Don Couch/HRW; 17 Layne Kennedy/CORBIS; 18 Victoria Smith/HRW; 1 Peter Van Steen; 5 (tc), Araldo de Luca/CORBIS; 5 (tl), Steve Vidler/SuperStock; 5 (br), The Art Archive/Napoleonic Museum Rome/Dagli Orti; 5 (tr), Bettmann/ CORBIS; 6 Dennis MacDonald/PhotoEdit Inc.; 9 (l), Peter David/Getty Images; 3 Sam Dudgeon/HRW; 9 (t), istockphoto; 9 (b), Sam Dudgeon/HRW; 50 Randall Hyman/HRW; 51 Sam Dudgeon/HRW Chapter Two: (bkgd), Ed Young/CORBIS; 70 Getty Images; 73 NASA; 77 Lester Lefkowitz/CORBIS; 78 Sam Dudgeon/HRW; 81 John Giustina/Bruce Coleman, Inc.; 86 Mark Tomalty/Masterfile; 88 Library of Congress; 91 (t), Lester Lefkowitz/CORBIS; 91 (b), Sam Dudgeon/HRW; 93 (b), Dean Conger/CORBIS; 98 Eric Gaillard/Reuters/CORBIS; 101 (t), Torsten Blackwood/AFP/Getty Images; 101 (b), Karl H. Switak/Photo Researchers, Inc.; 103 AP Photo/Eau Claire Leader- Telegram/Steve Kinderman; 10 (b), Jenny Thomas/HRW; 105 (b), Sam Dudgeon/HRW Chapter Three: (bkgd), Dr. Eric Chalker/Inde Stock Imagery, Inc.; 17 Buddy Mays/CORBIS; 19 (l), GK & Vikki Hart/Getty Images; 19 (r), Artiga Photo/CORBIS; 133 Andrew Syred/Science Photo Library/Photo Researchers, Inc.; 135 (b), Sam Dudgeon/HRW; 13 (l), Bettmann/CORBIS; 19 Sam Dudgeon/HRW; 15 (b), Jenny Thomas/HRW; 153 (t), Comstock, Inc.; 153 (b), Dean Fo/SuperStock; 155 Sam Dudgeon/HRW Chapter Four: (bkgd), Peter Ginter/Bilderberg; 17 S. Lowry/Univ. Ulster/Getty Images/Stone; 175 (t), Francois Gohier/Photo Researchers, Inc.; 175 (b), Flip Nicklin/Minden Pictures; 177 PEANUTS Universal Press Syndicate; 183 GK & Vikki Hart/Getty Images; 187 Joe McDonald/CORBIS; 193 Roberto Rivera; 195 David Young-Wolff/PhotoEdit, Inc.; 196 Sam Dudgeon/HRW; stained glass artist: Leanne Ohlenburg; 11 (t), Classic PIO Partners; 11 (bl), SciMAT/Photo Researchers, Inc.; 11 (br), SciMAT/Photo Researchers, Inc.; 1 (b), Randall Hyman/HRW; 13 Sam Dudgeon/HRW Chapter Five: 0-1 (bkgd), Jenny Thomas/HRW; (t), Dave Jacobs/Inde Stock Imagery, Inc.; 7 (c), Sam Dudgeon/HRW; 36 (t), 00 EyeWire Collection; 36 (c), Andrew Syred/Microscopi Photolibrary; 36 (b), Ed Reschke/Peter Arnold, Inc.; 0 (l), Jonathan Sprague/Redu; 3 (b), Robb dewall/crazy Horse Memorial; (t), Sam Dudgeon/HRW; 7 Layne Kennedy/ CORBIS; 8 Courtesy Troop 3, Arlington Heights, IL; 5 National Geographic Image Collection; 53 Digital Art/CORBIS; 55 David Young-Wolff/PhotoEdit Inc.; 57 Lee Snider/CORBIS; 59 (b), Richard Meier & Partners Architects LLP; 60 (t), PhotoLink/Getty Images; 60 (b), Ken Karp/HRW; 61 Sam Dudgeon/HRW Chapter Si: Ron Vesely/MLB Photos via Getty Images; 7 Charles Gullung/Photonica/Getty Images; 81 Peter Van Steen/HRW; 8 Sam Dudgeon/ HRW; 8 (green beans) Royalty Free/CORBIS; 88 Jeff Rotman/Photo Researchers Inc.; 89 Hans Reinhard/Bruce Coleman, Inc.; 91 Katy Winn/ CORBIS; 93 (cricket) Digital Image 00 PhotoDisc; 93 (wasp) Digital Image 00 PhotoDisc; 93 (black & white beetle) Stockbyte; 93 (ladybug) Digital Image 00 PhotoDisc; 93 (mantis) Stockbyte; 93 (ant) Brand X Pictures; 93 (harlequin beetle) Digital Image 00 Artville; 93 (earwig) Brand X Pictures; 93 (green beetle) Brand X Pictures; 93 (mantis with etended wings) Brand X Pictures; 97 (r) Lyn Topinka/USGS/Cascades Volcano Observatory; 97 (l) Katy Winn/CORBIS; 301 Sam Dudgeon/HRW; 307 Pornchai Kittiwongsakul/AFP/Getty Images; 309 (t) Stephanie Friedman/HRW; 309 (b) Sam Dudgeon/HRW; 310 (b) Victoria Smith/HRW; 311 Sam Dudgeon/HRW Chapter Seven: John Kelly/Getty Images; 35 (l) Stock Trek/ PhotoDisc/Picture Quest; 39 Schenectady Museum/Hall of Electrical History Foundation/CORBIS; 333 Ron Kimball Stock; 33 Chip Simons Photography; 337 Sam Dudgeon/HRW; 31 Andrew Sacks/Time Life Pictures/Getty Images; 357 Sindre Ellingsen/Alamy; 361 E.R. Degginger/Bruce Coleman, Inc.; 363 (tr), Harry Engels/Photo Researchers, Inc.; 363 (b), Alan and Sandy Carey/Photo Researchers, Inc.; 363 (tl), Stephanie Friedman/HRW; 36 (b), Randall Hyman/HRW; 365 Sam Dudgeon/HRW Chapter Eight: (all), VEER/Christopher Talbot Frank/Getty Images; Sol LeWitt/Artists Rights Society (ARS), New York; 387 Mark Schneider/Visuals Unlimited/Getty Images; 388 Rodolfo Arpia/Alamy; 398 (all), Courtesy of Lucasfilm, Ltd. Star Wars: Episode I - The Phantom Menace 1999 Lucasfilm Ltd. & TM. All rights reserved. Used under authorization. Unauthorized duplication is a violation of applicable law.; 06 (r), Seth Kushner/Getty Images/ Stone; 06 (l), Science Photo Library/Photo Researchers, Inc.; 10 Matthew Stockman/Getty Images; 16 Harry Lentz/Art Resource, NY; 1 Bob Burch/Inde Stock Imagery, Inc.; Jenny Thomas/HRW; 3 Sam Dudgeon/HRW Chapter Nine: (all), Richard Cummins/CORBIS; 39 Louie Psihoyos/ CORBIS; 3 (t), Royalty-Free/Corbis; 5 (b), Dave G. Houser/Houserstock; 6 (all), Archivo Iconografico, S.A./CORBIS; 58 Larry Lefever/Grant Heilman Photography; 61 (t), William Hamilton/SuperStock; 63 (t), PhotoDisc/Getty Images; 63 (b), Grant Heilman /Grant Heilman Photography, Inc.; 6 Jenny Thomas/HRW; 65 Sam Dudgeon/HRW Chapter Ten: 7-75 Robert Landau/CORBIS; 83 (tr), Charles & Josette Lenars/CORBIS; 83 (bl), Kevin Fleming/CORBIS; 83 (tl), Steve Vidler/SuperStock; 83 (br), R.M. Arakaki/Imagestate; 85 Kenneth Hamm/Photo Japan; 89 (r), Dallas and John Heaton/CORBIS; 89 (l), G. Leavens/Photo Researchers, Inc.; 90 Tor Eigeland/Alamy; 93 (l), Owen Franken/CORBIS; 93 (r), Steve Vidler/SuperStock; 95 (b), Sam Dudgeon/HRW; Kelly Houle; 505 (l), Robert & Linda Mitchell Photography; 506 Baldwin H. Ward & Kathryn C. Ward/CORBIS; 508 NASA/Corbis; 511 (t), Darryl Torckler/Getty Images/Stone; 511 (tc), Dwight Kuhn Photography; 511 (bc), Sinclair Stammers/Science Photo Library/Photo Researchers, Inc.; 511 (b), Ron Austing; Frank Lane Picture Agency/CORBIS; 515 Chris Lisle/CORBIS; The LEGO Group; 517 Victoria Smith/HRW; 518 Sam Dudgeon/HRW; 519 Sam Dudgeon/HRW Chapter Eleven: Court Mast/Marling Mast/Getty Images; 53 Digital Vision; 51 Karl Weatherly/CORBIS; 5 Peter Van Steen/HRW/Kittens courtesy of Austin Humane Society/SPCA; 58 Royalty Free/CORBIS; 560 AP Photo; 563 (l), Reuters/CORBIS; 563 (r), David Weintraub/Photo Researchers, Inc.; 56 Peter Van Steen/HRW; 568 Sam Dudgeon/HRW; 575 Design Pics; 576 Sam Dudgeon/HRW; 577 Sam Dudgeon/HRW Chapter Twelve: (all), Armando Arorizo/epa/Corbis; 590 Dave G. Houser/CORBIS; 599 (t), Paul Eekhoff/Masterfile; 599 (b), Private Collection/ Bridgeman Art Library/ 00 Fletcher Benton/Artists Rights Society (ARS),, New York; 601 Steve Gottlieb/Stock Connection/PictureQuest; 603 Sam Dudgeon/HRW; 60 Sam Dudgeon/HRW; 606 Stephen Mallon/The Image Bank/Getty Images; 61 Sam Dudgeon/HRW; 613 Victoria Smith/HRW; 615 Victoria Smith/HRW; 618 Mark Gibson Photography; 61 (b), Sam Dudgeon/HRW; 63 (t), istock Photo; 63 (bl), Jeff Greenberg/Photo Edit, Inc.; 63 (br), Photodisc/Getty Images; 6 (b), Sam Dudgeon/HRW; 65 (b), Sam Dudgeon/HRW; (all), Armando Arorizo/epa/Corbis Student Handbook TOC: 63 John Langford/HRW; 633 Sam Dudgeon/HRW Credits 911