Answers for Lesson 1-1

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1 Pearson Education, Inc., publishing as Pearson Prentice Hall. All rights reserved. Answers for Lesson - Exercises. natural numbers, whole numbers, integers, rational numbers, real numbers. irrational numbers, real numbers. irrational numbers, real numbers. integers, rational numbers, real numbers 5. whole numbers, integers, rational numbers, real numbers 6. rational numbers, real numbers 7. rational numbers, real numbers 8. irrational numbers, real numbers 9. whole numbers, rational numbers 0. natural numbers, rational numbers. real numbers = ,.,. =..., 5..,, , 0.9, ,., , -.8, ,., , "0., " , ", ". -. "5, "7, "7. "5. ". "5, "5, " Algebra Chapter

2 Answers for Lesson -. 00, , , , 7 8. ", " Qor " R 9. p, 0.., 50. p, p. Dist. Prop.. Comm. Prop. of Add.. Assoc. Prop. of Mult. 5. Comm. Prop. of Mult. 6. Identity Prop. of Add. 7. Inverse Prop. of Mult p Pearson Education, Inc., publishing as Pearson Prentice Hall. All rights reserved Answers may vary. Samples are given D 65. natural numbers, whole numbers, integers, rational numbers, real numbers 66. irrational numbers, real numbers 67. irrational numbers, real numbers 68. rational numbers, real numbers 69. irrational numbers, real numbers 70. irrational numbers, real numbers Algebra Chapter

3 Pearson Education, Inc., publishing as Pearson Prentice Hall. All rights reserved. Answers for Lesson , , 76., 77., 78., 79. Answers may vary. Sample: is a whole number, but is not a whole number. 80. Answers may vary. Sample: 7 is a natural number, but -7 is not a natural number is a whole number, and since -0 = 0, the opposite of 0 is a whole number. 8. Answers may vary. Sample: The integer - has - as its reciprocal, so - is an integer whose reciprocal is an integer. 8. Answers may vary. Sample: " and " are irrational numbers, but their product () is a rational number. 8. Check students work. 85. all except the Identity Prop. of Add. (since 0 is not in the set of natural numbers) and the inverse properties 86. all except the Inverse Prop. of Mult. and the Inverse Prop. of Add. 87. all except the Inverse Prop. of Mult. 88. all the properties 89. Comm., Assoc., and Distr. Prop. 90. No; explanations may vary. Sample: The only pairs of integers that have a product of - are - and, - and 6, - and, - and, -6 and, and - and. None of these pairs has a sum of -. Algebra Chapter

4 Pearson Education, Inc., publishing as Pearson Prentice Hall. All rights reserved. Answers for Lesson - Exercises ft 0. ft. 6 ft. 600 ft. 0.0 mm. 0.0 mm mm 6.. mm 7. $0 8. $ 9. $ $60.5. a. s 5. 9a b. 5. 0r 5s 6. 6w 5z xy x x 0.. 0y x. y 6x.. g 5. x y z a a. about 80 million voters b. about million voters; about 6 million voters c y +.65y d. about 87 million 5x 7. a b y 5. x 6y x y 5. F 55. C 6a b x x 6x 5 a 5b a 7y y 5 x y Algebra Chapter

5 Answers for Lesson A 57. G 58. B 59. H 60. E 6. I 6. D 6. Assoc. Prop. of Add., Comm. Prop. of Add., Assoc. Prop. of Add., Identity Prop. of Mult., Distr. Prop. of Add., Simplify. 6. Distr. Prop.; Simplify; Distr. Prop. 65. Answers may vary. Sample: x + x + x - x - x, -x + x + x - x - x, x - 5x + x - x 5 + x 5,x - x - x + 7x - 8x Pearson Education, Inc., publishing as Pearson Prentice Hall. All rights reserved. 66. Answers may vary. Sample: (b a) 5(b a) = ( 5)(b a) Dist. Prop. = 7(b a) Addition = 7b 7a Dist. Prop. 67. a. 8 b. x,8 c. Properties of operations were used to simplify the original expression. Those properties convert one expression into an equivalent expression, and equivalent expressions have equal values for all replacements of their variables. d. No; explanations may vary. Sample: Students should check each step in the simplification; they also should substitute more than one value for x in the original and simplified expressions. Algebra Chapter 5

6 Pearson Education, Inc., publishing as Pearson Prentice Hall. All rights reserved. Answers for Lesson - Exercises h = A b w = lh V 0. r = pt I... x = a b, a b. x = c c b, b c 5. x = a(c b) or ac ab, a 0 6. x = a(b 5) or ab 5a, a 0 7. x = (m n) or m n 8. x = 5g 9. h mi/h, 600 mi/h. width =.5 cm, length = 7.5 cm. 7 7 h = V pr c in., 5 in., 6 in.. cm, cm, 6.5 cm, 6.5 cm. 7.5 cm, 0 cm,.5 cm 5. a. x + (x + ) + (x + ) = 90; 9, 0, b. (x - ) + x + (x + ) = 90; 9, 0, g = s t r = S ph Algebra Chapter 6

7 Pearson Education, Inc., publishing as Pearson Prentice Hall. All rights reserved. Answers for Lesson - 6., or 7. 8., or , or r. h = S pr = Rr R = r r r r r R pr h = (v s ) v = h t 5t s 7. b = A h b 8. 08, , about 69. mi 5. <.0 m 5. $60; $ , 5, 7, 9 5., 6, 8, x = ab b a, b x = b c d a, b d x = a b 8, a b 59. ab c 60. x =, at cd x = cb 6, a, b, d at cd da a b x = a c m a, m 0, 65. a. t = s. 055 b. about 0.98F c. C = 5 9 (F ) d. about.98c x a 66. a. 0 cows, 0 chickens; Sample equation: c + (0 - c) = 00, where c is the number of cows. b. 80 legs; 0 legs; legs; 0 cows x = b d c a, a c x = x = b c 5 b c, b c a bc aq 5bp, 5bp aq x = 0c a, a 0 c. Answers may vary. Sample: In all, a repair shop has bicycles and tricycles to repair. These have a total of 6 wheels. How many bicycles and how many tricycles are there? 7 bicycles, tricycles Algebra Chapter 7

8 Pearson Education, Inc., publishing as Pearson Prentice Hall. All rights reserved. Answers for Lesson a. If you solve ax - b = c for x, you get x = b a c. Since b and c are integers, b + c is an integer. But a is a nonzero b c integer. So a is the quotient of two integers and b c hence, by the definition of a rational number, a is a rational number. b. Solutions are rational when $ 0, a 0, and is a perfect square (a whole number perfect square or, in simplest form, a fraction whose numerator and denominator are whole number perfect squares). Since x = c a b (a Z 0), x = "c a b or x = "c a b. For "c b c b and to be rational, must be "c b a nonnegative and also 68. about 69. ft a c b a c b a a c b a must be a perfect square. Algebra Chapter 8

9 Answers for Lesson - Exercises. x # 0 5. k a.. t # Pearson Education, Inc., publishing as Pearson Prentice Hall. All rights reserved. 5. y # y # x # 8 8. m, 0 9. n All real numbers are solutions. 0 Algebra Chapter 9

10 Answers for Lesson -. All real numbers are solutions. 0. All real numbers are solutions. 0. no solutions. The width is less than.5 in., and the length is in. greater than the width. 5. The longest side is less than cm. Pearson Education, Inc., publishing as Pearson Prentice Hall. All rights reserved. 6. The smaller number is an integer greater than or equal to students 8. -5, x, # x # # x, , x # x, or x Algebra Chapter 0

11 Answers for Lesson -. All real numbers are solutions. 0. x $ x # - or x $ between about 6. lb and 5.5 lb flour Pearson Education, Inc., publishing as Pearson Prentice Hall. All rights reserved. 7. between and days 8. between 0.6 cm and 0.0 cm 9. z $ 6 0. y # 0 5. x $ x, no solutions 5. All real numbers are solutions. 0 Algebra Chapter

12 Answers for Lesson - 5. Answers may vary. Sample: Mario has a coin collection that consists of dimes and nickels. There are half as many dimes as nickels. There are no more than 60 coins in the collection. Describe the collection. 6., AB, 6 7. between $0,000 and $5,000 Pearson Education, Inc., publishing as Pearson Prentice Hall. All rights reserved. 8. a. 0 makes y # 0 true, but it does not make (y 6) $ y + true. b. y # Dist. Prop.; arithmetic; Sub. Prop. of Inequality; Mult. Prop. of Inequality 0. Mult. Prop. of Inequality; Dist. Prop.; Add. Prop. of Inequality; Subt. Prop. of Inequality; Div. Prop. of Inequality. -, x, , y, no solutions. -7 # z, All real numbers are solutions b, or b Algebra Chapter

13 Answers for Lesson - 7. All real numbers are solutions no solutions 9. All real numbers are solutions no solutions 5. Answers may vary. Sample: x - 7 $ - Pearson Education, Inc., publishing as Pearson Prentice Hall. All rights reserved. 5. Answers may vary. Sample: -x Answers may vary. Sample: -9, 5x +, 6 5. Answers may vary. Sample: x + # 0 or -x - # a. no b. yes; values of a that are 8 or greater c. (a) yes; values of a that are less than 8, (b) no Algebra Chapter

14 Answers for Lesson -5 Exercises. -6, 6. -8, 8. -6,., 5. no solution 6. no solution 7. -8, , , , 8. -, x, - or x Pearson Education, Inc., publishing as Pearson Prentice Hall. All rights reserved. 7. x # - or x $ y # -9 or y $ All real numbers are solutions x # - or x $ 0 6. z, - or z , y, Algebra Chapter

15 Answers for Lesson -5., y, , x, no solution 6. # w # 5 0 Pearson Education, Inc., publishing as Pearson Prentice Hall. All rights reserved. 7. # t # u h. u # u k 50.5 u # u C 7.5 u # 0.5. u b 5.5 u #.5. u m 50 u # 50. u d u # no solutions , 6 8. no solutions , # x # , 8 5. x # -8 or x $ Algebra Chapter 5

16 Answers for Lesson All real numbers are solutions t, or t All real numbers are solutions x, or x. Pearson Education, Inc., publishing as Pearson Prentice Hall. All rights reserved x # -8. or x $ # x # , x, x, - or x Algebra Chapter 6

17 Pearson Education, Inc., publishing as Pearson Prentice Hall. All rights reserved. Answers for Lesson Region 0 # s # 0., u s 0.05 u # 0.05; 55. C Region 0. # s #, u s 0.55 u # 0.5; Region # s #, u s u # ; Region # s # 6, u s.5 u #.5; 56. The graph of u x u, a (where a. 0) is the set of all points on the number line that lie between the points for a and -a. The graph of u x u. a has two parts: the left part consists of the points to the left of the point for -a, and the right part consists of the points to the right of the point for a. 57. Answers may vary. Sample: u x u $ 0; u x u, x - 6.8«# 0.05, 6.75 # x # u x 9.55 u # 0.0, 9.5 # x # x is in inches: u x 600 u #, 596 # x # , a? 0; no solution, b + c, 0 b a c, b a c ab d c, ab c d 6., c? 0; no solution, ab, 0 ac d 6., ac d, ab? 0; no solution, d a, 0 ab ab 6. (-6 # x # -5) or (5 # x # 6) (x # -6) or (-5, x, 5) or (x $ 6) x $ Algebra Chapter 7

18 Pearson Education, Inc., publishing as Pearson Prentice Hall. All rights reserved. Answers for Lesson Exercises. or about 7%; or about 5%. the number :, or about 5.7%; the number : 67 or about 5 6.%; the number : 68 or out 6.8%; the number : 67 or 7 about 6.%; the number 5: 68 or about 7.5%; the number 6: or about 7.% Answers may vary. Sample: Generate random numbers between 0 and using a graphing calculator. In each random number, examine the first five digits. Let even digits represent correct answers and odd digits incorrect answers. If there are two or more even digits, make a tally mark for that number. Do this 00 times. Find the total number of tally marks. This, as a percent, gives the experimental probability. The simulated probability should be about 80%.. Answers may vary. Sample: Toss 5 coins. Keep a tally of the times or more heads are tossed. (A head represents a correct answer.) Do this 00 times. The total number of tally marks, as a percent, gives the experimental probability. The simulated probability should be about 50%. 5. Answers may vary. Sample: Generate 00 random numbers with a calculator. Record the first five digits of each number. Let 0 and represent correct answers and the other digits incorrect answers. Tally the recorded numbers with exactly one digit that represents a correct answer. Tally the recorded numbers with exactly two digits that represent correct answers. Tally the recorded numbers with exactly three digits that represent correct answers. The tally totals, as a percent, give the experimental probabilities. They should be about 0%, 0%, and 5%, respectively. Algebra Chapter 8

19 Pearson Education, Inc., publishing as Pearson Prentice Hall. All rights reserved. Answers for Lesson , or 0% 7., or 50% 8., or 80% 5 9., or 80% 0., or 8.%., or 5.% 0 5., or 8.%., or 56%., or 6.6% 5. {Gg, Gg, gg, gg};, or 50% 6. {Gg, Gg, Gg, Gg};, or 00% 6 7., or 6.5% 8., or 7.5% 9., or 5% 0., or 75%. a.. C b. 0. Answers may vary. Sample: Let odd digits represent heads and even digits represent tails. Use the first 50 digits of the table. The experimental probability of heads is , or 78.9% 5., or 5.% 6., or 9.% 7., or.% a. (, ), (, ), (, ), (, ), (, 5), (, 6), (, ), (, ), (, ), (, ), (, 5), (, 6), (, ), (, ), (, ), (, ), (, 5), (, 6), (, ), (, ), (, ), (, ), (, 5), (, 6), (5, ), (5, ), (5, ), (5, ), (5, 5), (5, 6), (6, ), (6, ), (6, ), (6, ), (6, 5), (6, 6) b. 6 outcomes c. d Algebra Chapter 9

20 Pearson Education, Inc., publishing as Pearson Prentice Hall. All rights reserved. Answers for Lesson <6.% 0. a. b. Answers may vary. Sample: Variables such as injuries make probability a poor predictor.. if there are any restrictions on the last digit of a ZIP code 5. or 6.7%. a. b. ; a a b a to b a or c. A game where the probability of winning is ; when the odds of winning are, the probability of winning is only.. Check students work. 5. a. about b. about a b a Algebra Chapter 0