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Solution Manual for College Algebra, 7th Edition

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    S OLUTIONS M ANUAL D ANIEL S. M ILLER Niagara County Community College C OLLEGE A LGEBRA S EVENTH E DITION Robert Blitzer Miami Dade College

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    iii TABLE OF CONTENTS C OLLEGE A LGEBRA 7 E Chapter P Fundamental Concepts of Algebra............................................................................. 1 Chapter 1 Equations and Inequalities ....................................................................................... 71 Chapter 2 Functions and Graphs............................................................................................. 201 Chapter 3 Polynomial and Rational Functions ....................................................................... 325 Chapter 4 Exponential and Logarithmic Functions ................................................................ 467 Chapter 5 Systems of Equations and Inequalities................................................................... 543 Chapter 6 Matrices and Determinants .................................................................................... 663 Chapter 7 Conic Sections........................................................................................................ 765 Chapter 8 Sequences, Induction, and Probability................................................................... 823

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    Chapter P Fundamental Concepts of Algebra 1 Section P.1 Check Point Exercises 1. 2 2 8 6( 3) 8 6(13 3) x + − = + − 2 8 6(10) 8 6(100) 8 600 608 = + = + = + = 2. a. Since 2014 is 14 years after 2000, substitute 14 for x . 2 2 4 330 3310 4(14) 330(14) 3310 8714 T x x = + + = + + = The average cost of tuition and fees at public U.S. colleges for the school year ending in 2014 was $8714. b. The formula underestimates the actual answer by $179. 3. The elements common to {3, 4, 5, 6, 7} and {3, 7, 8, 9} are 3 and 7. {3, 4,5, 6, 7} {3,7,8,9} {3, 7} ∩ = 4. The union is the set containing all the elements of either set. {3, 4,5, 6, 7} {3, 7,8,9} {3, 4,5, 6, 7,8,9} ∪ = 5. 9, 1.3, 0, 0.3, , 9, 10 2 π   − −     a. Natural numbers: 9 because 9 3 = b. Whole numbers: 0, 9 c. Integers: 9, 0, 9 − d. Rational numbers: 9, 1.3, 0, 0.3, 9 − − e. Irrational numbers: , 10 2 π f. Real numbers: 9, 1.3, 0, 0.3, , 9, 10 2 π − − 6. a. 1 2 − Because 2 1.4, ≈ the number inside the absolute value bars is negative. The absolute value of x when x < 0 is – x. Thus, ( ) 1 2 1 2 2 1 − = − − = − b. 3 π − Because 3.14, π ≈ the number inside the absolute value bars is positive. The absolute value of a positive number is the number itself. Thus, 3 3. π π − = − c. x x Because 0, . x x x > = Thus, 1 x x x x = = 7. 4 (5) 9 9 − − = − = The distance between –4 and 5 is 9. 8. 2 2 7(4 3 ) 2(5 ) x x x x + + + 2 2 2 2 2 7(4 3 ) 2(5 ) 28 21 10 2 38 23 x x x x x x x x x x = + + + = + + + = + 9. 6 4[7 ( 2)] x + − − 6 4[7 2)] 6 4[9 ] 6 36 4 42 4 x x x x = + − + = + − = + − = − Concept and Vocabulary Check P.1 1. expression 2. b to the n th power; base; exponent 3. formula; modeling; models 4. intersection; A B ∩ 5. union; A B ∪

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    Chapter P Prerequisites: Fundamental Concepts of Algebra 2 6. natural 7. whole 8. integers 9. rational 10. irrational 11. rational; irrational 12. absolute value; x ,  x 13. b a + ; ba 14. ( ) a b c + + ; ( ) ab c 15. ab ac + 16. 0; inverse; 0; identity 17. inverse; 1; identity 18. simplified 19. a Exercise Set P.1 1. 7 5(10) 7 50 57 + = + = 2. ( ) 8 6 5 8 30 38 + = + = 3. 6(3) 8 18 8 10 − = − = 4. ( ) 8 3 4 24 4 20 − = − = 5. 2 8 3(8) 64 24 88 + = + = 6. ( ) 2 6 5 6 36 30 66 + = + = 7. 2 7 6(7) 3 49 42 3 7 3 10 − + = − + = + = 8. ( ) 2 8 7 8 4 64 56 4 8 4 12 − + = − + = + = 9. 3 3 4 5(9 7) 4 5(2) 4 5(8) 4 40 44 + − = + = + = + = 10. ( ) ( ) ( ) 3 3 6 5 8 6 6 5 2 6 5 8 6 40 46 + − = + = + = + = 11. 2 8 3(8 2) 64 3(6) 64 18 46 − − = − = − = 12. ( ) ( ) 2 8 4 8 3 64 4 5 64 20 44 − − = − = − = 13. 5( 2) 5(10 2) 2 14 2(10) 14 5(12) 6 5 2 10 x x + + = − − = = ⋅ = 14. 7( 3) 7(9 3) 7(6) 7 3 21 2 16 2(9) 16 2 x x − − = = = ⋅ = − − 15. 2 3 ; 2, 4 1 x y x y x + = − = + ( ) ( ) 2 2 3 4 4 12 8 8 2 1 1 1 − + − + = = = = − − + − − 16. 2 ; 2 and 4 2 x y x y xy x + = − = − ( ) ( )( ) ( ) 2 2 4 4 4 0 0 2 4 2 2 8 4 4 − + − + = = = − − − − + 17. 5 (50 32) 9 C = − 5 (18) 10 9 = = 50 ° F is equivalent to 10 ° C. 18. 5 5 5 ( 32) (86 32) (54) 30 9 9 9 C F = − = − = = 86 ° F is equivalent to 30 ° C. 19. 2 2 4 60 16 4 60(2) 16(2) 4 120 16(4) 4 120 64 124 64 60 h t t = + − = + − = + − = + − = − = Two seconds after it is kicked, the ball’s height is 60 feet.

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    Section P.1 Algebraic Expressions, Mathematical Models, and Real Numbers 3 20. 2 2 4 60 16 4 60(3) 16(3) 4 180 16(9) 4 180 144 184 144 40 h t t = + − = + − = + − = + − = − = Three seconds after it is kicked, the ball’s height is 40 feet. 21. { } { } { } 1, 2,3, 4 2, 4,5 2, 4 =  22. { } { } { } 1,3, 7 2,3,8 3 =  23. { } { } { } , , , , , , s e t t e s s e t =  24. { } { } { } , , , , , , , , , r e a l l e a r r e a l =  25. { } { } { } 1,3,5, 7 2, 4, 6,8,10 =  The empty set is also denoted by . ∅ 26. { } { } { } 1,3,5, 7 5, 3, 1 − − − =  or ∅ 27. { } , , , a b c d ∅ = ∅  28. { } , , w y z ∅ = ∅  29. { } { } { } 1, 2,3, 4 2, 4,5 1, 2,3, 4,5 =  30. { } { } { } 1,3, 7,8 2,3,8 1, 2,3, 7,8 =  31. { } { } { } 1,3,5, 7 2, 4, 6,8,10 1, 2,3, 4,5, 6, 7,8,10 =  32. { } { } { } 0,1,3,5 2, 4, 6 0,1, 2,3, 4,5, 6 =  33. { } { } , , , , , , , , a e i o u a e i o u ∅ =  34. { } { } , , , , , , , , e m p t y e m p t y ∅ =  35. a. 100 b. 0, 100 c. 9, 0, 100 − d. 4 9, , 0, 0.25, 9.2, 100 5 − − e. 3 f. 4 9, , 0, 0.25, 3,9.2, 100 5 − − 36. a. 49 b. 0, 49 c. 7, 0, 49 − d. 7, 0.6, 0, 49 − − e. 50 f. 7, 0.6, 0, 49, 50 − − 37. a. 64 b. 0, 64 c. 11, 0, 64 − d. 5 11, , 0, 0.75, 64 6 − − e. 5, π f. 5 11, , 0, 0.75, 5, , 64 6 π − − 38. a. 4 b. 0, 4 c. 5, 0, 4 − d. 5, 0.3, 0, 4 − − e. 2 f. 5, 0.3, 0, 2, 4 − − 39. 0 40. Answers will vary. An example is 1 . 2 41. Answers will vary. An example is 2. 42. Answers will vary. An example is 2. − 43. true; –13 is to the left of –2 on the number line. 44. false; –6 is to the left of 2 on the number line. 45. true; 4 is to the right of –7 on the number line.

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    Chapter P Prerequisites: Fundamental Concepts of Algebra 4 46. true; –13 is to the left of –5 on the number line. 47. true; −π = −π 48. true; –3 is to the right of –13 on the number line. 49. true; 0 is to the right of –6 on the number line. 50. true; 0 is to the right of –13 on the number line. 51. 300 300 = 52. 203 203 − = 53. 12 12 − π = − π 54. 7 7 − π = − π 55. 2 5 5 2 − = − 56. 5 13 13 5 − = − 57. 3 3 1 3 3 − − = = − − 58. 7 7 1 7 7 − − = = − − 59. 3 7 3 7 4 4 − − − = − = − = 60. 5 13 5 13 8 8 − − − = − = − = 61. 2 ( 5) 3 3 x y + = + − = − = 62. 2 ( 5) 7 7 x y − = − − = = 63. 2 5 2 5 7 x y + = + − = + = 64. 2 5 2 5 3 x y − = − − = − = − 65. 5 5 1 5 5 y y − − = = = − − 66. 2 5 2 5 1 ( 1) 0 2 5 2 5 x y x y − + = + = + = + − = − − 67. The distance is 2 17 15 15 − = − = . 68. The distance is 4 15 11 11 − = − = . 69. The distance is 2 5 7 7 − − = − = . 70. The distance is 6 8 14 14 − − = − = . 71. The distance is 19 ( 4) 19 4 15 15 − − − = − + = − = . 72. The distance is 26 ( 3) 26 3 23 23 − − − = − + = − = . 73. The distance is 3.6 ( 1.4) 3.6 1.4 2.2 2.2 − − − = − + = − = . 74. The distance is 5.4 ( 1.2) 5.4 1.2 4.2 4.2 − − − = − + = − = . 75. 6 + (–4) = (–4) + 6; commutative property of addition 76. 11 (7 4) 11 7 11 4; ⋅ + = ⋅ + ⋅ distributive property of multiplication over addition 77. 6 + (2 + 7) = (6 + 2) + 7; associative property of addition 78. 6 (2 3) 6 (3 2); ⋅ ⋅ = ⋅ ⋅ commutative property of multiplication 79. (2 + 3) + (4 + 5) = (4 + 5) + (2 + 3); commutative property of addition 80. 7 (11 8) (11 8) 7; ⋅ ⋅ = ⋅ ⋅ commutative property of multiplication 81. 2 (–8 + 6) = –16 + 12; distributive property of multiplication over addition 82. 8(3 11) 24 ( 88) − + = − + − ; distributive property of multiplication over addition 83. ( ) 1 3 1; 3 3 x x x + = ≠ − + , inverse property of multiplication 84. ( ) ( ) 4 4 0; x x   + + − + =   inverse property of addition 85. 5(3 4) 4 5 3 5 4 4 15 20 4 15 16 x x x x + − = ⋅ + ⋅ − = + − = +

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    Section P.1 Algebraic Expressions, Mathematical Models, and Real Numbers 5 86. 2(5 4) 3 2 5 2 4 3 10 8 3 10 5 x x x x + − = ⋅ + ⋅ − = + − = + 87. 5(3 2) 12 5 3 5 2 12 15 10 12 27 10 x x x x x x x − + = ⋅ − ⋅ + = − + = − 88. 2(5 1) 14 2 5 2 1 14 10 2 14 24 2 x x x x x x x − + = ⋅ − ⋅ + = − + = − 89. 7(3 5) 2(4 3) 7 3 7 5 2 4 2 3 21 35 8 6 29 29 y y y y y y y − + + = ⋅ − ⋅ + ⋅ + ⋅ = − + + = − 90. 4(2 6) 3(5 10) 4 2 4 6 3 5 3 10 8 24 15 30 23 6 y y y y y y y − + + = ⋅ − ⋅ + ⋅ + ⋅ = − + + = + 91. ( ) ( ) 5 3 2 7 2 15 10 7 2 8 12 y y y y y − − + = − − − = − 92. 4(5 3) (6 3) 20 12 6 3 14 15 y y y y y − − + = − − − = − 93. ( ) [ ] 7 4 3 4 5 7 4 3 4 5 y y   − − − = − − +   [ ] 7 4 8 4 7 32 16 16 25 y y y = − − = − + = − 94. [ ] [ ] 6 5[8 (2 4)] 6 5 8 2 4 6 5 12 2 6 60 10 10 54 y y y y y − − − = − − + = − − = − + = − 95. ( ) ( ) 2 2 2 2 2 2 2 2 2 2 2 2 18 4 6 2 5 18 4 6 12 5 18 4 6 7 18 4 6 7 18 6 4 7 18 6 11 12 11 x x x x x x x x x x x x   + − − +     = + − − +     = + − −   = + − + = − + + = − + = + 96. ( ) ( ) 2 2 2 2 2 2 2 2 2 2 2 2 14 5 7 2 4 14 5 7 14 4 14 5 7 10 14 5 7 10 14 7 5 10 14 7 15 7 15 x x x x x x x x x x x x   + − − +     = + − − +     = + − −   = + − + = − + + = − + = + 97. –(–14 x ) = 14 x 98. ( ) 17 17 y y − − = 99. –(2 x – 3 y – 6) = –2 x + 3 y + 6 100. ( ) 5 13 1 5 13 1 x y x y − − − = − + + 101. [ ] 1 (3 ) (4 ) ( 4 ) 0 3 x y y x x + + − = + = 102. ( ) ( ) 1 2 7 7 0 2 y x x y y   + − + = + =   103. 6 3 6 3 6 3 − − > Since 6 3, 6 3 . > − > − 104. 20 50 20 50 20 50 − − < Since 20 50, 20 50 . < − < − 105. 3 0.6 5 0.6 0.6 0.6 0.6 0.6 0.6 − − = Since 3 0.6 0.6, 0.6 . 5 = = −

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    Chapter P Prerequisites: Fundamental Concepts of Algebra 6 106. 5 2.5 2 2.5 2.5 .5 2.5 2.5 2.5 2 − − = Since 5 2.5 2.5, 2.5 . 2 = = − 107. 30 3 14 15 40 4 15 14 30 30 14 40 40 − ⋅ − 15 15 ⋅ 14 0 1 0 1 < Since 30 3 14 15 0 1, 40 4 15 14 < − < ⋅ . 108. 17 18 50 5 18 17 60 6 17 ⋅ − 18 18 ⋅ 17 50 50 60 60 1 0 1 0 − > Since 17 18 50 5 1 0, > 18 17 60 6 > ⋅ − . 109. 8 8 1 13 13 8 13 1 13 8 1 1 1 1 ÷ − ⋅ = Since 8 8 1 1, = 1 . 13 13 = ÷ − 110. 4 4 2 17 17 4 17 2 17 4 2 1 2 1 − ÷ ⋅ > Since 4 4 2 1, 2 > . 17 17 > − ÷ 111. 2 2 8 16 2 4 3 64 16 4 4 3 64 4 4 3 64 16 3 48 3 45 − ÷ ⋅ − = − ÷ ⋅ − = − ⋅ − = − − = − = 112. 2 2 10 100 5 2 3 100 100 25 2 3 100 4 2 3 100 8 3 92 3 89 − ÷ ⋅ − = − ÷ ⋅ − = − ⋅ − = − − = − = 113. 2 2 2 2 2 2 5 2 3 5 2 9 [3 ( 2)] [9 ( 2)] 10 9 [9 2] 10 9 11 1 121 ⋅ − ⋅ − = − − − − − = + − = = 114. 2 2 2 10 2 3 4 5 12 (12 3 2) (12 6) 17 6 17 36 ÷ + ⋅ + = − ⋅ − = = 115. 8 3[ 2(2 5) 4(8 6)] 8 3[ 2( 3) 4(2)] 8 3[6 8] 8 3[ 2] 8 6 14 − − − − − = − − − − = − − = − − = + = 116. 8 3[ 2(5 7) 5(4 2)] 8 3[ 2( 2) 5(2)] 8 3[4 10] 8 3[ 6] 8 18 26 − − − − − = − − − − = − − = − − = + = 117. 2( 2) 4( 3) 4 12 5 8 3 8 3 8 3 − − − − + = − − = − = −

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    Section P.1 Algebraic Expressions, Mathematical Models, and Real Numbers 7 118. 6( 4) 5( 3) 24 15 9 10 1 9 1 9 − − − − + = − − − = − = 119. 2 2 2 (5 6) 2 3 7 ( 1) 2 4 89 3 25 89 3 5 1 2(4) 89 75 1 8 14 7 14 1 2 − − − − − − = − ⋅ − ⋅ − = − − = − = = − 120. 2 2 2 12 3 5 2 3 12 3 5 4 9 7 3 36 7 3 6 4 5 13 10 36 20(13) 26 260 26 10 ÷ ⋅ + ÷ ⋅ + = + − + − ⋅ = − = − = − = − 121. ( ) 4 4 4 x x x x − + = − − = − 122. ( ) 8 8 2 8 x x x x x − − = − + = − 123. ( ) 6 5 30 x x − = − 124. ( ) 10 4 40 x x − = − 125. 5 2 3 x x x − = 126. ( ) 6 2 6 2 8 x x x x x − − = + = 127. ( ) 8 3 6 8 3 6 5 6 x x x x x − + = − − = − 128. ( ) 8 3 6 8 3 18 3 10 x x x − + = − − = − − 129. a. ( ) ( ) ( ) 7 220 10 7 220 20 10 7 200 10 140 H a H = − = − = = The lower limit of the heart rate for a 20-year- old with this exercise goal is 140 beats per minute. b. ( ) ( ) ( ) 4 220 5 4 220 20 5 4 200 5 160 H a H = − = − = = The upper limit of the heart rate for a 20-year- old with this exercise goal is 160 beats per minute. 130. a. ( ) ( ) ( ) 1 220 2 1 220 30 2 1 190 2 95 H a H = − = − = = The lower limit of the heart rate for a 30-year- old with this exercise goal is 95 beats per minute. b. ( ) ( ) ( ) 3 220 5 3 220 30 5 3 190 5 114 H a H = − = − = = The upper limit of the heart rate for a 30-year- old with this exercise goal is 114 beats per minute. 131. a. 2 2 21 862 15,552 21(14) 862(14) 15,552 31, 736 T x x = + + = + + = The formula estimates the cost to have been $31,736 in 2014.

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    Chapter P Prerequisites: Fundamental Concepts of Algebra 8 b. This overestimates the value in the graph by $35. c. 2 2 21 862 15,552 21(20) 862(20) 15,552 41,192 T x x = + + = + + = The formula projects the cost to be $41,192 in 2020. 132. a. 2 2 21 862 15,552 21(12) 862(12) 15,552 28,920 T x x = + + = + + = The formula estimates the cost to have been $28,920 in 2012. b. This underestimates the value in the graph by $136. c. 2 2 21 862 15,552 21(22) 862(22) 15,552 44, 680 T x x = + + = + + = The formula projects the cost to be $44,680 in 2022. 133. a. ( ) 0.05 0.12 10,000 0.05 1200 0.12 1200 0.07 x x x x x + − = + − = − b. 1200 0.07 1200 0.07(6000) $780 x − = − = 134. a. 0.06 0.5(50 ) 0.06 25 0.5 25 0.44 t t t t t + − = + − = − b. 0.06(20) 0.5(50 20) 1.2 0.5(30) 1.2 15 16.2 miles + − = + = + = 135. – 143. Answers will vary. 144. does not make sense; Explanations will vary. Sample explanation: Models do not always accurately predict future values. 145. does not make sense; Explanations will vary. Sample explanation: To use the model, substitute 0 for x . 146. makes sense 147. does not make sense; Explanations will vary. Sample explanation: The commutative property changes order and the associative property changes groupings. 148. false; Changes to make the statement true will vary. A sample change is: Some rational numbers are not integers. 149. false; Changes to make the statement true will vary. A sample change is: All whole numbers are integers. 150. true 151. false; Changes to make the statement true will vary. A sample change is: Some irrational numbers are negative. 152. false; Changes to make the statement true will vary. A sample change is: The term x has a coefficient of 1. 153. false; Changes to make the statement true will vary. A sample change is: 5 3( 4) 5 3 12 3 7. x x x + − = + − = − 154. false; Changes to make the statement true will vary. A sample change is: 2 . x x x − − = − 155. true 156. 2 1.4 1.4 1.5 2 1.5 ≈ < < 157. 3.5 π − > − 158. 3.14 1.57 2 1.571 2 1.57 1.571 3.14 2 2 − = − π − ≈ − − > − π − > − 159. a. 4 3 7 ( )( ) b b b b b b b b b b ⋅ = ⋅ ⋅ ⋅ ⋅ ⋅ = b. 5 5 10 ( )( ) b b b b b b b b b b b b b ⋅ = ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ = c. add the exponents

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    Section P.2 Exponents and Scientific Notation 9 160. a. 7 4 3 b b b b b b b b b b b b b ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ = = ⋅ ⋅ b. 8 6 2 b b b b b b b b b b b b b ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ = = ⋅ c. subtract the exponents 161. 3 6.2 10 6.2 10 10 10 6200 × = × × × = It moves the decimal point 3 places to the right. Section P.2 Check Point Exercises 1. a. 3 2 3 2 5 3 3 3 3 or 243 + ⋅ = = b. ( )( ) 3 4 2 6 3 2 4 6 4 10 4 10 x y x y x x y y = ⋅ ⋅ ⋅ ⋅ ⋅ 3 2 4 6 5 10 40 40 x y x y + + = ⋅ = 2. a. 6 3 3 ( 3) ( 3) 27 ( 3) − = − = − − b. 14 8 14 8 14 3 8 5 11 3 3 5 3 5 27 27 9 9 3 3 x y x y x y x y x y x y − − = ⋅ ⋅ = = 3. a. 2 2 1 1 5 25 5 − = = b. 3 3 1 1 1 ( 3) 27 27 ( 3) − − = = = − − − c. 2 2 2 2 1 1 4 1 4 16 1 1 4 4 − = = ⋅ = = d. 4 6 4 4 6 6 1 3 3 3 y x y y x x − = ⋅ ⋅ = 4. a. ( ) 2 3 3 2 6 3 3 3 or 729 ⋅ = = b. ( ) 2 7 7( 2) 14 14 1 y y y y − − − = = = c. ( ) 4 3 3( 4) 12 b b b − − − − = = 5. 3 3 3 3 ( 4 ) ( 4) ( ) 64 x x x − = − = − 6. a. ( ) 5 5 5 5 2 2 32 y y y −   − − = =     b. ( ) 3 3 5 5 15 3 3 27 3 x x x   = =       7. a. ( ) ( ) ( ) ( ) 4 4 4 4 3 6 3 6 12 24 2 2 16 x y x y x y = = b. ( )( ) ( ) 2 5 3 2 5 3 3 8 6 3 6 3 18 x y xy x x y y x y − = − ⋅ ⋅ ⋅ ⋅ ⋅ = − c. 12 2 12 2 16 4 16 4 100 100 20 20 x y x y x y x y − −       =               12 16 2 ( 4) 4 6 6 4 5 5 5 x y x y y x − − − − = = = d. ( ) ( ) ( ) 2 2 2 4 2 4 5 5 x x y y − − − −   =       ( ) ( ) ( ) 2 2 2 4 2 2 8 8 2 2 8 2 5 5 5 25 x y x y y x y x − − − − − − = = = = 8. a. 9 2.6 10 2, 600, 000, 000 − × = − b. 6 3.017 10 0.000003017 − × = 9. a. 9 5, 210, 000, 000 5.21 10 = × b. 8 0.00000006893 6.893 10 − − = − ×

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    Chapter P Prerequisites: Fundamental Concepts of Algebra 10 10. ( ) 7 2 7 410 10 4.1 10 10 × = × × ( ) 2 7 9 4.1 10 10 4.1 10 = × × = × 11 a. ( )( ) 5 7 7.1 10 5 10 − × × ( ) ( ) 5 7 2 1 2 1 2 1 7.1 5 10 10 35.5 10 3.55 10 10 3.55 10 10 3.55 10 − − − − − = ⋅ × ⋅ = × = × × = × × = × b. 6 6 3 3 1.2 10 1.2 10 3 3 10 10 − − × = ⋅ × 6 ( 3) 9 8 0.4 10 0.4 10 4 10 − − = × = × = × 12. 10 10 10 5 5 5 4.08 10 4.08 10 4.08 10 680, 000 6.8 6.8 10 10 0.6 10 60, 000 × × = = ⋅ × = × = The average salary was $60,000 per U.S. police officer. Concept and Vocabulary Check P.2 1. m n b + ; add 2. m n b − ; subtract 3. 1 4. 1 n b 5. false 6. n b 7. true 8. a number greater than or equal to 1 and less than 10; integer 9. true 10. false Exercise Set P.2 1. 2 5 2 (5 5) 2 25 2 50 ⋅ = ⋅ ⋅ = ⋅ = 2. 2 6 2 (6 6) 2 36 2 72 ⋅ = ⋅ ⋅ = ⋅ = 3. 6 ( 2) ( 2)( 2)( 2)( 2)( 2)( 2) 64 − = − − − − − − = 4. 4 ( 2) ( 2)( 2)( 2)( 2) 16 − = − − − − = 5. 6 2 2 2 2 2 2 2 64 − = − ⋅ ⋅ ⋅ ⋅ ⋅ = − 6. 4 2 2 2 2 2 16 − = − ⋅ ⋅ ⋅ = − 7. 0 ( 3) 1 − = 8. 0 ( 9) 1 − = 9. 0 3 1 − = − 10. 0 9 1 − = − 11. 3 3 1 1 1 4 4 4 4 64 4 − = = = ⋅ ⋅ 12. 6 6 1 1 1 2 2 2 2 2 2 2 64 2 − = = = ⋅ ⋅ ⋅ ⋅ ⋅ 13. 2 3 2 3 5 2 2 2 2 2 2 2 2 2 32 + ⋅ = = = ⋅ ⋅ ⋅ ⋅ = 14. 3 2 3 2 5 3 3 3 3 3 3 3 3 3 243 + ⋅ = = = ⋅ ⋅ ⋅ ⋅ = 15. 2 3 2 3 6 (2 ) 2 2 2 2 2 2 2 2 64 ⋅ = = = ⋅ ⋅ ⋅ ⋅ ⋅ = 16. 3 2 3 2 6 (3 ) 3 3 3 3 3 3 3 3 729 ⋅ = = = ⋅ ⋅ ⋅ ⋅ ⋅ = 17. 8 8 4 4 4 2 2 2 2 2 2 2 16 2 − = = = ⋅ ⋅ ⋅ = 18. 8 8 4 4 4 3 3 3 3 3 3 3 81 3 − = = = ⋅ ⋅ ⋅ = 19. 3 3 1 2 2 1 1 1 3 3 3 3 3 3 9 3 − − + − ⋅ = = = = = ⋅ 20. 3 3 1 2 2 1 1 1 2 2 2 2 2 2 4 2 − − + − ⋅ = = = = = ⋅ 21. 3 3 7 4 7 4 2 1 1 1 2 2 2 2 2 2 16 2 2 − − = = = = = ⋅ ⋅ ⋅

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    Section P.2 Exponents and Scientific Notation 11 22. 4 4 7 3 7 3 3 1 1 1 3 3 3 3 3 27 3 3 − − = = = = = ⋅ ⋅ 23. 2 2 2 1 y x y y x x − = ⋅ = 24. 3 3 3 1 x xy x y y − = ⋅ = 25. 0 5 5 5 1 x y y y = ⋅ = 26. 7 0 7 7 1 x y x x ⋅ = ⋅ = 27. 3 7 3 7 10 x x x x + ⋅ = = 28. 11 5 11 5 16 x x x x + ⋅ = = 29. 5 10 5 10 5 x x x x − − + ⋅ = = 30. 6 12 6 12 6 x x x x − − + ⋅ = = 31. 3 7 3 7 21 ( ) x x x ⋅ = = 32. 11 5 11 5 55 ( ) x x x ⋅ = = 33. 5 3 5 3 15 15 1 ( ) x x x x − − ⋅ − = = = 34. 6 4 6 4 24 24 1 ( ) x x x x − − ⋅ − = = = 35. 14 14 7 7 7 x x x x − = = 36. 30 30 10 20 10 x x x x − = = 37. 14 14 ( 7) 14 7 21 7 x x x x x − − + − = = = 38. 30 30 ( 10) 30 10 40 10 x x x x x − − + − = = = 39. 3 2 2 3 2 2 3 2 6 (8 ) 8 ( ) 8 64 x x x x ⋅ = = = 40. 4 2 2 4 2 2 4 2 8 (6 ) (6) ( ) 6 36 x x x x ⋅ = = = 41. 3 3 3 3 4 ( 4) 64 x x x −   − = = −     42. 3 3 3 3 6 ( 6) 216 y y y   − − = = −     43. 2 5 2 2 2 2 5 2 2 2 5 2 4 10 ( 3 ) ( 3) ( ) ( ) 9 9 x y x y x y x y ⋅ ⋅ − = − ⋅ = = 44. 4 6 3 3 4 3 6 3 4 3 6 3 12 18 ( 3 ) ( 3) ( ) ( ) 27 27 x y x y x y x y ⋅ ⋅ − = − = − = − 45. 4 7 4 7 4 7 11 (3 )(2 ) 3 2 6 6 x x x x x x + = ⋅ ⋅ = = 46. 5 12 5 12 5 12 17 (11 )(9 ) 11 9 99 99 x x x x x x + = ⋅ = = 47. 3 6 4 3 6 4 3 6 1 4 9 5 ( 9 )( 2 ) ( 9)( 2) 18 18 x y x y x x yy x y x y + + − − = − − = = 48. 4 7 11 4 7 11 4 7 1 11 11 12 ( 5 )( 6 ) ( 5)( 6) 30 30 x y x y x x yy x y x y + + − − = − − = = 49. 20 20 20 4 16 4 4 8 8 4 4 2 2 x x x x x x −     = = =           50. 24 24 24 6 18 6 6 20 20 2 2 10 10 x x x x x x −     = = =         51. 13 4 13 4 2 3 2 3 13 2 4 3 11 25 25 5 5 5 5 a b a b a b a b a b a b − −    ⋅   =        − − ⋅     = − = − 52. 14 6 14 6 7 3 7 3 14 7 6 3 7 3 35 35 7 7 5 5 a b a b a b a b a b a b − −      =        − −     = − = − 53. 7 7 7 14 7 14 14 7 14 14 2 2 2 7 7 b b b b b b b − −     = = ⋅ = =        

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    Chapter P Prerequisites: Fundamental Concepts of Algebra 12 54. 10 10 20 20 10 20 10 10 20 20 10 10 2 2 2 b b b b b b b − −     =         = = = 55. 3 2 2 3 2 2 6 2 6 6 (4 ) (4 )( ) 4 1 4 1 16 x x x x x − − − − − = = = = 56. 2 3 3 2 ( 3) 3 6 3 6 6 (10 ) 10 10 1 10 1 1000 x x x x x − − ⋅ − − − = = = = 57. 3 5 3 7 5 ( 9) 7 9 4 14 14 4 24 3 4 32 3 4 3 4 x y x y x y x y y x − − − − − ⋅ = = = 58. 4 9 4 12 9 ( 3) 12 3 8 12 12 8 10 1 3 30 1 3 3 x y x y x y x y y x − − − − − = = = 59. 2 3 2 6 2 6 5 5 2 25 x x y y x y − − −   = =     −   60. 3 3 4 4 3 3 4 3 3 12 3 3 3 27 x y y x y x y x − ⋅     =           = = 61. ( ) 3 3 2 3 4 2 10 3 10 4 3 5 6 15 18 15 3 5 3 27 a b b a b a b a b a − − − −     − −   =             − =       − = 62. ( ) 3 3 8 2 14 8 17 2 17 14 3 10 30 9 30 3 10 3 3 27 a b b a b a b a b a − − − −     − −   =             − =       − = 63. 0 5 2 3 4 3 1 12 a b a b − −   =       64. 0 5 3 3 5 4 1 12 a b a b − −   =       65. 2 3.8 10 380 × = 66. 2 9.2 10 920 × = 67. 4 6 10 0.0006 − × = 68. 5 7 10 0.00007 − × = 69. 6 7.16 10 7,160, 000 − × = − 70. 6 8.17 10 8,170, 000 − × = − 71. 1 7.9 10 0.79 − × = 72. 1 6.8 10 0.68 − × =

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