AN102 Answers: Appendix APPENDIX Review A.1 Assess Your Understanding (page A10) 1. variable 2. origin 3. strict 4. base; exponent or power 5. d 6. b 7. a 8. T 9. F 10. T 11. { } 1, 2, 3, 4, 5, 6, 7, 8, 9 13. { }4 15. { } 1, 3, 4, 6 17. { } 0, 2, 6, 7, 8 19. { } 0, 1, 2, 3, 5, 6, 7, 8, 9 21. { } 0, 1, 2, 3, 5, 6, 7, 8, 9 23. 0.25 1 3 4 5 2 22.5 21 0 25. > 27. > 29. > 31. = 33. < 35. > x 0 37. < x 2 39. ≤ x 1 41. 22 43. 21 45. 1 47. 2 49. 6 51. 4 53. −28 55. 4 5 57. 0 59. 1 61. 5 63. 1 65. 22 67. 2 69. = x 0 71. = x 3 73. None 75. = = = − x x x 0, 1, 1 77. { } ≠ x x 5 79. { } ≠ − x x 4 81. °0 C 83. ° 25 C 85. 16 87. 1 16 89. 1 9 91. 9 93. 5 95. 4 97. x 64 6 99. x y 4 2 101. x y 103. − x z y 8 9 3 105. x y 16 9 2 2 107. −4 109. 5 111. 4 113. 2 115. 5 117. 1 2 119. 10; 0 121. 81 123. 304,006.671 125. 0.004 127. 481.890 129. 0.000 131. = A lw 133. π = C d 135. = A x 3 4 2 137. π = V r 4 3 3 139. = V x3 141. (a) $6000 (b) $8000 143. − ≥ x 4 6 145. (a) ≤ 2 5 (b) > 6 5 147. (a) Yes (b) No 149. No; 1 3 is larger; 0.000333 . . . 151. No A.2 Assess Your Understanding (page A19) 1. right; hypotenuse 2. = A bh 1 2 3. π = C r 2 4. similar 5. c 6. b 7. T 8. T 9. F 10. T 11. T 12. F 13. 13 15. 26 17. 25 19. Right triangle; 5 21. Not a right triangle 23. Right triangle; 25 25. Not a right triangle 27. 42 in.2 29. 28 in.2 31. π π = = A C 25 m; 10 m 2 33. = = V S 240 ft ; 236 ft 3 2 35. π π = = V S 500 3 cm ; 100 cm 3 2 37. π π = = V S 648 in.; 306 in. 3 2 39. π square units 41. π2 square units 43. = = ° = ° = ° x A B C 4 units; 90 ; 60 ; 30 45. = = ° = ° = ° x A B C 67.5 units; 60 ; 95 ; 25 47. About 16.8 ft 49. 64 ft2 51. π π + ≈ + ≈ 24 2 30.28 ft ; 16 2 22.28 ft 2 53. 160 paces 55. About 5.477 mi 57. From 100 ft: 12.2 mi; From 150 ft: 15.0 mi 59. No. The area quadruples. A.3 Assess Your Understanding (page A30) 1. 4; 3 2. − x 16 4 3. − x 8 3 4. F 5. F 6. T 7. F 8. add; 25 4 9. quotient; divisor; remainder 10. a 11. c 12. b 13. d 14. c 15. Monomial; variable: x; coefficient: 2; degree: 3 17. Not a monomial; the exponent of the variable is not a nonnegative integer 19. Not a monomial; it has more than one term 21. Not a monomial; the exponent of one of the variables is not a nonnegative integer 23. Not a monomial; it has more than one term 25. Yes; 2 27. Yes; 0 29. No; the exponent of one of the variables is not a nonnegative integer 31. Yes; 3 33. No; the polynomial of the denominator has a degree greater than 0 35. + + x x7 2 2 37. − + + x x x 4 9 7 3 2 39. − + − x x 2 18 18 3 2 41. − + y y 15 27 30 2 43. + − x x x4 3 2 45. + + x x6 8 2 47. + + x x 2 9 10 2 49. − x 49 2 51. − x4 9 2 53. + + x x8 16 2 55. − + x x 4 12 9 2 57. − + − x x x 6 12 8 3 2 59. + + + x x x 8 12 6 1 3 2 61. − + x x 4 11 23; 2 remainder −45 63. −x4 3; remainder +x 1 65. − x5 13; 2 remainder +x 27 67. x2 ;2 remainder − + + x x 1 2 69. − + x x2 1 2 ; 2 remainder +x 5 2 1 2 71. − − − x x 4 3 3; 2 remainder −7 73. − − x x 1; 2 remainder +x2 2 75. + + x ax a ; 2 2 remainder 0 77. ( )( ) + − x x 6 6 79. ( )( ) + − x x 2 1 2 1 2 81. ( )( ) + + x x 1 10 83. ( )( ) − − x x 7 3 85. ( ) − + x x 4 2 8 2 87. Prime 89. ( )( ) − − + x x 5 3 91. ( )( ) + − x x 3 2 6 93. ( )( ) + + y y y 5 6 2 95. ( ) +x2 3 2 97. ( )( ) + + x x 2 3 1 1 99. ( ) ( )( ) − + + x x x 3 3 9 2 101. ( ) ( ) − + + x x x 1 1 2 2 2 103. ( )( ) − + x x x 1 1 5 105. ( ) +x4 3 2 107. ( )( ) − − + x x 4 5 4 1 109. ( )( ) − − y y 2 5 2 3 111. ( ) ( )( ) − − + + x x x 3 1 3 1 1 2 113. ( )( ) + − x x 3 6 115. ( )( ) + − x x 2 3 117. ( ) ( ) − − + x x x 3 5 9 3 7 2 119. ( )( ) + + x x 5 3 11 121. ( )( )( ) − + + x x x 1 1 2 123. ( ) ( )( ) − + − + x x x x 1 1 1 2 125. 25; ( ) +x 5 2 127. ( ) −y 9; 3 2 129. ( ) −x 1 16 ; 1 4 2 131. ( )( ) + + x x 2 3 4 9 13 133. ( ) + x x 2 3 5 135. ( )( ) ( ) + − + x x x 5 3 2 1 2 137. ( )( ) − − x x 3 4 3 4 1 139. ( )( ) ( ) − + − x x x 6 3 5 2 1 5 4 2 141. ( ) + −x x 1 4 2 143. ( ) ( ) ( ) [ ] + + − = + − − x x x x x x 1 1 1 2 2 2 145. The possibilities are ( )( ) ± ± = ± + x x x x 1 4 5 4 2 or ( )( ) ± ± = ± + x x x x 2 2 4 4, 2 none of which equals + x 4. 2 A.4 Assess Your Understanding (page A34) 1. quotient; divisor; remainder 2. ) − − 3 2 0 5 1 3. d 4. a 5. T 6. T 7. − − x x5 5 2 ; remainder 0 9. + + x x 3 11 32; 2 remainder 99 11. − + − + x x x x 3 5 15 46; 4 3 2 remainder −138 13. + + + + + x x x x x 4 4 2 2; 5 4 3 2 remainder 7 15. − + x x 0.1 0.11 0.321; 2 remainder −0.3531 17. + + + + x x x x 2 4 8 16; 4 3 2 remainder 0 19. No 21. Yes 23. Yes 25. No 27. Yes 29. −9 A.5 Assess Your Understanding (page A42) 1. lowest terms 2. least common multiple 3. T 4. F 5. d 6. a 7. −x 3 3 9. x 3 11. − x x 4 2 1 13. ( ) + + y y 5 2 1 15. ( ) − x x 3 5 2 17. ( ) + + + x x x x 2 4 16 4 2 19. ( ) −x 4 5 1 21. ( ) − −x x 4 4 2 23. ( )( ) − + − x x x 2 2 2 3 25. ( ) ( )( ) − − + x x x x 2 2 2 2 2 27. ( )( )( ) − − + x x x x 5 6 1 4 29. ( ) ( )( )( ) + − − + + x x x x x 2 2 5 2 2 2 3 2 31. ( ) ( ) + − + x x x 5 1 1 1 2 2 33. + − x x 1 1 35. ( ) ( ) ( ) − − + − − x x x x x 2 2 2 3 2 2 37. ( ) −x 19 3 5 2 39. ( ) ( )( ) + − + x x x 1 1 1 2 2 41. ( ) ( ) + + x x x 3 2 3 1 2 43. ( ) ( )( ) − + − + x x x 33 1 1 2 2 45. ( ) ( ) = ⋅ − + f R R n R R 1 ; 2 15 m 1 2 1 2 A.6 Assess Your Understanding (page A55) 5. equvalent equations 6. identity 7. F 8. T 9. add; 81 4 10. discriminant; negative 11. F 12. F 13. b 14. d 15. 7{ } 17. 3 { } − 19. 4{ } 21. 5 4{ } 23. 1 { } − 25. 18 { } − 27. 3 { } − 29. 16 { } − 31. 0.5 { } 33. 2{ } 35. 2{ } 37. 3{ } 39. 0, 9 { } 41. 0, 9 { }
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