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R22 Respuestas sumar y restar. d) 5. Figuras semejantes son figuras cuyos ángulos correspondientes son iguales y cuyos lados correspondientes están en la misma proporción. 7. No, x � 3 hace que esté indefinida. 9. 5 11. 13. 3 15. 17. Todos los números reales 19. 21. 23. No hay solución 25. 27. 29. 8 31. 1 33. 3.76 35. 37. 39. 41. 5 43. No hay solución 45. 47. 49. 12, 2 51. 12, 4 53. 55. 57. 59. 61. 63. 65. 67. 69. 71. 73. 75. 77. 79. 81. a) b) 83. a) b) No hay solución 85. c Z 0, no puede dividirse entre 0. 87. f(x): gráfica b); g(x): gráfica a); f(x) está indefinida cuando x � 3 89. a) $ 6250 b) 91. a) 20 pies/min2 b) 93. a) b) c) 95. 150 ohms 97. L0.101 metros 99. a) b) Ya que 9.71% � 7.68%, debe invertir en el portafolio del mercado de dinero que está libre de impuestos. 101. Una respuesta es 4 y �2 hacen que la fracción esté indefinida. 103. Una respuesta es 105. 106. intercepción con el eje y, 107. 108. 2 pies Examen de mitad de capítulo 1. [6.1] 2. [6.1] 3. [6.1] 4. [6.1] 5. o [6.1] 6. [6.1] 7. [6.2] 8. 5 [6.2] 9. [6.2] 10. [6.2] 11. [6.3] 12. [6.3] 13. [6.3] 14. Una raíz extraña es un número que se obtiene al resolver una ecuación, pero que no es solución de la ecuación original. Siempre que una variable aparezca en el denominador, debe verificar la aparente solución. [6.4] 15. 5. [6.4] 16. No hay solución [6.4] 17. [6.4] 18. [6.4] 19. [6.4] 20. 14 y 5 [6.4] Conjunto de ejercicios 6.5 1. Igual a ya que les toma exactamente el mismo tiempo a cada uno de ellos. 3. a) Velocidad de Tiempo Parte del trabajo Trabajador trabajo completado realizado Bill x Bob x x 9 1 9 x 7 1 7 1 2 r = x - 4 x a = bc b + c 4, -3 y25x - 8 6x2 - x 9b + a 3 - c -2x - 7 1x - 421x + 4212x - 32 20y2 + ax 6x2 y3 1x + 521x - 621x + 224a + 3b 6 4a2 + 8a + 3 2a2 - 19a + 9 12a + 1212a + 32 12a - 121a - 92 x - 3 x + 1 55b a2 - ab + b2 x + 5 2x - 3 {x ƒx Z 0, x Z -5 y x Z 5} 3x2 y - 7xy - 4y2 - 9xa0, 14 3 b . m = - 1 3 ;-1 6 x … 3 1 x + 1 x = 2 x . 1 x - 4 + 1 x + 2 = 0; L9.71%R = D P D = PRL22.5%t1 = t2 + v1 - v2 a R = AC 0.80I 4 b + 5 - 9 2 2x + 9 1x - 221x + 22V0 = S - S0 - gt2 t T1 = T2 P1 V1 P2 V2 G = Fd2 m1m2 d = an - a1 n - 1 a = v2 - v1 t2 - t1 q = pf p - f w = fl - df d x = zs + x y = y1 + m1x - x12V2 = V1 P1 P2 P2 = V1 P1 V2 3 2 25 2 1, -2 17 4 -5 - 5 2 -5-1, -6- 4 3 ,L -1.63 6 5 11 3 1 4 -5 11 2 7 x - 3 -x + 24 12 b) c) Menos; debe tomar menos tiempo que a la persona más rápida ya que están trabajando juntas. 5. 1.5 meses 7. 2 horas 9. 18.75 minutos 11. 4 horas 13. L2.48 días 15. 2.4 horas 17. L3.08 horas 19. 100 horas 21. 7.8 meses 23. 75 minutos 25. L15.27 minutos 27. L1.62 horas 29. 12 horas 31. 5 33. 2.4 35. 4, 6 x 7 + x 9 = 1 37. 20 39. 41. L0.064 millas por hora 43. L1.53 pies por segundo 45. 7.5 millas 47. 36 millas por hora 49. L30.59 yardas 51. Local: L10.93 millas por hora, expreso: L16.13 millas por hora 53. Automóvil: 60 millas por hora, tren: 30 millas por hora 55. 60 millas por hora 57. 120 kilómetros por hora 59. 2 horas a 6 millas por hora, a 10 millas por hora 61. 18 pies por minuto 63. 108,000 millas 65. Las respuestas variarán. 67. a) 10 minutos b) 15 millas c) 165 millas por hora 68. 69. 70. $ 2500 71. 72. Conjunto de ejercicios 6.6 1. a) Conforme una cantidad aumenta la otra aumenta b), c) Las respuestas variarán. 3. Una cantidad varía conforme al producto de dos o más cantidades. 5. a) Decrease b) Disminuye b) Variación inversa; por definición de variación inversa 7. Directa 9. Inversa 11. Directa 13. Directa 15. Directa 17. Inversa 19. Directa 21. Inversa 23. Inversa 25. a) b) 72 27. a) b) 306 29. a) b) 31. a) b) 9 33. a) b) 20x = kyA = kB C 1 20 R = k W y = kRx = ky a12a2 - 521a - 12y 5 �5 5�5 x y � �x � � 2 9.26 * 109x8 72 1 2 hora 2 3 , 1 Respuestas R23 35. a) b) 20 37. a) b) 0.96 39. a) b) 25 41. a) b) 40 43. Se duplica 45. Se divide entre dos 47. Se duplica 49. No cambia 51. Se duplica 53. 55. $8814 57. 3096 miligramos 59. 1.05 pulgadas 61. 6400 centímetros cúbicos 63. 3.12 horas 65. 45 pies-bujías 67. 117.6 pies 69. 126 metros cúbicos 71. 4600 DVD 73. L133.25 libras 75. L121,528 llamadas 77. de la luz del flash 79. a) b) 0.43 c) L337.9 pies 80. 81. 132 82. 83. Ejercicios de repaso del capítulo 6 1. 5 2. 3. Ninguna 4. 5. 6. 7. x 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 1 27. 28. 29. 30. 31. 32. 33. 34. 1 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. a) b) c) d) 52. a) b) c) d) 53. 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 52 64. 2.4 65. 5 66. 67. 68. 69. 70. 71. 72. 73. 60 ohms 74. 2 centímetros 75. 10, 2 76. 21, 3 77. L17.14 minutos 78. 14 horas 79. 3 80. 81. 5 millas por hora 82. automóvil: 50 millas por hora, aeroplano: 150 millas por hora 83. 20 84. 85. 86. $8.40 87. 1600 pies 88. 200.96 unidades cuadradas 89. 2.38 minutos Examen de práctica del capítulo 6 1. y 4 [6.1] 2. [6.1] 3. [6.1] 4. [6.1] 5. [6.1] 6. [6.1] 7. [6.1] 8. [6.1] 9. [6.2] 10. [6.2] 11. [6.2] 12. [6.2] 13. [6.1] 14. a) b) [6.2] 15. [6.1] 16. [6.3] 17. [6.3] 18. [6.3] 19. 20 [6.4] 20. 12 [6.4] 21. [6.4] 22. 0.75 watt [6.6] 23. 6 [6.6] 24. L4.44 horas [6.5] 25. [6.5] Examen de repaso acumulativo 1. [1.2] 2. [1.4] 3. [2.1] 4. a) 28% b) [1.3] 5. 62 [1.4] 6. [1.5] 7. [2.2] 8. 6% [2.2] 9. 11 A.M. [2.4] 10. [2.6] 11. [3.1] 12. 5 [3.2] 13. [3.4] 14. [3.5] 15. [4.1] 16. [5.2] 17. [5.6] 18. [3.1] 19. [6.2] 20. 4 [6.4] 3x - 4 1x - 121x - 22y 5 �5 5�5 x y � �x � � 2 31x - 522 9x4 - 25y2a1 2 , 3b2x + 3y = 4- 1 7 y x 5 �5 5�5 y � x2 � 2 e - 32 3 , 22 3 fm = rF v2 x3 8y3 L44,000-3-27 3 45 3 � 19 4 6 2 3 millasC = 2b + Ad A 7x - 6 4x2 - x b1a - b2 a y + 2x y - 3x x + 5 x + 2 ex ` x Z -5 y x Z - 3 2 f 3x2 + 2x - 9 1x + 5212x + 32x + 3 x1x + 102 12x - 1221x + 32 m16m + n2 16m + 5n212m - n212m + 3n2 -3x - 1 1x - 321x + 321x + 12 5x2 + 2x + 2 x21x + 12x2 + y27 a1a + b2 1 x + 2 1 x4 y2 x - 6y x + y 5x5 y + 8 + 11xy2ex ` x Z -4 y x Z 1 2 f-7 L426.7 25 2 5 6 x = x - szb = ac a - c -10-6-28-18-9-2 18 5 o 3 3 5 x2 + 6x + 8 x + 3 x2 + 3x + 2 x + 5 3x2 - 29x + 68 4x2 - 6x - 54 3x + 1 -x + 1 5a + 1 2 3y - 1 7y2 + 1 4x + 2y x2 + xy3 3ac2 b3{x ƒx Z 3 y x Z -3} x2 + 8x + 12 1x + 321x - 32{x ƒx Z 3}{x ƒx Z 3 y x Z -3}{x ƒx Z -2 y x Z -4} 2x2 + 7x + 4 1x + 221x + 42{x ƒx Z -4}{x ƒx Z -2} x - 4 x - 6 x2 + 6x - 24 1x - 121x + 92 a + 2b2 3 x + 6 x - 4 a + 3 a + 5 - 1 x - 3 21x - 42 1x - 321x - 52 22x + 5 1x - 521x - 1021x + 52 3 a3 161x - 2y2 31x + 2y2 -x + 5 1x + 221x - 221x - 32 x + 5 x + 6 - 21x + 12 x2 - 4 x2 + 5 1x + 521x - 52 2a2 + 9a + 4 4a1a + 224x1x - 5y2x + 1 2x - 1 a2 + c2 ac 1 31a + 32 a2 - b2 a2 6b - 8 b - 1 6a + 7 a + 1 2x + 1 3x + 1 30x + 3y2 5x2 y 3x + 2 1x - y2y2 4x3 11x + 6 3x29x3 z5 - x 6 12xz21x + 2221x - 221x + 321x + 721x - 521x + 221x + 2y21x - 2y2 x1x + 422x - 3 x2 - 2x + 4 9x2 - 3xy + y2 3x - y a2 + 2ab + 4b2 a + 2b x - 3 x + 1 x - 1 x - 2 -1x - 6 {x ƒx Z 2 y x Z -6}{x ƒx Z 0}{x ƒx Z -3}-1 1x + 321x - 22-14x3 - 22x2 + 47x - 15 h = 3V 4pr2P = 14.7 + kx 1 49 y = k x ; k = 5 F = kM1 M2 d x = k P2S = k G y = kR2 R24 Respuestas Capítulo 7 Conjunto de ejercicios 7.1 1. a) Dos, positiva y negativa. b) c) Raíz cuadrada principal d) 7 3. No existe número real tal que cuando se eleva al cuadrado se obtenga �81. 5. No; si el radicando es negativo, la respuesta no es un número real. 7. a) 1.3 b) 1.3 9. a) 3 b) c) 11. 6 13. 15. 17. 19. 1 21. No es un número real 23. 25. No es un número real 27. No es un número real 29. 31. 33. 35. 37. 39. 7 41. 19 43. 119 45. 235.23 47. 0.06 49. 51. 53. 55. 57. 59. 61. 63. 65. 67. 7x 69. 71. 73. 75. 2 77. 8 79. 9 81. 83. 85. 87. 97 89. 11 91. 45 93. Seleccione un valor menor a 95. 97. 99. a) Todos los números reales b) c) Todos los números reales 101. Si n es par, se determina la raíz par de un número positivo. Si n esimpar, la expresión es real. 103. 105. d 107. a 109. Una respuesta es 111. a) No b) Sí, cuando c) Sí 113. a) pies por segundo b) pies por segundo. 115. 117. 119. 121. 123. 127. 128. 129. 130. Conjunto de ejercicios 7.2 1. a) Cuando n es par y a � 0 o n es impar b) 3. a) Siempre es real b) a c) a d) 5. a) No; b) No; 7. 9. 11. 13. 15. 17. 19. 21. 23. 25. 27. 29. 31. 33. 35. 37. 39. 41. 43. 45. 47. 49. 19.3 51. 53. 55. 57. 59. 61. 63. 5 65. 4 67. 16 69. No es un número real 71. 73. 75. 77. 79. 81. 83. 85. No es un número real 87. 24 89. 91. 93. 95. 97. 1 99. 101. 103. 105. 107. 109. 111. 113. 115. 117. 119. 121. 123. 125. n es impar, o n es par y a � 0. 127. 129. 131. 133. 135. 137. a) b) 139. a) mil millones b) mil millones 141. 9 143. 145. a) b) 147. 2; 149. c) es una función 150. 151. 0, 3 152. L441.67 millas por hora. Conjunto de ejercicios 7.3 1. a) Elevando al cuadrado los números naturales b) 1, 4, 9, 16, 25, 36 3. a) Elevando los números naturales a la quinta potencia. b) 1, 32, 243, 1024, 3125 5. Si n es par y a o b son negativos, los números no son números reales. 7. Si n es par y a o b son negativos; los números no son números reales; 9. 11. 13. 15. 17. 19. 21. 23. 25. 27. 29. 31. 33. 35. 37. 39. 41. 43. 45. o 47. 49. 51. 53. 55. 57. 59. 61. 63. 65. 5 67. 69. 3 71. 73. 75. 77. 79. 2 81. 83. 85. 87. 89. 91. 93. 95. 97. 99. 101. 103. No; un ejemplo es 118>12 = 3.1a # b21>2 = a1>2 b1>2 = 1a 1b x314 10y 3 y213 5y x2 13 5y 2x42x2 y12y3x2 212a2 b623 a2b2c2 4 4x2 5y5 r2 2 1 2 1 3 1 2 1 4 9 10 2a2 b225 b23a2 b214 b 2x2 y2 z424 2yz33a2 b223 3b22x7 y10 z1316xzab425 ab3xy213 y10y412y3y425 y3x1xx26 x3 b524 b38z1023 z2a51ax1xx2b3 -215 2214 3213 5213 4313 2213 2 2110513512412216212 b2 + a3 b a3 - b z 1 4 #1 5 #1 a #1 3 = z 1 60a; z 1 60a = z 1 120, 60a = 120; a = 2 1x - 6221x - 622{x ƒx Ú 7}2.692163 = $172.162.69273 L $49.82 21012 L 1448 bacterias210 = 1024 bacterias 1 + y2 y2>5y1>311 - y211 + y2 x1>21x + 12111>3 + 11>323 Z 1 + 1; 8 Z 2141>2 + 91>222 Z 4 + 9; 25 Z 13 L0.03L20.53L3.32L13.4212x13>6 - 18x25 x5 + 20 x3>28z7>2 - 4 x y20 64 a66>5 121 x1>7 1 2x1>3 12 x11>6 y5>3 12 1 x x1>6x9>211 28 3 4 1 64 1 4 -4-9 1 2 5 3 210 a9 29 x2 y18 y14 x1xyzx5 y101y13 yx3a3123 b3 - d 15 6a + 5b A 25 11b2 c B 3224x323 1852c51a¢ 2x6 11y7 ≤ 1>513a + 8b21>61x9 z521>41a3 b21>4 y14>397>4710>3z5>395>2a3>21xy2-1>2 = x-1>2 y-1>2 = 1 x1>2 y1>21xy21>2 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