Algebra-Intermedia 2-páginas-65

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SIN SIGLA

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29/4/2024
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Álgebra II

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Respuestas R19
85. a) o b) 87. a) Las respuestas variarán.
b) Las respuestas variarán. 89. a) b) 91. a) b)
92. 1 93. 94. L17.3 libras del de $5.20; L12.7 libras del de $6.30 95.
96.
Cómo usar su calculadora graficadora, 5.8 1. 2. 3.
Conjunto de ejercicios 5.8 1. El grado de una función polinomial es el mismo que el grado del término principal.
3. 5. a) La propiedad del factor cero sólo se cumple cuando un lado de la ecuación es 0. b) y 
7. a) Las respuestas variarán. b) 9. a) Catetos b) Hipotenusa 11. �8 y �2; en las intersecciones con el eje x se tiene que y � 0.
13. Sí, si la gráfica no cruza al eje x 15. Sí, si la gráfica cruza al eje x dos veces. 17. 19. 0, 1 21. 23. 25.
27. 0, 3 29. 31. 0, 6 33. 0, 9 35. 37. 39. 41. 43. 45. 47. 49.
51. 53. 55. 57. 59. 61. 63. 65. 67. 69.
71. 73. 75. (4, 0), (6, 0) 77. 79. 81. 83. 85. 87. d) 89. b)
91. 93. 95. 97. Ancho � 2 pies, largo � 5 pies
99. Base � 10 pies, altura � 16 pies 101. 2 pies 103. 3 pies 105. 2 segundos 107. Tim: 5 millas; Bob: 12 millas 109. 13 pies
111. 50 bicicletas 113. 13 pulgadas por 13 pulgadas 115. a) V � a3 � ab2 b) V � a(a � b)(a � b) c) 3 pulgadas
117. a) b) c) Un número infinito; cualquier función de la forma
d) Un número infinito; cualquier ecuación de la forma
119. a) Las respuestas variarán. Ejemplos son: b) Ninguna (sin intercepciones con el eje x), una
(una intercepción con el eje x) o dos (dos
intercepciones con el eje x)
121. 73.721949 mph 123. 128.
129. 130. 131. 132.
Ejercicios de repaso del capítulo 5 1. a) Binomio, b) c) 2 2. a) Trinomio, b) c) 3
3. No es un polinomio 4. a) Polinomio, b) c) 4 5. 6.
7. 8. 9. 10. 11. 12. 13. 21
14. 15. 16. 17. a) $780.46 mil millones b) Sí 18. a) $773.13 mil millones b) Sí
19. 20. 21. 22. 23.
24. 25. 26. 27. 28.
29. 30. 31. 32. 33.
34. 35. 36. 37.
38. 39. a) b) 0 40. a) b) 12 41. a) b) 9
42. a) b) 77 43. 44. 45. 46. 47. 48.
49. 50. 51. 52. 53.
54. 55. 56. 57. 10 58.
59. 60. 0; es un factor 61. 62. 63. 64.
65. 66. 67. 68. 69.
70. 71. 72. 73. 74.
75. 76. 77. 78. 79.
80. 81. 82. 83. 84.
85. 86. 87. 88. 89. 90.
91. 92. 93. 94. 95.
96. 97. 98. 99. 100. 101.
102. 103. 104. 105.
106. 107. 108.
109. 110. 111. 112.
113. 114. 115. 116. 117.
118. 119. 120. 121. 122. 5x2
 y1x + 2224y1x + 221x2
- 2x + 423y1y2
+ 521y2
- 523xy41x - 221x + 625x1x - 421x - 22
y41x + 321x - 524a1a + c21a - c212x - y214x2
+ 2xy + y221a + 2b21a - 2b21x + 321x - 32
1a + 521a2
+ 7a + 1321x - 121x2
+ 4x + 721x - 521x2
- x + 721y - 4z21y2
+ 4yz + 16z22
12a + 3b214a2
- 6ab + 9b2215x - 12125x2
+ 5x + 121y + 4z21y2
- 4yz + 16z22
1x - 321x2
+ 3x + 9216b - 5c2214x + y221a + 3b + 6c21a + 3b - 6c2
1x + 4 + y21x + 4 - y21m2
- 10221p2
+ 92213y + 5213y - 721x - 221x + 6214y - 322
12a + 1221x2
+ 421x + 221x - 221x2
+ 921x + 321x - 321x + 1121x - 1121x + 621x - 62
1x + 1021x + 221x + 1021x + 12x1x - 921x + 921x + 721x2
- 721x2
+ 921x2
+ 321x2
+ 72
12p - 5q213p - 2q21x - 18y21x + 3y2y3112y + 121y + 52a314a - 521a - 12x214x - 5212x + 52
x12x + 121x + 62-1x - 1221x - 12-1x - 1521x + 321x - 821x - 221x - 721x + 42
1x - 221x + 521x + 621x + 3214x + 5215x - 22117x + 3219x - 7217x + 9212x - 12
15x + 22113x - 7213x - 72116x - 21212x - 521x + 9213a + 2b214a + 5b215x - y21x + 6y2
6xy2
 z214y2
 z + 2xy - 5x2
 z22a2
 b315a - 7b323x415x + 2 - 4xy3241x2
+ 2x + 82- 
53
9
 o -5.8
-2362x2
+ 2x + 6x4
+ 2x3
+ 4x2
+ 8x + 16 +
14
x - 2
2y4
- 2y3
- 8y2
+ 8y - 7 +
5
y + 1
3x2
+ 7x + 21 +
73
x - 3
2x2
+ 3x - 4 +
3
2x + 3
x + 4 -
10
x - 3
2a3
+ a2
- 3a - 4x3
- 2x2
+ 3x + 7
4x - 3
x2
4y
+ x +
3y
2
7
4
 a2
- 4a + 89p - 5q - 3
1
4
 t51
5
 x6
 y2x4
- 4
x3
- x2
- 5x + 62x3
- 4x2
- 6x + 12x2
- 2x - 3x2
+ xy + 4y + xz
x2
+ 8x + 104x4
+ 12x3
+ 6x2
+ 16x - 66x3
- x2
- 24x + 184p2
- 4pq + q2
- 20p + 10q + 25
x2
+ 6xy + 9y2
+ 4x + 12y + 481a4
- 4b416x2
 y2
- 364a2
- 25b449x2
- 25y2
16x2
- 24xy + 9y24a2
+ 36ab + 81b26p2
 q2
+ 11pqr - 7r210x2
 y + 8xy2
- 5x - 4ya2
- 22ab + 121b2
x2
+ 16xy + 64y250a2
- 5a - 36x2
+ 17x - 45-3x4
 y2
- 3x2
 y6
+ 12xy76x3
- 14x2
+ 10x
2x2
+ 24x + 233x2
+ 27-76
-10a2
 b + ab5x2
+ 7x + 3-3ab + b2
- 2a3x2
 y + 3xy - 9y26x3
- 9x + 133a - 8b + 7
5x2
+ 11x - 4x2
- 3x + 142x4
- 10x2
 y + 6xy3
- 3,
4x3
+ 5x - 7,3x2
+ 9,
1x + 321x - 22-8412, -12
5
12
23
12
x4
16y6;2, ;3L
y
x
5
�5
5�5
Dos
y
x
5
�5
5�5
Una
y
x
5
�5
5�5
Ninguna
a1x2
+ 7x + 102 = 0, a Z 0
f1x2 = a1x2
+ 7x + 102, a Z 0x2
+ 7x + 10 = 0f1x2 = x2
+ 7x + 10
y = 6x2
- 7x - 10y = x2
- 2x - 8y = x2
- 6x + 5
x = 9x = 5x = 110, 02, a4
3
, 0b , a5
2
, 0b1-8, 026, -5
3
5
, 
5
2
-2, - 
1
3
0, -3, -5
5
2
, 
4
3
-1, -4-3, -11-11, 90, -3, 3- 
3
2
, 
3
2
5, -50, - 
1
2
, 
4
3
0, -4, 30, 6, -3-4, 6
3
2
, -2- 
1
2
, 5-4-4, 3-1, -50, -5
2
3
, 
1
7
0, -4, 9-1, 70, -3
4
3
, - 
5
4
-5-2ax2
+ bx + c = 0
y = x2
+ 4xy = x2
- x - 6y = x2
- 6x + 5
1x + 3212x2
- 52
5x3
- x2
+ 16x + 16{z ƒz 6 -6 o z 7 0}
x-3>215x - 321x + 12x-3>215x2
+ 2x - 32x-51x - 321x + 12x-51x2
- 2x - 32
21a + b21a - b22a1a - b2 + 2b1a - b2a1a - b2 + a1a - b2 + b1a - b2 + b1a - b2
R20 Respuestas
123. 124. 125. 126.
127. 128. 129. 130. 131.
132. 133. 134. 135.
136. 137. 138. 139. 140.
141. 142. 143. 144. 145. 0, 2 146. 147. 148. 149. 7, 1
150. 0, 2, 4 151. 152. 153. 154. 155. 156.
157. 158. 159. Ancho � 9 pies, longitud � 12 pies 160. Altura � 4 pies, base � 13 pies
161. 3 pulgadas, 7 pulgadas 162. 9 segundos 163. 9
Examen de práctica del capítulo 5 1. a) Trinomio b) c) 4 d) [5.1] 2. [5.1]
3. [5.2] 4. [5.2] 5. [5.2] 6. [5.3]
7. [5.3] 8. [5.3] 9. [5.3] 10. [5.4]
11. [5.5] 12. [5.4] 13. [5.5] 14. [5.5] 15. [5.5]
16. [5.6] 17. a) b) [5.2] 18. [5.5] 19. [5.5]
20. [5.8] 21. [5.8] 22. [5.8] 23. [5.8]
24. Altura � 4 metros, base � 11 metros[5.8] 25. 7 segundos [5.8]
Examen de repaso acumulativo 1. [1.2] 2. [1.2] 3. [1.3] 4. [1.4]
5. [1.5] 6. 5 [2.1] 7. [2.2] 8. 13 metros por 13 metros [2.3] 9. 620 páginas [2.3] 10. [2.5] 11. No [3.1]
12. [3.3] 13. [3.4] 14. [3.6] 15. [3.7] 16. (10, 4) [4.1] 17. (4, 1, 2) [4.2] 18. 18 [4.5]
19. [5.3]
20. [5.6]
Capítulo 6
Conjunto de ejercicios 6.1 1. a) Una expresión racional es una expresión de la forma p y q polinomios y q Z 0
b) Las respuestas variarán. 3. a) Una función racional es una función de la forma p y q polinomios, q Z 0 b) Las respuestas
variarán. 5. a) El dominio de una función racional es el conjunto de valores que pueden reemplazar a la variable. b)
7. a) Factorice �1 del numerador o del denominador y reduzca. b) 9. a) Invierta la segunda fracción, factorice todas las expresiones,
simplifique y luego multiplique los numeradores y multiplique los denominadores. b) 11. 4 13. 15. Ninguno 17.
19. 21. 23. 25. 27. 29.
31. 33. x 35. 37. 39. 41. 43. 45. 47. 49.
51. 53. 1 55. 57. 59. 61. 63. 65. 67.
69. 71. 73. 1 75. 77. 79. Una respuesta posible es el denominador es
cero en x � 2 y x � �3 81. El numerador nunca es 0. 83. a) 4, hace que el numerador sea 0 b) 6 y �6, cada uno, hacen que el
denominador sea 0 85. Una respuesta posible es el numerador es 0 en x � 2, el denominador es 0 en x � 3 y x � �1
87. x � 5; el numerador debe ser x � 5 89. y2 � 4y � 5, los factores deben ser (y � 5)(y � 1) 91. x2 � x � 2; los factores deben ser
(x � 1)(x � 2) 93. 2x2 � x � 6; los factores deben ser (x � 2)(2x � 3). 95. 97. 99. 101.
103. 105. xy1
x41x - p2n
x - 1
x + 3
1x + 2213x + 12
12x - 321x + 1221a + b23a + b
2
f1x2 =
x - 2
1x - 321x + 12 ;
1
1x - 221x + 32 ;
r + 5s
2r + 5s
p - q
p + q
1a - b21a + b2
a2
+ ab + b2
x3
x + 2
x - y
x + y
1x + 221x - 22
1x2
+ 2x + 421x2
+ 42
x - 4
4x + 1
1a + 122
91a + b22
7
x - 4
r3
r - 8
x + 5
4
12x3
 y2
xy2
15
x - 4
x2
- 3x + 9
a + 7
a + 5
2x - 5
2
4x2
+ 10xy + 25y2a - 5
a + 3
-1p + 42-1
x - 4y
3
1 - y{a ƒa Z -6 y a Z 6}{x ƒx es un número real}ea ` a Z
1
2
 y a Z -2 f{x ƒx Z -3 y x Z 2}{p ƒp Z 2}
9, -95, 
5
2
1
r + 6
-1
{x ƒx Z -5 y x Z 5}
f1x2 =
p
q
,
p
q
,
14x - 3y2116x2
+ 12xy + 9y22
2x2
+ 12x + 63 +
393
x - 6
5�5 x
y
3
�7
-180- 
2
9
6x - 3y = 2
34 … x 6 84e=
k - 2d
2
8r6
 s15
-34- 
3
32�5
A ´ B = {2, 3, 4, 5, 6, 8}
y = x2
- 9x + 14a1
4
, 0b , a - 
3
2
, 0b0, -5, 2
3
7
, -4
1x + 1121x + 4241x + y21x - y2-63x2
- 19x + 20q613p - 2219p2
+ 6p + 42
1x + 721x + 324x1x - 5212b2
+ 921b2
- 221a + 2b212a + 3b2x1x - 321x + 12
2xy16x2
+ 5xy3
- 7y22-853x3
+ 3x2
+ 15x + 15 +
76
x - 5
x - 5 +
24
2x + 3
4x4
- 5y +
7
x24x3
+ 8x2
 y - 9xy2
- 6y310a2
- 13ab - 3b2
-8x8
 y3
+ 24x6
 y4
- 12x4
 y2
4x2
 y - 14y2
+ 4x + 6y-6-6x4
- 4x2
+ 3x
y = 12x2
+ 32x + 5y = x2
- 2x - 24
a6
5
, 0b , a5
4
, 0b1-3, 02, 16, 023
4
, - 
2
5
4
3
, - 
1
4
2, -34, -4
5, -6-4, -30, - 
4
3
- 
5
2
, - 
10
3
2, - 
1
4
1a + b2212a + b21a + 3b2
2b1a + b21a + 2b21a - 2b21y + 1021y + 521x + 921x + 22ax -
2
3
 y2b ax2
+
2
3
 xy2
+
4
9
 y4b
3x2
 y51x + 3212x - 32213a + 5214a + 3214y + x + 2214y - x - 2213x2
- 222
12pq - 3213pq + 2213a - b213x + 7y21x + 1221x - 2212x2
- 1212x2
+ 3214x + 1214x + 52
1x + 421x - 121x + 6251x + 2y21x2
- 2xy + 4y221x + 5 + z21x + 5 - z23x12x + 121x - 42
Respuestas R21
107. a) b)
�10
�10
10
10
{x ƒx Z 2}
d) No; el numerador nunca puede ser 0. 113.
114. 115. 116. 0.1 117.
118.
Conjunto de ejercicios 6.2 1. a), b) Las respuestas variarán. c) 3. a) No todo el numerador 
se restó. b) 5. 7. 9. 11. 13. 15.
17. 19. 21. 23. 25. 27. 29. 31.
33. 35. 37. 39. 41. 43. 45.
47. 49. 51. 53. 55. 57.
59. 61. 0 63. 65. 67. 69.
71. 0 73. 75. No 77. Sí, si multiplica cualquier fracción por obtiene la otra fracción.
79. a) b) c) d) 81. 83.
85. 87. 89. 91.
93. a) 4 b) 95. 97.
99. 101. 103. a) b) 79.2 105. 107. No 109. a)
b) c) d) 111. 112. a) 6 minutos
b) 960 cajas 113. 114. 115. 116. 117.
Conjunto de ejercicios 6.3 1. Una que tiene una expresión fraccionaría en su numerador o en su denominador o en ambos.
3. 5. 7. 9. 11. 13. 15. 17. 19. 21. 23.
25. 27. 29. 31. 33. 35. 37. 39.
41. 43. 45. 47. 49. 51. 53.
55. 57. a) b) 59. 61. a 63. 65.
67. 69. 71. 72. 73. 74. 75. Ninguna
Conjunto de ejercicios 6.4 1. Un número obtenido cuando se resuelve una ecuación que no es una solución verdadera.
3. a) Multiplique ambos lados por 12 para eliminar a las fracciones. b) �24 c) Escriba cada término con el MCD, de 12, de modo que pueda
e3, 
5
3
fa -23, - 
34
5
b13
48
5
12
4a2
+ 1
4a12a2
+ 12
-2a - h
a21a + h22
-1
1a + 121a + h + 12
-1
a1a + h2RT =
R1 R2 R3
R2 R3 + R1 R3 + R1 R2
1
5
2
9
x2
+ 3x - 4
x + 1
x2
+ 9x + 14
x + 1
2y - 8xy + 5y2
3y2
- 4x
15y - x
3xy
1a + b22
ab
9a2
+ b
b1b + 12
b2
- a3
 b
a3
+ ab
b11 + a2
a11 - b2
ab
b + a
2 + a2
 b
a2
a1a + 32
1a - 221a + 12
x2
+ 5x - 6
x1x - 22
x
51x - 32
a2
+ 1
2a
x - 1
x + 1
-a + 1
1a + 1212a + 12
31x + 22
x5-1
x - y
y
- 
a
b
5
3a2
xy + 5
y + x
x1y - 12
8 + x
y - x
3xy
3z4
4xy4
12x3
y6
75a
b5
1
3
, 73x - 7 +
27
2x + 3
-11- 
2
3
{x ƒ -2 6 x 6 8}
-h
1a + 121a + h + 12
xn
+ xn - 1
+ xn - 2
+
Á
+ 1
xn
x4
+ x3
+ x2
+ x + 1
x4
x2
+ x + 1
x2
x + 1
x
a - b + 1
1a - b22
ax + bn - bx
n
-x2
+ 4x + 5
1
1a - 521a + 32
3x + 10
x - 2
7x2
- 6x + 6; 5x2
- 17x22 = -2x2, -1-6x2 = 6x, -6 - 162 = -12
a2
- b2
a2
ad
bd
+
bc
bd
=
ad + bc
bd
2x
x4
+ x3
- 10x2
- 4x + 24
x2
+ 5x + 4
1x + 221x - 221x + 32R: {y ƒy Z 1}D: {x ƒx Z 2},
3x2
+ 19x + 7
1x + 221x + 32
2x2
+ 8x - 3
1x + 121x + 22{x ƒx Z 3 y x Z -4}
2x2
+ 3x + 8
1x - 321x + 42{x ƒx Z -4}{x ƒx Z 3}
-1
-1
1
2x + 3y
12m2
+ 7mn
12m + 3n213m + 2n212m + n2
x2
- 18x - 30
15x + 621x - 22
18r2
+ 11r - 25
14r - 5212r + 32
15x2
- 70x + 30
13x - 221x - 42
16
r - 4
2x2
- 4xy + 4y2
1x - 2y221x + 2y2
3a - 1
4a + 1
4x2
+ 11x - 39
1x + 521x - 22
2x + 3
1x - 821x - 12
2x2
+ 4x + 4
1x - 121x + 421x - 22
6a + 7
1a + 222
5x2
+ 3x - 12
1x - 421x + 12
2a
a - b
2b2
- a2
b1a - b2
15y2
+ 8x2
40x4
 y3
5x - 3
12x2
26
3r
1x - 3212x - 1212x + 32
1a - 821a + 321a + 82x41x - 223z - 61x + 321x + 926a4
 b540x4
 y66a3x + 5
x + 3
x - 5
x - 3
x - 1
7x - 11
x - 8
x + 7
x + 3
7x - 2
x - 5
3x + 5
x + 2
x2
- 4x - x2
- x + 2
1x + 321x - 22
18x + 11218x - 1121x - 22
13x + y + 2213x + y - 22
12, -12-28, 32a - q , 
3
2
b
y = x + 2
c) Decreciente
d) Creciente
109. a) b)
�10
�10
10
10
{x ƒx Z 2}
c) Decreciente
d) Creciente
111. a) b) 100, 10, 2, 1, 0.1 c) y
x
5
�5
5�5
f(x) � 1
x
-0.1, -1, -2, -10, -100,{x ƒx Z 0}
<<
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 /UsePrologue false
 /ColorSettingsFile (Color Management Off)
 /AlwaysEmbed [ true
 ]
 /NeverEmbed [ true
 ]
 /AntiAliasColorImages false
 /CropColorImages true
 /ColorImageMinResolution 150
 /ColorImageMinResolutionPolicy /OK
 /DownsampleColorImages true
 /ColorImageDownsampleType /Bicubic
 /ColorImageResolution 300
 /ColorImageDepth -1
 /ColorImageMinDownsampleDepth 1
 /ColorImageDownsampleThreshold 1.50000
 /EncodeColorImages true
 /ColorImageFilter /DCTEncode
 /AutoFilterColorImages true
 /ColorImageAutoFilterStrategy /JPEG
 /ColorACSImageDict <<
 /QFactor 0.15
 /HSamples [1 1 1 1] /VSamples [1 1 1 1]
 >>
 /ColorImageDict <<
 /QFactor 0.15
 /HSamples [1 1 1 1] /VSamples [1 1 1 1]
 >>
 /JPEG2000ColorACSImageDict <<
 /TileWidth 256
 /TileHeight 256
 /Quality 30
 >>
 /JPEG2000ColorImageDict <<
 /TileWidth 256
 /TileHeight 256
 /Quality 30
 >>
 /AntiAliasGrayImages false
 /CropGrayImages true
 /GrayImageMinResolution 150
 /GrayImageMinResolutionPolicy /OK
 /DownsampleGrayImages true
 /GrayImageDownsampleType /Bicubic
 /GrayImageResolution 300
 /GrayImageDepth -1
 /GrayImageMinDownsampleDepth 2
 /GrayImageDownsampleThreshold 1.50000
 /EncodeGrayImages true
 /GrayImageFilter /DCTEncode
 /AutoFilterGrayImages true
 /GrayImageAutoFilterStrategy /JPEG
 /GrayACSImageDict <<
 /QFactor 0.15
 /HSamples [1 1 1 1] /VSamples [1 1 1 1]
 >>
 /GrayImageDict <<
 /QFactor 0.15
 /HSamples [1 1 1 1] /VSamples [1 1 1 1]
 >>
 /JPEG2000GrayACSImageDict <<
 /TileWidth 256
 /TileHeight 256
 /Quality 30
 >>
 /JPEG2000GrayImageDict <<
 /TileWidth 256
 /TileHeight 256
 /Quality 30
 >>
 /AntiAliasMonoImages false
 /CropMonoImages true
 /MonoImageMinResolution 1200
 /MonoImageMinResolutionPolicy /OK
 /DownsampleMonoImages true
 /MonoImageDownsampleType /Bicubic
 /MonoImageResolution 1200
 /MonoImageDepth -1
 /MonoImageDownsampleThreshold 1.50000
 /EncodeMonoImages true
 /MonoImageFilter /FlateEncode
 /MonoImageDict <<
 /K -1
 >>
 /AllowPSXObjects false
 /CheckCompliance [
 /None
 ]
 /PDFX1aCheck false
 /PDFX3Check false
 /PDFXCompliantPDFOnly false
 /PDFXNoTrimBoxError true
 /PDFXTrimBoxToMediaBoxOffset [
 0.00000
 0.00000
 0.00000
 0.00000
 ]
 /PDFXSetBleedBoxToMediaBox true
 /PDFXBleedBoxToTrimBoxOffset [
 0.00000
 0.00000
 0.00000
 0.00000
 ]
 /PDFXOutputIntentProfile (None)/PDFXOutputConditionIdentifier ()
 /PDFXOutputCondition ()
 /PDFXRegistryName (http://www.color.org)
 /PDFXTrapped /Unknown
 /Description <<
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 >>
>> setdistillerparams
<<
 /HWResolution [2400 2400]
 /PageSize [612.000 792.000]
>> setpagedevice
<<
 /ASCII85EncodePages false
 /AllowTransparency false
 /AutoPositionEPSFiles true
 /AutoRotatePages /None
 /Binding /Left
 /CalGrayProfile (Gray Gamma 1.8)
 /CalRGBProfile (Apple RGB)
 /CalCMYKProfile (U.S. Sheetfed Uncoated v2)
 /sRGBProfile (sRGB IEC61966-2.1)
 /CannotEmbedFontPolicy /Warning
 /CompatibilityLevel 1.4
 /CompressObjects /Off
 /CompressPages true
 /ConvertImagesToIndexed true
 /PassThroughJPEGImages true
 /CreateJDFFile false
 /CreateJobTicket false
 /DefaultRenderingIntent /Default
 /DetectBlends true
 /DetectCurves 0.1000
 /ColorConversionStrategy /LeaveColorUnchanged
 /DoThumbnails false
 /EmbedAllFonts true
 /EmbedOpenType false
 /ParseICCProfilesInComments true
 /EmbedJobOptions true
 /DSCReportingLevel 0
 /EmitDSCWarnings false
 /EndPage -1
 /ImageMemory 1048576
 /LockDistillerParams false
 /MaxSubsetPct 100
 /Optimize true
 /OPM 1
 /ParseDSCComments true
 /ParseDSCCommentsForDocInfo true
 /PreserveCopyPage true
 /PreserveDICMYKValues true
 /PreserveEPSInfo true
 /PreserveFlatness true
 /PreserveHalftoneInfo false
 /PreserveOPIComments false
 /PreserveOverprintSettings true
 /StartPage 1
 /SubsetFonts true
 /TransferFunctionInfo /Remove
 /UCRandBGInfo /Preserve
 /UsePrologue false
 /ColorSettingsFile (Color Management Off)
 /AlwaysEmbed [ true
 ]
 /NeverEmbed [ true
 ]
 /AntiAliasColorImages false
 /CropColorImages true
 /ColorImageMinResolution 150
 /ColorImageMinResolutionPolicy /OK
 /DownsampleColorImages true
 /ColorImageDownsampleType /Bicubic
 /ColorImageResolution 300
 /ColorImageDepth -1
 /ColorImageMinDownsampleDepth 1
 /ColorImageDownsampleThreshold 1.50000
 /EncodeColorImages true
 /ColorImageFilter /DCTEncode
 /AutoFilterColorImages true
 /ColorImageAutoFilterStrategy /JPEG
 /ColorACSImageDict <<
 /QFactor 0.15
 /HSamples [1 1 1 1] /VSamples [1 1 1 1]
 >>
 /ColorImageDict <<
 /QFactor 0.15
 /HSamples [1 1 1 1] /VSamples [1 1 1 1]
 >>
 /JPEG2000ColorACSImageDict <<
 /TileWidth 256
 /TileHeight 256
 /Quality 30
 >>
 /JPEG2000ColorImageDict <<
 /TileWidth 256
 /TileHeight 256
 /Quality 30
 >>
 /AntiAliasGrayImages false
 /CropGrayImages true
 /GrayImageMinResolution 150
 /GrayImageMinResolutionPolicy /OK
 /DownsampleGrayImages true
 /GrayImageDownsampleType /Bicubic
 /GrayImageResolution 300
 /GrayImageDepth -1
 /GrayImageMinDownsampleDepth 2
 /GrayImageDownsampleThreshold 1.50000
 /EncodeGrayImages true
 /GrayImageFilter /DCTEncode
 /AutoFilterGrayImages true
 /GrayImageAutoFilterStrategy /JPEG
 /GrayACSImageDict <<
 /QFactor 0.15
 /HSamples [1 1 1 1] /VSamples [1 1 1 1]
 >>
 /GrayImageDict <<
 /QFactor 0.15
 /HSamples [1 1 1 1] /VSamples [1 1 1 1]
 >>
 /JPEG2000GrayACSImageDict <<
 /TileWidth 256
 /TileHeight 256
 /Quality 30
 >>
 /JPEG2000GrayImageDict <<
 /TileWidth 256
 /TileHeight 256
 /Quality 30
 >>
 /AntiAliasMonoImages false
 /CropMonoImages true
 /MonoImageMinResolution 1200
 /MonoImageMinResolutionPolicy /OK
 /DownsampleMonoImages true
 /MonoImageDownsampleType /Bicubic
 /MonoImageResolution 1200
 /MonoImageDepth -1
 /MonoImageDownsampleThreshold 1.50000
 /EncodeMonoImages true
 /MonoImageFilter /FlateEncode
 /MonoImageDict <<
 /K -1
 >>
 /AllowPSXObjects false
 /CheckCompliance [
 /None
 ]
 /PDFX1aCheck false
 /PDFX3Check false
 /PDFXCompliantPDFOnly false
 /PDFXNoTrimBoxError true
 /PDFXTrimBoxToMediaBoxOffset [
 0.00000
 0.00000
 0.00000
 0.00000
 ]
 /PDFXSetBleedBoxToMediaBox true
 /PDFXBleedBoxToTrimBoxOffset [
 0.00000
 0.00000
 0.00000
 0.00000
 ]
 /PDFXOutputIntentProfile (None)
 /PDFXOutputConditionIdentifier ()
 /PDFXOutputCondition ()
 /PDFXRegistryName (http://www.color.org)
 /PDFXTrapped /Unknown
 /Description <<
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 >>
>> setdistillerparams
<<
 /HWResolution [2400 2400]
 /PageSize [612.000 792.000]
>> setpagedevice
<<
 /ASCII85EncodePages false
 /AllowTransparency false
 /AutoPositionEPSFiles true
 /AutoRotatePages /None
 /Binding /Left
 /CalGrayProfile (Gray Gamma 1.8)
 /CalRGBProfile (Apple RGB)
 /CalCMYKProfile (U.S. Sheetfed Uncoated v2)
 /sRGBProfile (sRGB IEC61966-2.1)
 /CannotEmbedFontPolicy /Warning
 /CompatibilityLevel 1.4
 /CompressObjects /Off
 /CompressPages true
 /ConvertImagesToIndexed true
 /PassThroughJPEGImages true
 /CreateJDFFile false
 /CreateJobTicket false
 /DefaultRenderingIntent /Default
 /DetectBlends true
 /DetectCurves 0.1000
 /ColorConversionStrategy /LeaveColorUnchanged
 /DoThumbnails false
 /EmbedAllFonts true
 /EmbedOpenType false
 /ParseICCProfilesInComments true
 /EmbedJobOptions true
 /DSCReportingLevel 0
 /EmitDSCWarnings false
 /EndPage -1
 /ImageMemory 1048576
 /LockDistillerParams false
 /MaxSubsetPct 100
 /Optimize true
 /OPM 1
 /ParseDSCComments true
 /ParseDSCCommentsForDocInfo true
 /PreserveCopyPage true
 /PreserveDICMYKValues true
 /PreserveEPSInfo true
 /PreserveFlatness true
 /PreserveHalftoneInfo false
 /PreserveOPIComments false
 /PreserveOverprintSettings true
 /StartPage 1
 /SubsetFonts true
 /TransferFunctionInfo /Remove
 /UCRandBGInfo /Preserve
 /UsePrologue false
 /ColorSettingsFile (Color Management Off)
 /AlwaysEmbed [ true
 ]
 /NeverEmbed [ true
 ]
 /AntiAliasColorImages false
 /CropColorImages true
 /ColorImageMinResolution 150
 /ColorImageMinResolutionPolicy /OK
 /DownsampleColorImages true
 /ColorImageDownsampleType /Bicubic
 /ColorImageResolution 300
 /ColorImageDepth -1
 /ColorImageMinDownsampleDepth 1
 /ColorImageDownsampleThreshold 1.50000
 /EncodeColorImages true
 /ColorImageFilter /DCTEncode
 /AutoFilterColorImages true
 /ColorImageAutoFilterStrategy /JPEG
 /ColorACSImageDict <<
 /QFactor 0.15
 /HSamples [1 1 1 1] /VSamples [1 1 1 1]
 >>
 /ColorImageDict <<
 /QFactor 0.15
 /HSamples [1 1 1 1] /VSamples [1 1 1 1]
 >>
 /JPEG2000ColorACSImageDict <<
 /TileWidth 256
 /TileHeight 256
 /Quality 30
 >>
 /JPEG2000ColorImageDict <<
 /TileWidth 256
 /TileHeight 256
 /Quality 30
 >>
 /AntiAliasGrayImages false
 /CropGrayImages true
 /GrayImageMinResolution 150
 /GrayImageMinResolutionPolicy /OK
 /DownsampleGrayImages true
 /GrayImageDownsampleType /Bicubic
 /GrayImageResolution 300
 /GrayImageDepth -1
 /GrayImageMinDownsampleDepth 2
 /GrayImageDownsampleThreshold 1.50000
 /EncodeGrayImages true
 /GrayImageFilter /DCTEncode
 /AutoFilterGrayImages true
 /GrayImageAutoFilterStrategy /JPEG
 /GrayACSImageDict <<
 /QFactor 0.15
 /HSamples [1 1 1 1] /VSamples [1 1 1 1]
 >>
 /GrayImageDict <<
 /QFactor 0.15
 /HSamples [1 1 1 1] /VSamples [1 1 1 1]
 >>
 /JPEG2000GrayACSImageDict <<
 /TileWidth 256
 /TileHeight 256
 /Quality 30
 >>
 /JPEG2000GrayImageDict <<
 /TileWidth 256
 /TileHeight 256
 /Quality 30
 >>
 /AntiAliasMonoImages false
 /CropMonoImages true
 /MonoImageMinResolution 1200
 /MonoImageMinResolutionPolicy /OK
 /DownsampleMonoImages true
 /MonoImageDownsampleType /Bicubic
 /MonoImageResolution 1200
 /MonoImageDepth -1
 /MonoImageDownsampleThreshold 1.50000
 /EncodeMonoImages true
 /MonoImageFilter /FlateEncode
 /MonoImageDict <<
 /K -1
 >>
 /AllowPSXObjects false
 /CheckCompliance [
 /None
 ]
 /PDFX1aCheck false
 /PDFX3Check false
 /PDFXCompliantPDFOnly false
 /PDFXNoTrimBoxError true
 /PDFXTrimBoxToMediaBoxOffset [
 0.00000
 0.00000
 0.00000
 0.00000
 ]
 /PDFXSetBleedBoxToMediaBox true
 /PDFXBleedBoxToTrimBoxOffset [
 0.00000
 0.00000
 0.00000
 0.00000
 ]
 /PDFXOutputIntentProfile (None)
 /PDFXOutputConditionIdentifier ()
 /PDFXOutputCondition ()
 /PDFXRegistryName (http://www.color.org)
 /PDFXTrapped /Unknown
 /Description <<
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 >>
>> setdistillerparams
<<
 /HWResolution [2400 2400]
 /PageSize [612.000 792.000]
>> setpagedevice