Section 11.2 AN85 61. 22.5 lb 63. Smartphone: $775; tablet: $890 65. Average wind speed 25 mph; average airspeed 175 mph 67. 80 $25 sets and 120 $45 sets 69. $9.96 71. Mix 50 mg of first compound with 75 mg of second. 73. a b c 4 3 , 5 3 , 1 = = − = 75. Y r 9000, 0.06 = = 77. I I I 10 71 , 65 71 , 55 71 1 2 3 = = = 79. 100 orchestra, 210 main, and 190 balcony seats 81. 1.5 chicken, 1 corn, 2 milk 83. If x price = of hamburgers, y price = of fries, and z price = of colas, then x z y z z 2.75 , 41 60 1 3 , $0.60 $0.90. = − = + ≤ ≤ There is not sufficient information: x $2.13 $2.01 $1.86 y $0.89 $0.93 $0.98 z $0.62 $0.74 $0.89 85. It will take Beth 30 h, Dan 24 h, and Edie 40 h. 87. x c a y a b z b c c a a b b c , , ; , , ( ) = = = 91. y y 5 2 x 6 (1, 1) (0, 21) 6 26 26 92. (a) x x x x 2 2 3 5 10 9 20 3 3 3 2 ( )( ) ( ) − + − + (b) x x 7 3 5 3 1 2 3 2 ( ) ( ) − + − − 93. 9 π 94. i e 2 cos 5 6 sin 5 6 2 i 5 6 π π ( ) + = π ⋅ 95. 6, 12, 18, 24, 30 { } 96. x y 100 36 1 2 2 + = 97. zw i e z w i e 12 cos 7 12 sin 7 12 12 ; 3 cos 11 12 sin 11 12 3 i i 7 12 11 12 π π π π ( ) ( ) = + = = + = π π ⋅ ⋅ 98. $4709.29 99. 3 π − 100. 31.5 square units 11.2 Assess Your Understanding (page 780) 1. matrix 2. augmented 3. third; fifth 4. b 5. T 6. c 7. 1 5 4 3 5 6 ⎡ − ⎣ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ 9. 2 3 4 6 6 2 − − ⎡ ⎣ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ 11. 0.01 0.03 0.13 0.10 0.06 0.20 ⎡ − ⎣ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ 13. ⎡ − ⎣ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ 1 1 1 3 3 0 1 1 2 10 5 2 15. − − − ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ 1 1 1 3 2 0 5 3 1 2 2 1 17. − − − − − ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ 1 1 1 2 1 2 3 4 0 4 5 1 10 1 5 0 19. x y x y 3 2 1 2 5 5 2 ; 1 3 0 1 2 9 ( ) ( ) − =− − = ⎧ ⎨ ⎪⎪ ⎩ ⎪⎪ ⎡ − − ⎣ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ 21. x y z x y z x y z 3 4 3 1 3 5 6 6 2 5 3 4 6 3 ; 1 3 4 0 4 6 0 12 24 3 3 21 ( ) ( ) ( ) − + = − + = − + + = ⎧ ⎨ ⎪⎪ ⎪⎪ ⎩ ⎪⎪ ⎪⎪ − − − − ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ 23. x y z x y z x y z 3 2 6 1 2 5 3 4 2 3 6 4 6 3 ; 1 3 2 0 1 1 0 15 10 6 8 12 ( ) ( ) ( ) − + = − − + =− − − + = ⎧ ⎨ ⎪⎪ ⎪⎪ ⎩ ⎪⎪ ⎪⎪ − − − − − ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ 25. ( ) ( ) ( ) − + = − − + =− − + + = ⎧ ⎨ ⎪⎪ ⎪⎪ ⎩ ⎪⎪ ⎪⎪ − − − − ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ x y z x y z x y z 5 3 2 1 2 5 6 2 2 4 4 6 3 ; 1 7 11 2 5 6 0 9 16 2 2 2 27. x y 5 1 = = − ⎧ ⎨ ⎪⎪ ⎩⎪⎪ Consistent; x y 5, 1 or 5, 1 ( ) = = − − 29. x y 1 2 0 3 = = = ⎧ ⎨ ⎪⎪ ⎪ ⎩ ⎪⎪ ⎪⎪ Inconsistent 31. x z y z 2 1 4 2 0 0 + = − − = − = ⎧ ⎨ ⎪⎪ ⎪ ⎩ ⎪⎪ ⎪⎪ Consistent: x z y z z 1 2 2 4 is any real number or = − − = − + ⎧ ⎨ ⎪⎪ ⎪⎪ ⎩ ⎪⎪ ⎪⎪ {( ) = − − x y z x z , , 1 2 , } = − + y z z 2 4, isanyreal number 33. x x x x x 1 2 2 3 1 2 4 3 4 = + = + = ⎧ ⎨ ⎪⎪ ⎪⎪ ⎩ ⎪⎪ ⎪⎪ Consistent: x x x x x x 1, 2 3 2 is any real number or 1 2 4 3 4 4 = = − = − ⎧ ⎨ ⎪⎪ ⎪⎪ ⎩ ⎪⎪ ⎪⎪ {( ) = x x x x x , , , 1, 1 2 3 4 1 } = − = − x x x x x 2 , 3 2 , is any real number 2 4 3 4 4 35. x x x x x 4 2 3 3 0 0 1 4 2 3 4 + = + + = = ⎧ ⎨ ⎪⎪ ⎪⎪ ⎩ ⎪⎪ ⎪⎪ Consistent: x x x x x x x 2 4 3 3 , are any real numbers or 1 4 2 3 4 3 4 = − = − − ⎧ ⎨ ⎪⎪ ⎪⎪ ⎩ ⎪⎪ ⎪⎪ {( ) = − x x x x x x , , , 2 4 , 1 2 3 4 1 4 x x x x x 3 3, , are 2 3 4 3 4 = − − any real numbers} 37. + =− + = − = = ⎧ ⎨ ⎪⎪ ⎪⎪ ⎪ ⎩ ⎪⎪ ⎪⎪ ⎪⎪ x x x x x x 2 2 2 0 0 0 1 4 2 4 3 4 Consistent: x x x x x x x 2 2 2 is any real number or 1 4 2 4 3 4 4 = − − = − = ⎧ ⎨ ⎪⎪ ⎪⎪ ⎪⎪ ⎩ ⎪⎪ ⎪⎪ ⎪⎪ {( ) = − − x x x x x x , , , 2 , 1 2 3 4 1 4 = − = x x x x x 2 2 , , is any 2 4 3 4 4 } real number 39. ( ) = = x y 6, 2; 6, 2 41. ( ) = = x y 1 3 , 5 6 ; 1 3 , 5 6 43. = − x y 4 2 , y is any real number; { } ( ) = − x y x y y , 4 2, isanyrealnumber 45. ( ) = = x y 3 2 , 1; 3 2 , 1 47. ( ) = = x y 4 3 , 1 5 ; 4 3 , 1 5 49. ( ) = = = x y z 8, 2, 0; 8, 2, 0 51. ( ) = = = − − x y z 1, 2, 1; 1,2, 1 53. Inconsistent 55. = − = − x z y z 5 2, 4 3, where z is any real number; ( ) { } = − = − x y z x z y z z , , 5 2, 4 3, isanyrealnumber 57. Inconsistent 59. ( ) = = = − − x y z 1, 3, 2; 1,3, 2 61. ( ) = − = = − x y z 3, 1 2 , 1; 3, 1 2 , 1 63. ( ) = = = x y z 1 3 , 2 3 , 1; 1 3 , 2 3 , 1 65. ( ) = = = = x y z w 1, 2, 0, 1; 1, 2, 0, 1 67. = = − y z x 0, 1 , x is any real number; ( ) { } = = − x y z y z x x , , 0, 1 , isanyrealnumber 69. = = − x y z 2, 3, z is any real number; { } ( ) = = − x y z x y z z , , 2, 3, is any real number 71. = = = x y z 13 9 , 7 18 , 19 18 ; ( ) 13 9 , 7 18 , 19 18 73. = − − = − + + x z w y z w 7 5 3 5 2 5 , 8 5 7 5 13 5 , where z and w are any real numbers; { } ( ) = − − = − + + x y z w x z w y z w z w , , , 7 5 3 5 2 5 , 8 5 7 5 13 5 , and areanyrealnumbers 75. = − + + y x x 2 3 2 77. ( ) = − + f x x x 3 4 5 3 2 79. 1.5 salmon steak, 2 baked eggs, 1 acorn squash
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