1 Unit Lesson 3 Section 1.1 3. y = 4 - x - 2 (a) (1, 5) : 5 = 4 - 1 - 2 5 4 -1 No, the point is not on the graph. (b) ( 6, 0 ) : 0 = 4 - 6 - 2 0 4-4 Yes, the point is on the graph. 7. y = x 2 - 3 x x -1 y 4 ( x, y ) ( - 1, 4)
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Practice Answers
0 0 ( 0, 0)
4 2 -2 -2
1 -2 (1, - 2)
2 -2 ( 2, - 2)
3 0 ( 3, 0)
2
4
11. y = 2 x 3 - 4 x 2 x - intercepts : 0 = 2 x 3 - 4 x 2 0 = 2 x 2 ( 2 x - 2) x = 0 and x = 2 ( 0, 0) , ( 2, 0)
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y - intercept : y = 2( 0 ) - 4( 0 ) y=0 ( 0, 0) 13. x 2 - y = 0
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( - x ) 2 - y = 0 x 2 - y = 0 y - axis symmetry x 2 - ( - y ) = 0 x 2 + y = 0 No x - axis symmetry ( - x ) 2 - ( - y ) = 0 x 2 + y = 0 No origin symmetry
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Unit 1 Lesson 3 17. y = x x +1 -x -x y= y= 2 No y - axis symmetry 2 x +1 ( - x) + 1 x -x -y= 2 y= 2 No x - axis symmetry x +1 x +1 -x -x x -y= -y = 2 y = 2 Origin symmetry 2 x +1 x +1 ( - x) + 1
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Practice Answers
23. Origin symmetry
4 2 -2 2 4 4
31. y = x - 3 Domain : [ 3, ) Intercept : ( 3, 0 ) No axis or origin symmetry x 3 4 7 12 y 0 1 2 3
6 4 2 (3, 0) 2 4 6 8
35. x = y 2 - 1 Intercepts : ( 0, 0 ) , ( 0, 1) , ( - 1, 0 ) (-1, 0) x - axis symmetry x -1 0 3 y 0 1 2
(0, 1) 1 (0, -1) 3
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Unit 1 Lesson 3 41. y = 2x x -1
Practice Answers
43. y = 3 x
47. y = x + 3
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Unit 1 Lesson 3 51. Center : ( 2,-1) ; radius : 4
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Practice Answers
Standard form : ( x - 2 ) + ( y - ( - 1) ) = 4 2
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( x - 2) 2 + ( y + 1) 2 = 16
55. Endpoints of a diameter : ( 2, - 1) , ( 6, 8) 0+6 0+8 Center : , = ( 3, 4 ) 2 2
( x - 3) 2 + ( y - 4) 2 = r 2 ( 0 - 3) 2 + ( 0 - 4) 2 = r 2 25 = r 2 2 2 Standard Form : ( x - 3) + ( y - 4) = 25
59. ( x - 1) + ( y + 3) = 9
2 2
Center: ( 1, -3) Radius: 3
63. y = 225, 000 - 20, 000t , 0 t
250000
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200000 Depreciated value
150000
100000
50000
0 0 1 2 3 4 Year 5 6 7 8 9
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Unit 1 Lesson 3
Practice Answers
65. (a) w x (b) 2 x + 2 w = 12 w = 6 - x A = x = x ( 6 - x) w (c)
(d) The area is maximum when x = 3 and w = 6 - 3 = 3. x = 3 meters w = 3 meters
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Unit 1 Lesson 3 Section 1.2 3. 3 x 2 + 2 x - 5 = 2 x 2 - 2 (a) 3( - 3) + 2( - 3) - 5 = 2( - 3) - 2 16 = 16 x = -3 is a solution.
2 2 ?
Practice Answers
(b) 3(1) + 2(1) - 5 = 2(1) - 2 0=0 x = 1 is a solution.
2 2
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(c) 3( 4) + 2( 4 ) - 5 = 2( 4 ) - 2 51 30 x = 4 is not a solution.
2 2
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(d) 3( - 5) + 2( - 5) - 5 = 2( - 5) - 2 60 48 x = -5 is not a solution.
2 2
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7. 3 x - 2 = 4 (a) 3( 3) - 2 = 4 74 x = 3 is not a solution. (b) 3( 2) - 2 = 4 44 x = 2 is not a solution. (c) 3( 9 ) - 2 = 4 25 4 x = 9 is not a solution. (d) 3( - 6) - 2 = 4 - 20 4 x = -6 is not a solution. 13. - 6( x - 3) + 5 = -2 x + 10 is conditional. there are real values of x for which the equation is not true.
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Unit 1 Lesson 3 17. x - 42 - 11 = x 2 - 8 x + 16 - 11 = x 2 - 8 x + 5 Thus, x 2 - 8 x + 5 = ( x - 4 ) - 11 is an identity by simplification. It is true for all real values of x.
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Practice Answers
19. 3 +
1 4x = is conditional. There are real values of x x +1 x +1 for which the equation is not true. 4 x + 32 = 83 4 x + 32 - 32 = 83 - 32 4 x = 51 4 x 51 = 4 4 51 x= 4 Original Equation Subtract 32 fom both sides Simplify Divide both sides by 4 Simplify
21.
29. 2( x + 5) - 7 = 3( x - 2 ) 2 x + 10 - 7 = 3 x - 6 2 x + 3 = 3x - 6 3x - 3 x + 3 = 3 x - 3 x - 6 - x + 3 = -6 - x + 3 3 - = -6 - 3 - x = -9 x=9 33. 5x 1 1 + = x- 4 2 2 5x 1 1 4 + 4 = 4( x ) - 4 4 2 2 5x + 2 = 4 x - 2 x = -4
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Unit 1 Lesson 3
Practice Answers
45. y = 20 - ( 3 x - 10 ) 0 = 20 - ( 3 x - 10 ) 0 = 20 - 3 x + 10 0 = 30 - 3 x 3 x = 30 x = 10 The x-intercept is at 10. The solution to 0 = 20 - ( 3 x - 10 ) and the x-intercept of y = 20 - ( 3 x - 10 ) are the same. They are both x = 10. The x-intercept is (10, 0 ).
51. y = -3( 2 x + 1) x - intercept : 0 = -3( 2 x + 1) 0 = 2 x + 1 x = - y - intercept : y = -3( 2( 0 ) + 1) y = -3 1 2
1 The x-intercept is - , 0 and the y-intercept is ( 0, - 3). 2 63. 5x - 4 2 = 5x + 4 3 3( 5 x - 4 ) = 2( 5 x + 4) 15 x - 12 = 10 x + 8 5 x = 20 x=4 1 2 + ( x - 4)( x - 2) x - 4 x - 2 2 = 1( x - 2 ) + 2( x - 4 ) 2 = x - 2 + 2x - 8 2 = 3 x - 10 12 = 3 x 4=x = 2 Multiply both sides by ( x - 4)( x - 2 ).
71.
77.
( x + 2) 2 + 5 = ( x + 3) 2
x2 + 4x + 4 + 5 = x2 + 6x + 9 4x + 9 = 6x + 9 - 2x = 0 x=0
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Unit 1 Lesson 3
Practice Answers
83.
6 x + ax = 2 x + 5 4 x + ax = 5 x( 4 + a ) = 5 5 x= , a -4 4+a
101. False. x( 3 - x ) = 10 3 x - x 2 = 10 This is a quadratic equation. The equation cannot be written in the form ax + b = 0.
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Unit 1 Lesson 3 Section 1.3 11. Verbal Model: (Sum) = (first number) + (second number) Labels: Sum = S, first number = n, second number = n + 1 Expression: S = n + (n + 1) = 2n + 1 13. Verbal Model: Product = (first odd integer)(second odd integer) Labels: Product = P, first odd integer = 2n 1, second odd integer = 2n 1 + 2 = 2n+1 Expression: P = (2n 1)(2n + 1) = 4n2 1 19. Verbal Model: Perimeter = 2(width) + 2(length) Labels: Perimeter = P, width = x, length = 2(width) = 2x Expression: P = 2x + 2(2x) = 6x
Practice Answers
21. Verbal Model: (Total cost) = (unit cost)(number of units) + (fixed cost) Labels: Total cost = C, fixed cost = $1200, unit cost = $25, number of units = x Expression: C = 25x + 1200 23. Verbal Model: Thirty percent of the list price L Expression: 0.30L 29. Verbal Model: Sum = (first number) + (second number) Labels: Sum = 525, first number = n, second number = n + 1 Equation: 525 = n + (n + 1) 525 = 2n + 1 524 = 2n n = 262 Answer: First number = n = 262, second number = n + 1 = 263 37. 432 = percent 1600 432 = p (1600) 432 =p 1600 p = 0.27 = 27% 41. Verbal Model: Loan payments = 58.6% * Annual income Labels: Loan payments = 13,077.75 Annual income = I Equation: 13,077.75 = 0.586I I 22, 316.98 The family's annual income is $22,316.98
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Unit 1 Lesson 3
Practice Answers
51. Model: Labels: Equation:
Average =
( test #1) + ( test #2) + ( test #3) + ( test #4)
Answer: 53. Rate =
4 Average = 90, test #1 = 87, test #2 = 92, test #3 = 84, test #4 = x 87 + 92 + 84 + x 90 = 4 360 = 263 + x x = 97 test #4 = x = 97
distance 50 kilometers = = 100 kilometers/hour 1 time hour 2 total distance 300 kilometers Total time = = = 3 hours rate 100 kilometers/hour
67. Let x = amount in the 3% fund. 1 Then 25,000 - x = amount in the 4 % fund. 2 1000 = 0.03x + 0.045(25,000 - x) 1000 = 0.03x + 1125 - 0.045 x - 125 = -0.015 x x $8333.33 at 3% 1 25,000 - x $16,666,67 at 4 % 2 75. Cost = Fixed cost + Variable cost * Number of units $85,000 = $10,000 + $9.30 x 75,000 x= 8064.52 units 9.3 At most the company can manufacture 8064 units.
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