Lesson Warm Up 29 1. inconsistent 2. 25 3. (3, 2) Lesson Practice ...
Lesson
29
Warm Up 29 1. inconsistent 2. 25 3. (3, 2) Lesson Practice 29 a.
(_23 , _43 , 1)
b. infinitely many solutions c. no solution d. no solution, inconsistent e. infinitely many solutions, consistent f. 12%: $1400; 15%: $2200; 18%: $1800
© 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
LSN 29–1
Saxon Algebra 2
Lesson Practice 29
29
13. 0.025 ft/min
1. (1, -1, -2)
14. 12 ft/min
2. no solution
15. yes
3. (12x + 1)(12x - 1)
16. m = -2; b = -3
4. (3x + 5)(3x - 5)
17. Possible answer: The student forgot to change the inequality sign when dividing by -4. x ≤ -4
5. -7 6. 4 7. -10 8. 2 9. x = 1, x = -7 10. no solution 2 11. x = 0, x = _ 3
12. First terms a · a = a2 Outer terms a · b = ab Inner terms b · a = ab Last terms b · b = b2 Add the terms: a2 + ab + ab + b2 The outer and inner terms in this case will always be the same, leaving you with the product a2 + 2ab + b2. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
18. 3 19. C 20. Possible answer: Factor v2 - 7v + 10 to (v - 5)(v - 2). Area is length times width, and the side length for the side along the x-axis is the difference between the x values. So, let v - 5 = x - (4 + v). Then, x = 2v - 1. So, a possible adjacent vertex is (2v - 1, 0). 21. 36
LSN 29–2
Saxon Algebra 2
Lesson 22. Continuous function; This is a linear function with no holes or points of discontinuity. 75 Height
60 45 30 15 0
5
10 15 20 25 Age
⎧4n + 2r = 37.20 23. a. ⎨ ⎩2n + 4r = 26.40 b. Solving the first equation for r, r = 18.60 - 2n. Substituting into second equation, 2n + 4(18.60 - 2n) = 26.40; 2n + 74.4 8n = 26.40. Solving for n, n = 8, so the almonds cost $8 per pound. Then, raisins cost $2.60 per pound; r = 18.60 - 2n = 18.60 - 2(8) = 2.6. One pound of each should cost $8 + $2.60 = $10.60.
© 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
29
24. First see if the x- or y-terms are opposites. If they are, add the two equations and solve for the variable that is not eliminated. Substitute into either original equation to solve for the other variable. If neither of the variable terms are opposites, multiply one or both equations by a constant so that either the x- or y-terms become opposites. 25. A 26. ≈ 6.858 feet per second 27. The transformation moves the graph to the right 3 units. The original function equals 1 at x = -1 and x = 1. The new function equals 1 at x = 2 and x = 4.
LSN 29–3
Saxon Algebra 2
Lesson 28.
29
Population in Millions California 33.9 Texas 20.9 New York 19 Florida 16 Illinois 12.4 State
29. x = 3; y = -1 3 30. _ s
© 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
LSN 29–4
Saxon Algebra 2
29
Warm Up 29 1. inconsistent 2. 25 3. (3, 2) Lesson Practice 29 a.
(_23 , _43 , 1)
b. infinitely many solutions c. no solution d. no solution, inconsistent e. infinitely many solutions, consistent f. 12%: $1400; 15%: $2200; 18%: $1800
© 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
LSN 29–1
Saxon Algebra 2
Lesson Practice 29
29
13. 0.025 ft/min
1. (1, -1, -2)
14. 12 ft/min
2. no solution
15. yes
3. (12x + 1)(12x - 1)
16. m = -2; b = -3
4. (3x + 5)(3x - 5)
17. Possible answer: The student forgot to change the inequality sign when dividing by -4. x ≤ -4
5. -7 6. 4 7. -10 8. 2 9. x = 1, x = -7 10. no solution 2 11. x = 0, x = _ 3
12. First terms a · a = a2 Outer terms a · b = ab Inner terms b · a = ab Last terms b · b = b2 Add the terms: a2 + ab + ab + b2 The outer and inner terms in this case will always be the same, leaving you with the product a2 + 2ab + b2. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
18. 3 19. C 20. Possible answer: Factor v2 - 7v + 10 to (v - 5)(v - 2). Area is length times width, and the side length for the side along the x-axis is the difference between the x values. So, let v - 5 = x - (4 + v). Then, x = 2v - 1. So, a possible adjacent vertex is (2v - 1, 0). 21. 36
LSN 29–2
Saxon Algebra 2
Lesson 22. Continuous function; This is a linear function with no holes or points of discontinuity. 75 Height
60 45 30 15 0
5
10 15 20 25 Age
⎧4n + 2r = 37.20 23. a. ⎨ ⎩2n + 4r = 26.40 b. Solving the first equation for r, r = 18.60 - 2n. Substituting into second equation, 2n + 4(18.60 - 2n) = 26.40; 2n + 74.4 8n = 26.40. Solving for n, n = 8, so the almonds cost $8 per pound. Then, raisins cost $2.60 per pound; r = 18.60 - 2n = 18.60 - 2(8) = 2.6. One pound of each should cost $8 + $2.60 = $10.60.
© 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
29
24. First see if the x- or y-terms are opposites. If they are, add the two equations and solve for the variable that is not eliminated. Substitute into either original equation to solve for the other variable. If neither of the variable terms are opposites, multiply one or both equations by a constant so that either the x- or y-terms become opposites. 25. A 26. ≈ 6.858 feet per second 27. The transformation moves the graph to the right 3 units. The original function equals 1 at x = -1 and x = 1. The new function equals 1 at x = 2 and x = 4.
LSN 29–3
Saxon Algebra 2
Lesson 28.
29
Population in Millions California 33.9 Texas 20.9 New York 19 Florida 16 Illinois 12.4 State
29. x = 3; y = -1 3 30. _ s
© 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
LSN 29–4
Saxon Algebra 2
