Lesson Warm Up 32 1. matrix 2.
Lesson ⎡ 3.4 f. X = ⎢ ⎣-1.6
Warm Up 32 1. matrix
32
27.2⎤ -12.8⎦
g. x = 2, y = 0, z = -6
2. [-2 -6 8]
h. 150 grams of beans, 90 grams of chicken, 110 grams of rice
⎡2 14⎤ 3. ⎢ ⎣3 23⎦ Lesson Practice 32 a. yes b. no ⎡-1 c. A-1 = ⎢ ⎣-3
-2⎤ -5⎦
⎡0.5 d. B-1 = ⎢ ⎣ 0
0 ⎤ 0.5⎦
e.
© 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
LSN 32–1
Saxon Algebra 2
Lesson ⎡ 3 6. ⎢ ⎣-2
Practice 32 1. no
32
-1⎤⎡x⎤ ⎢ 1⎦⎣y⎦
⎡ 5⎤ = ⎢ (1, -2) ⎣-4⎦
2. a. -3.7 b. 17.0
7. C
c. -52
8. 5.3(1.3) - (0.8)(-2.7) = 9.05; -3.0(1.3) + 1.4(-2.7) = -7.68
d. The outlier decreases the mean from ≈1.7 to -3.7, and increases the standard deviation from ≈5.6 to ≈17.0.
9. 9x7y2 10. a. 6 meters
3. all real numbers 3t + 4 < 2(t + 3) + t; 3t + 4 < 3t + 6; 4 < 6
b. 36 square meters 11. a.
4. A 5. No; Possible explanation: Any even power of x is nonnegative, and any positive coefficient times any nonnegative value is nonnegative. So, the value of the polynomial is the sum of nonnegative values, and that sum is therefore nonnegative. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
LSN 32–2
A vertical shift of 30 units down transforms the first graph to the second.
Saxon Algebra 2
Lesson b. Quadrant I; time is positive and the lowest height is ground level. (Quadrant IV could make sense if scenario involved negative elevations.)
17. The student changed 5 - r to r - 5 without first factoring out -1. The numerator should be -2(r - 5), making the simplified 2 . expression -_ r-5 18. a. direct
⎡2 4 1⎤⎡x⎤ ⎡ 16⎤ 12. 1 -5 1 y = -5 1 1⎦⎣z⎦ ⎣ 7⎦ ⎣1
⎢
⎢ ⎢
⎡3 0 13. 0 15 0 ⎣0
4⎤⎡x⎤ ⎡13⎤ -2 y = 20 6⎦⎣ z⎦ ⎣ 6⎦
⎢
b. joint 2r + 2h 19. a. _ rh r + 2h b. _ rh
⎢ ⎢
c. The larger container is more economical because r + 2h 2r + 2h _ _ < . rh rh (r and h have only positive values.)
1 14. a = -2, h = _ , k = -5 2
15. Possible answer: Combine the like terms x, 4x, and -x to get 4x, and then write the terms in descending order by 2 degree to get -5x + 4x + 12. 16. 20 grams of Swiss cheese, 60 grams of ham, 40 grams of rye bread
© 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
32
20. a. ⎪x - 155⎥ < 25 b. 130 < x < 180 3
y 21. _ x
22. a. (x + 24)(x - 10) 2 2 = x + 14x - 240 ft b. (60) 2 + 14(60) - 240 = 4200 ft 2
LSN 32–3
Saxon Algebra 2
Lesson 23. Possible answer: To solve AX = B, both sides must be multiplied by A-1. To get X = BA-1, A-1 would have to be written as a matrix factor on the right of both sides of AX = B, and the result would be AXA-1 = BA-1. But the left side of this equation does not equal X. 24.
8 (f + g)(x) = 2x + 6 (-3, 0) -8
O
b. No solution; The second and third equations have coefficients that are multiples of each other but the constants are not multiples. c. No solution 29. x = 9 or x = -4 30. The middle term should be subtracted; the determinant is 5 - (-6) + 0 = 11.
y (0, 6) x 4
32
8
-4 -8
1 25. _ 2+x
26. x = -16, y = 9 17 27. -_ 2
28. a. 9x - y + 3z = -21 -8x + 4y - 6z = 10 56x - 28y + 42z = 2
© 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
LSN 32–4
Saxon Algebra 2
Warm Up 32 1. matrix
32
27.2⎤ -12.8⎦
g. x = 2, y = 0, z = -6
2. [-2 -6 8]
h. 150 grams of beans, 90 grams of chicken, 110 grams of rice
⎡2 14⎤ 3. ⎢ ⎣3 23⎦ Lesson Practice 32 a. yes b. no ⎡-1 c. A-1 = ⎢ ⎣-3
-2⎤ -5⎦
⎡0.5 d. B-1 = ⎢ ⎣ 0
0 ⎤ 0.5⎦
e.
© 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
LSN 32–1
Saxon Algebra 2
Lesson ⎡ 3 6. ⎢ ⎣-2
Practice 32 1. no
32
-1⎤⎡x⎤ ⎢ 1⎦⎣y⎦
⎡ 5⎤ = ⎢ (1, -2) ⎣-4⎦
2. a. -3.7 b. 17.0
7. C
c. -52
8. 5.3(1.3) - (0.8)(-2.7) = 9.05; -3.0(1.3) + 1.4(-2.7) = -7.68
d. The outlier decreases the mean from ≈1.7 to -3.7, and increases the standard deviation from ≈5.6 to ≈17.0.
9. 9x7y2 10. a. 6 meters
3. all real numbers 3t + 4 < 2(t + 3) + t; 3t + 4 < 3t + 6; 4 < 6
b. 36 square meters 11. a.
4. A 5. No; Possible explanation: Any even power of x is nonnegative, and any positive coefficient times any nonnegative value is nonnegative. So, the value of the polynomial is the sum of nonnegative values, and that sum is therefore nonnegative. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
LSN 32–2
A vertical shift of 30 units down transforms the first graph to the second.
Saxon Algebra 2
Lesson b. Quadrant I; time is positive and the lowest height is ground level. (Quadrant IV could make sense if scenario involved negative elevations.)
17. The student changed 5 - r to r - 5 without first factoring out -1. The numerator should be -2(r - 5), making the simplified 2 . expression -_ r-5 18. a. direct
⎡2 4 1⎤⎡x⎤ ⎡ 16⎤ 12. 1 -5 1 y = -5 1 1⎦⎣z⎦ ⎣ 7⎦ ⎣1
⎢
⎢ ⎢
⎡3 0 13. 0 15 0 ⎣0
4⎤⎡x⎤ ⎡13⎤ -2 y = 20 6⎦⎣ z⎦ ⎣ 6⎦
⎢
b. joint 2r + 2h 19. a. _ rh r + 2h b. _ rh
⎢ ⎢
c. The larger container is more economical because r + 2h 2r + 2h _ _ < . rh rh (r and h have only positive values.)
1 14. a = -2, h = _ , k = -5 2
15. Possible answer: Combine the like terms x, 4x, and -x to get 4x, and then write the terms in descending order by 2 degree to get -5x + 4x + 12. 16. 20 grams of Swiss cheese, 60 grams of ham, 40 grams of rye bread
© 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
32
20. a. ⎪x - 155⎥ < 25 b. 130 < x < 180 3
y 21. _ x
22. a. (x + 24)(x - 10) 2 2 = x + 14x - 240 ft b. (60) 2 + 14(60) - 240 = 4200 ft 2
LSN 32–3
Saxon Algebra 2
Lesson 23. Possible answer: To solve AX = B, both sides must be multiplied by A-1. To get X = BA-1, A-1 would have to be written as a matrix factor on the right of both sides of AX = B, and the result would be AXA-1 = BA-1. But the left side of this equation does not equal X. 24.
8 (f + g)(x) = 2x + 6 (-3, 0) -8
O
b. No solution; The second and third equations have coefficients that are multiples of each other but the constants are not multiples. c. No solution 29. x = 9 or x = -4 30. The middle term should be subtracted; the determinant is 5 - (-6) + 0 = 11.
y (0, 6) x 4
32
8
-4 -8
1 25. _ 2+x
26. x = -16, y = 9 17 27. -_ 2
28. a. 9x - y + 3z = -21 -8x + 4y - 6z = 10 56x - 28y + 42z = 2
© 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
LSN 32–4
Saxon Algebra 2
