Lesson Warm Up 44 1. radicand 2. - 3. 8 â 6 4. 20 Lesson Practice 44 ...
Lesson
44
Warm Up 44 1. radicand 1 2. - _ 3
6 3. 8 √ 4. 20 Lesson Practice 44 2 √ 7 a. _ 35 √ 15 b. _ 10
4 + 2 √ 7 -4 - 2 √ 7 _ c. _ or -3 3
d.
√ 4_ 6 - √ 3 93
5 e. -2 - √
© 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
LSN 44–1
Saxon Algebra 2
Lesson Practice 44
44
8. Sample: 10 items taken 4 at a time C(10,4) = 210 and 10 items taken 6 at a time C(10,6) = 210 are the same. Another way to think of this is that when you take 4 items from 10 you leave 6 items behind. The number of ways you can take 4 must be the same as the number of ways you can leave 6 items behind.
5 √ 3 1. _ 9 8 - 4 √ 7
2. - _ 3 3 √ 10 3. _ 10
4. 5.4 miles 5. infinitely many solutions 6. The incorrect half-plane is shaded for 2x - y ≤ 2. Correct graph: y 6 4
9. About 6.7 seconds O
x 2
4
6
7. Each letter of the alphabet is replaced with a number.
10. B 11. No. The quadratic has no factors of the form x + d; therefore, dividing by x + d will result in a nonzero remainder. 12. a. No. A triangle can be both obtuse and isosceles; b. Yes. A triangle cannot be both acute and right.
© 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
LSN 44–2
Saxon Algebra 2
Lesson 13. y1 = y4
22. Student B. Student A incorrectly exchanges the x and y coordinates in the point-slope form.
14. x2yz(xyz2 + z - 3x) 3(x + 1) 15. _ 2x
⎡ .15 16. A´ = ⎢ ⎣-.05
44
2
23. 3x + 6x + 8 ft
.025⎤ .075⎦
24. 4mp2y(4mp - 2py3 + my)
17. The graph of y = 5x 2 is narrower.
25. The maximum length is 11.5 inches and the maximum height is 6 inches.
18. a. 2x + 3y - 2z = 0 4x + 5y - 4z = 0 3x - 2y + 5z = 0
3 2 1 ; 26. x - x + x - 1 - _ x+1 1 (x3 - x2 + x - 1 - _ x + 1)
b. One solution; No two equations are multiples of each other in any way.
4 (x + 1) = x - 1 x+1 = x4 - 2 -_ x+1
c. (0, 0, 0) 19. About 37.8 feet 20. a = 3, b = 0, c = 0 21. No real zeros; Possible explanation: Because a < 0, the graph opens down. Because the graph opens down and the vertex is in Quadrant III, the graph does not intersect the x-axis. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
27. Sample: One way is to pick a point in either half-plane. If the point is a solution, then shade that half-plane; if the point is not a solution, then shade the other half-plane. Another way is to solve the inequality for 1 x + 3. y, getting y > - _ 2 Because this has the form y > mx + b, shade above the boundary line.
LSN 44–3
Saxon Algebra 2
Lesson
44
28. a. -1 or -13 b. (6, -1) 29. If the order of the flavors is not important, for example if the frozen yogurt was in a dish, use combinations: C(5,3) = 10. If the order of the flavors is important, for example if the flavors were stacked in a cone, use permutations P(5,3) = 60. 27 ; 30. -3x + 6x - 12 - _ -x - 2 2
27 (-x - 2) (-3x2 + 6x - 12 - _ -x - 2 ) 27(x + 2) = 3x 3 + _ + 24 -x - 2 3 = 3x - 3
© 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
LSN 44–4
Saxon Algebra 2
44
Warm Up 44 1. radicand 1 2. - _ 3
6 3. 8 √ 4. 20 Lesson Practice 44 2 √ 7 a. _ 35 √ 15 b. _ 10
4 + 2 √ 7 -4 - 2 √ 7 _ c. _ or -3 3
d.
√ 4_ 6 - √ 3 93
5 e. -2 - √
© 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
LSN 44–1
Saxon Algebra 2
Lesson Practice 44
44
8. Sample: 10 items taken 4 at a time C(10,4) = 210 and 10 items taken 6 at a time C(10,6) = 210 are the same. Another way to think of this is that when you take 4 items from 10 you leave 6 items behind. The number of ways you can take 4 must be the same as the number of ways you can leave 6 items behind.
5 √ 3 1. _ 9 8 - 4 √ 7
2. - _ 3 3 √ 10 3. _ 10
4. 5.4 miles 5. infinitely many solutions 6. The incorrect half-plane is shaded for 2x - y ≤ 2. Correct graph: y 6 4
9. About 6.7 seconds O
x 2
4
6
7. Each letter of the alphabet is replaced with a number.
10. B 11. No. The quadratic has no factors of the form x + d; therefore, dividing by x + d will result in a nonzero remainder. 12. a. No. A triangle can be both obtuse and isosceles; b. Yes. A triangle cannot be both acute and right.
© 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
LSN 44–2
Saxon Algebra 2
Lesson 13. y1 = y4
22. Student B. Student A incorrectly exchanges the x and y coordinates in the point-slope form.
14. x2yz(xyz2 + z - 3x) 3(x + 1) 15. _ 2x
⎡ .15 16. A´ = ⎢ ⎣-.05
44
2
23. 3x + 6x + 8 ft
.025⎤ .075⎦
24. 4mp2y(4mp - 2py3 + my)
17. The graph of y = 5x 2 is narrower.
25. The maximum length is 11.5 inches and the maximum height is 6 inches.
18. a. 2x + 3y - 2z = 0 4x + 5y - 4z = 0 3x - 2y + 5z = 0
3 2 1 ; 26. x - x + x - 1 - _ x+1 1 (x3 - x2 + x - 1 - _ x + 1)
b. One solution; No two equations are multiples of each other in any way.
4 (x + 1) = x - 1 x+1 = x4 - 2 -_ x+1
c. (0, 0, 0) 19. About 37.8 feet 20. a = 3, b = 0, c = 0 21. No real zeros; Possible explanation: Because a < 0, the graph opens down. Because the graph opens down and the vertex is in Quadrant III, the graph does not intersect the x-axis. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
27. Sample: One way is to pick a point in either half-plane. If the point is a solution, then shade that half-plane; if the point is not a solution, then shade the other half-plane. Another way is to solve the inequality for 1 x + 3. y, getting y > - _ 2 Because this has the form y > mx + b, shade above the boundary line.
LSN 44–3
Saxon Algebra 2
Lesson
44
28. a. -1 or -13 b. (6, -1) 29. If the order of the flavors is not important, for example if the frozen yogurt was in a dish, use combinations: C(5,3) = 10. If the order of the flavors is important, for example if the flavors were stacked in a cone, use permutations P(5,3) = 60. 27 ; 30. -3x + 6x - 12 - _ -x - 2 2
27 (-x - 2) (-3x2 + 6x - 12 - _ -x - 2 ) 27(x + 2) = 3x 3 + _ + 24 -x - 2 3 = 3x - 3
© 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
LSN 44–4
Saxon Algebra 2
