Lesson Warm Up 36 1. point-slope 2. 1.25 3. y = x - 4
Lesson
36
Warm Up 36 1. point-slope 2. 1.25 3 x-4 3. y = _ 7
Lesson Practice 36 a. The lines are parallel. b. The lines are perpendicular. c. y = -13x + 15 d. y = -.04x + 37.04 e. The lines are parallel. f. The lines are perpendicular. g. x = 21 h. y = 5 i. The slope of the line that crosses (-1, 6) 3 and (3, 3) is -_ 4
© 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
LSN 36–1
Saxon Algebra 2
Lesson Practice 36 7 1. - _ 4 1 2. _ 2
3. No variation 4. Direct when b = 0 5. x6y-12
36
11. Instead of correctly using x2 + bx + c = (x + u)(x + v) with u + v = b and uv = c, Carmen wrote u + v = c, and uv = b. 12. The graph of the linear function is a connected graph.
6. m9p-3
8
7. x = -1, x = 5
O
y
4 -8
-4
10. Possible answer: Write the denominator as a product of four algebraic expressions so that when each expression is set equal to zero, the solution is different. The excluded values 1 for __ x(x - 1)(x + 1)(x - 2) are 0, 1, -1, and 2.
8
-4
8. x = 2.25, y = 0.6 1 1 _ x y = 9. _ 7 11
x 4
13. x = -5 2x 3 14. _ 3
15. x(x + 25) = 1250 x2 + 25x = 1250 x2 + 25x - 1250 = 0 (x + 50)(x - 25) = 0 x = -50 or x = 25 Choose the positive solution. x = 25 and x + 25 = 50. The dimensions are 25 meters and 50 meters. 16. x = 77, y = 72, z = 31
© 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
LSN 36–2
Saxon Algebra 2
Lesson 17. y = -136x2 + 1,904x - 1644 18. Rate of change = 2; Possible description: The fare increases $2.00 per mile, or $0.40 for every 0.2 mile.
36
25. If a were zero, then there would be no term raised to the second power because zero times any number is zero. The function would be linear. 26. C
Fare ($)
12
27. a.
8 4 0
(c, d) 2 4 Miles
(a + c, b + d)
(a, b)
19. x = 5t and y = 20t 20. Student B incorrectly transposed the coordinates.
b. Area of parallelogram is (a + c)(b + d) ab - cd - 2bc.
21. B
c. Area of parallelogram simplifies to the determinant ad - bc.
22. Yes. The line containing (-4, 6) and (4, 4) is perpendicular to the line containing (4, 4) and (1, -8).
28. 1320
23. The minimum is $840.50; week 22 24. x = -1 and x = -6
© 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
LSN 36–3
Saxon Algebra 2
Lesson
36
29. Plot the vertex (2, 2), find the value of y for several values of x that are either all less than 2 or greater than 2, and plot those ordered pairs. Sketch the axis of symmetry, x = 2, and plot the points that are mirror images of the points already found. 30. A
© 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
LSN 36–4
Saxon Algebra 2
36
Warm Up 36 1. point-slope 2. 1.25 3 x-4 3. y = _ 7
Lesson Practice 36 a. The lines are parallel. b. The lines are perpendicular. c. y = -13x + 15 d. y = -.04x + 37.04 e. The lines are parallel. f. The lines are perpendicular. g. x = 21 h. y = 5 i. The slope of the line that crosses (-1, 6) 3 and (3, 3) is -_ 4
© 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
LSN 36–1
Saxon Algebra 2
Lesson Practice 36 7 1. - _ 4 1 2. _ 2
3. No variation 4. Direct when b = 0 5. x6y-12
36
11. Instead of correctly using x2 + bx + c = (x + u)(x + v) with u + v = b and uv = c, Carmen wrote u + v = c, and uv = b. 12. The graph of the linear function is a connected graph.
6. m9p-3
8
7. x = -1, x = 5
O
y
4 -8
-4
10. Possible answer: Write the denominator as a product of four algebraic expressions so that when each expression is set equal to zero, the solution is different. The excluded values 1 for __ x(x - 1)(x + 1)(x - 2) are 0, 1, -1, and 2.
8
-4
8. x = 2.25, y = 0.6 1 1 _ x y = 9. _ 7 11
x 4
13. x = -5 2x 3 14. _ 3
15. x(x + 25) = 1250 x2 + 25x = 1250 x2 + 25x - 1250 = 0 (x + 50)(x - 25) = 0 x = -50 or x = 25 Choose the positive solution. x = 25 and x + 25 = 50. The dimensions are 25 meters and 50 meters. 16. x = 77, y = 72, z = 31
© 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
LSN 36–2
Saxon Algebra 2
Lesson 17. y = -136x2 + 1,904x - 1644 18. Rate of change = 2; Possible description: The fare increases $2.00 per mile, or $0.40 for every 0.2 mile.
36
25. If a were zero, then there would be no term raised to the second power because zero times any number is zero. The function would be linear. 26. C
Fare ($)
12
27. a.
8 4 0
(c, d) 2 4 Miles
(a + c, b + d)
(a, b)
19. x = 5t and y = 20t 20. Student B incorrectly transposed the coordinates.
b. Area of parallelogram is (a + c)(b + d) ab - cd - 2bc.
21. B
c. Area of parallelogram simplifies to the determinant ad - bc.
22. Yes. The line containing (-4, 6) and (4, 4) is perpendicular to the line containing (4, 4) and (1, -8).
28. 1320
23. The minimum is $840.50; week 22 24. x = -1 and x = -6
© 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
LSN 36–3
Saxon Algebra 2
Lesson
36
29. Plot the vertex (2, 2), find the value of y for several values of x that are either all less than 2 or greater than 2, and plot those ordered pairs. Sketch the axis of symmetry, x = 2, and plot the points that are mirror images of the points already found. 30. A
© 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
LSN 36–4
Saxon Algebra 2
