For Exercises 15–20, solve the equations and inequalities. (See Example 3) a. − x 2 − 10 x − 9 = 0 b. − x 2 − 10 x − 9 < 0 c. − x 2 − 10 x − 9 ≤ 0 d. − x 2 − 10 x − 9 > 0 e. − x 2 − 10 x − 9 ≥ 0
For Exercises 15–20, solve the equations and inequalities. (See Example 3) a. − x 2 − 10 x − 9 = 0 b. − x 2 − 10 x − 9 < 0 c. − x 2 − 10 x − 9 ≤ 0 d. − x 2 − 10 x − 9 > 0 e. − x 2 − 10 x − 9 ≥ 0
Solution Summary: The author explains the formula used to determine the solution of the equation -x2-10x-9=0.
In Exercises 11–12, find the solution set for each equation.
11. |5x + 3| = 7
12. |6x + 1| = [4x + 15||
Exercises 38–40 will help you prepare for the material covered in
the first section of the next chapter.
In Exercises 38-39, simplify each algebraic expression.
38. (-9x³ + 7x? - 5x + 3) + (13x + 2r? – &x – 6)
39. (7x3 – 8x? + 9x – 6) – (2x – 6x? – 3x + 9)
40. The figures show the graphs of two functions.
y
y
201
10-
....
-20-
flx) = x³
glx) = -0.3x + 4x + 2
For Exercises 41–54, write the equation in the form (x – h + (y – k)' = c. Then if the equation represents a circle, identify
the center and radius. If the equation represents a degenerate case, give the solution set. (See Examples 3-4)
41. x +
y? -
+ 6x – 2y + 6 = 0
42. x + y + 12x – 14y + 84 = 0
43. x + y
22x + 6y + 129 = 0
44. x + y?
- 10x + 4y – 20 = 0
45. x + y - 20y – 4 = 0
46. x + y + 22x – 4 = 0
47. 10x + 10y² – 80x + 200y + 920 = 0
(Hint: Divide by 10 to make the x and y2
term coefficients equal to 1.)
48. 2x + 2y?
32x + 12y + 90 = 0
49. x + y? – 4x – 18y + 89 = 0
50. x + y - 10x –
22y + 155 = 0
51. 4x? + 4y
20y + 25 = 0
52. 4x + 4y?
12x + 9 = 0
53. x + y - x -
3
3
-y -
54. x + v?
2
= 0
= 0
9.
-X -
2
4
3
3
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