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Problem 127
Rationalize each denominator. See Example 8. 3 ———— 4 + √5
Problem 129
Rationalize each denominator. See Example 8. 6/(√5 + √3)
Problem 131
Rationalize each denominator. See Example 8. (√3 + 1)/(1 - √3)
Problem 133
Rationalize each denominator. See Example 8. (√2 - √3)/(√6 - √5)
Problem 135
Simplify. See Example 9. (-√2/3)/(√7/3)
Problem 137
Simplify. See Example 9. (√7/5)/(√3/10)
Problem 139
Simplify. See Example 9. (1/2)/(1 - (√5/2))
Problem 141
Simplify. See Example 9. (√3/2)/(1 - (√3/2))
Problem 147
For Individual or Group Work (Exercises 147 – 150)In calculus, it is sometimes desirable to rationalize a numerator. To do this, we multiply the numerator and the denominator by the conjugate of the numerator. For example, (6 - √2)/4 = (6 - √2)/4 × (6 + √2)/(6 + √2) = (36 - 2)/(4(6 + √2)) = 34/(4(6 + √2)) = 17/(2(6 + √2)) = 17/(6 + √2). Rationalize each numerator. (6 - √3)/8
Problem 149
For Individual or Group Work (Exercises 147 – 150)In calculus, it is sometimes desirable to rationalize a numerator. To do this, we multiply the numerator and the denominator by the conjugate of the numerator. For example, (6 - √2)/4 = (6 - √2)/4 × (6 + √2)/(6 + √2) = (36 - 2)/(4(6 + √2)) = 34/(4(6 + √2)) = 17/(2(6 + √2)) = 17/(6 + √2).
2√10 + √7 30
Problem 6
CONCEPT PREVIEW Which one is not a linear equation? A. 5x + 7 (x - 1) = -3x B. 9x² - 4x + 3 = 0 C. 7x + 8x = 13 D. 0.04x - 0.08x = 0.40
Problem R.6.93
Solve each inequality. Give the solution set using interval notation. See Example 10. -5 < 5 + 2x < 11
Problem R.6.51
Solve each quadratic equation using the zero-factor property. See Example 5. 25x² + 30x + 9 = 0
Problem R.6.61
Solve each quadratic equation using the quadratic formula. See Example 7. 2x² - x - 28 = 0
Problem R.6.37
Determine whether each equation is an identity, a conditional equation, or a contradiction. Give the solution set. See Example 4. -2(x + 3) = -6(x + 7)
Problem R.6.42
Solve each quadratic equation using the zero-factor property. See Example 5.
x² + 2x - 8 = 0
Problem R.6.69
Solve each quadratic equation using the quadratic formula. See Example 7. -2x² + 4x + 3 = 0
Problem R.6.75
Solve each inequality. Give the solution set using interval notation. See Examples 8 and 9. 5x +2 ≤ -48
Problem R.6.47
Solve each quadratic equation using the zero-factor property. See Example 5. x² - 100 = 0
Problem R.6.70
Solve each quadratic equation using the quadratic formula. See Example 7.
-3x² + 6x + 5 = 0
Problem R.6.57
Solve each quadratic equation using the square root property. See Example 6. (3x - 1)² = 12
Problem R.6.43
Solve each quadratic equation using the zero-factor property. See Example 5. 5x² - 3x - 2 = 0
Problem R.6.59
Solve each quadratic equation using the quadratic formula. See Example 7. x² - 4x + 3 = 0
Problem R.6.91
Solve each inequality. Give the solution set using interval notation. See Example 10. -9 ≤ x + 5 ≤ 15
Problem R.6.77
Solve each inequality. Give the solution set using interval notation. See Examples 8 and 9. -2x + 8 ≤ 16
Problem R.6.99
Solve each inequality. Give the solution set using interval notation. See Example 10.
- 4 ≤ (x + 1)/2 ≤ 5
Problem R.6.53
Solve each quadratic equation using the square root property. See Example 6. x² = 16
Problem R.6.39
Determine whether each equation is an identity, a conditional equation, or a contradiction. Give the solution set. See Example 4. 4(x + 7) = 2(x + 12) + 2(x + 1)
Problem R.6.81
Solve each inequality. Give the solution set using interval notation. See Examples 8 and 9. -3(x - 6) > 2x - 2
Problem R.6.55
Solve each quadratic equation using the square root property. See Example 6. x² - 27 = 0