1. Equations & Inequalities

Solve each equation in Exercises 47–64 by completing the square. $3x^2-2x-2=0$

Solve each equation using the quadratic formula. -4x² = -12x + 11

Solve each equation for the specified variable. (Assume no denominators are 0.) F = kMv²/r , for v

Use Choices A–D to answer each question. A. 3x² - 17x - 6 = 0 B. (2x + 5)² = 7 C. x² + x = 12 D. (3x - 1)(x - 7) = 0 Only one of the equations is set up so that the values of a, b, and c can be determined immediately. Which one is it? Solve it.

Solve each equation using the zero-factor property. x² - 5x + 6 = 0

Radius of a Can A can of Blue Runner Red Kidney Beans has surface area 371 cm². Its height is 12 cm. What is the radius of the circular top? Round to the nearest hundredth.

Solve each equation for the specified variable. (Assume no denominators are 0.) See Example 8. $s=\left(\frac{1}{2}\right)g{t}^2$, for t

Solve each equation using the zero-factor property. x² - 64 = 0

In Exercises 109–114, find the x-intercept(s) of the graph of each equation. Use the x-intercepts to match the equation with its graph. The graphs are shown in [- 10, 10, 1] by [- 10, 10, 1] viewing rectangles and labeled (a) through (f). y = x² - 2x + 2

Length of a Walkway A nature conservancy group decides to construct a raised wooden walkway through a wetland area. To enclose the most interesting part of the wetlands, the walkway will have the shape of a right triangle with one leg 700 yd longer than the other and the hypotenuse 100 yd longer than the longer leg. Find the total length of the walkway.

Solve each equation using the zero-factor property. -6x² + 7x = -10

Solve each equation using the zero-factor property. x² + 2x - 8 = 0

Use the following facts. If x represents an integer, then x+1 represents the next consecutive integer. If x represents an even integer, then x+2 represents the next consecutive even integer. If x represents an odd integer, then x+2 represents the next consecutive odd integer. Find two consecutive odd integers whose product is 63.

Solve each equation using the quadratic formula. x² = 2x - 5

Solve each equation in Exercises 83–108 by the method of your choice. 3/(x - 3) + 5/(x - 4) = (x² - 20)/(x² - 7x + 12)