91Ó°ÊÓ

Factor the trinomial. $$8 x^{2}-14 x-15$$

A small-appliance manufacturer finds that if he produces \(x\) toaster ovens in a month, his production cost is given by the equation $$y=6 x+3000$$ (where \(y\) is measured in dollars). (a) Sketch a graph of this linear equation. (b) What do the slope and \(y\) -intercept of the graph represent?

Make a table of values and sketch the graph of the equation. Find the x- and y-intercepts and test for symmetry. $$y=\sqrt{4-x^{2}}$$

Simplify the fractional expression. (Expressions like these arise in calculus.) $$\frac{1}{\frac{1+x+h}{1+x}}-\frac{1}{h}$$

Simplify the expression and eliminate any negative exponent(s). Assume that all letters denote positive numbers. (a) \(\left(\frac{x^{-2 / 3}}{y^{1 / 2}}\right)\left(\frac{x^{-2}}{y^{-3}}\right)^{1 / 6}\) (b) \(\left(\frac{4 y^{3} z^{2 / 3}}{x^{1 / 2}}\right)^{2}\left(\frac{x^{-3} y^{6}}{8 z^{4}}\right)^{1 / 3}\)

Solve the nonlinear inequality. Express the solution using interval notation and graph the solution set. $$\frac{x+2}{x+3}<\frac{x-1}{x-2}$$

Evaluate each expression. (a) \(|(-2) \cdot 6|\) (b) \(\left|\left(-\frac{1}{3}\right)(-15)\right|\)

Evaluate each expression. (a) \(\left|\frac{-6}{24}\right|\) (b) \(\left|\frac{7-12}{12-7}\right|\)

Simplify the fractional expression. (Expressions like these arise in calculus.) $$\frac{\frac{1}{\sqrt{x+h}}-\frac{1}{\sqrt{x}}}{h}$$

Factor the trinomial.$$6 y^{2}+11 y-21$$