Find expressions for the revenue, cost, and profit from selling x thousand items.

$$\begin{array}{lll} \text{Item Price} & \text{Fixed Costs} & \text{Variable Costs}\\ \$8.50 & \$225,000 & 4200x \end{array}$$

Add or subtract as indicated in each of the following. Write all answers in lowest terms.

$$\frac{8}{y+2}-\frac{3}{y}$$

Fill in the blank with $<,=$, or $>$ so that the resulting statement is true.

$3 / 4$ $.75$

Which of the following statements are correct? Choose all that apply.

a.

$$\lim _{x \rightarrow 1^{+}} \frac{1}{1-x}$$

does not exist.

b.

$$\lim _{x \rightarrow 1^{+}} \frac{1}{1-x}=\infty.$$

c.

$$\lim _{x \rightarrow 1^{+}} \frac{1}{1-x}=-\infty.$$

Find expressions for the revenue, cost, and profit from selling x thousand items.

$$\begin{array}{lll} \text{Item Price} & \text{Fixed Costs} & \text{Variable Costs}\\ \$5.00 & \$200,000 & 1800x \end{array}$$

Add or subtract as indicated in each of the following. Write all answers in lowest terms.

$$\frac{1}{m-1}+\frac{2}{m}$$

Factor each polynomial completely. Factor out the greatest common factor as necessary.

$$3 a^2+2 a-5$$

Simplify each expression. Assume all variables represent positive real numbers. Write answers with only positive exponents.

$$\left(q^{-5} r^3\right)^{-1}$$

Use the quadratic formula to solve each equation. If the solutions involve square roots, give both the exact and approximate solutions.

$$1+\frac{7}{2 a}=\frac{15}{2 a^2}$$

Perform each operation.

$$\frac{2 m^2-4 m+2}{m^2-1} \div \frac{6 m+18}{m^2+2 m-3}$$

Fill in the blank with $<,=$, or $>$ so that the resulting statement is true.

$-6$ $-2$

Solve each equation.

$$\left|\frac{5}{r-3}\right|=10$$

Use the quadratic formula to solve each equation. If the solutions involve square roots, give both the exact and approximate solutions.

$$3 k^2+k=6$$

Is the absolute value of the sum of two numbers always equal to the sum of their absolute values? Explain.