91Ó°ÊÓ

Describe the vertical asymptotes and holes for the graph of each rational function. $$ y=\frac{x+5}{x+5} $$

Solve each equation. Check each solution. $$ \frac{y}{5}+\frac{y}{2}=7 $$

Simplify each sum. \(\frac{d-3}{2 d+1}+\frac{d-1}{2 d+1}\)

The weight \(P\) in pounds that a beam can safely carry is inversely proportional to the distance \(D\) in feet between the supports of the beam. For a certain type of wooden beam, \(P=\frac{9200}{D} .\) Use a graphing calculator and the Intersect feature to find the distance between supports that is needed to carry each given weight. 1200 \(\mathrm{lb}\)

Two standard number cubes are tossed. State whether the events are mutually exclusive. Explain your reasoning. The numbers are equal; the sum is odd.

Describe the vertical asymptotes and holes for the graph of each rational function. $$ y=\frac{x+3}{(2 x+3)(x-1)} $$

Solve each equation. Check each solution. $$ \frac{2 x}{3}-\frac{1}{2}=\frac{2 x+5}{6} $$

Two standard number cubes are tossed. State whether the events are mutually exclusive. Explain your reasoning. The product is greater than \(20 ;\) the product is a multiple of \(3 .\)

Multiply. State any restrictions on the variables. $$ \frac{x^{2}-5 x+6}{x^{2}-4} \cdot \frac{x^{2}+3 x+2}{x^{2}-2 x-3} $$

Is the relationship between the values in each table a direct variation, an inverse variation, or neither? Write equations to model the direct and inverse variations. $$ \begin{array}{|c|c|c|c|c|}\hline x & {10} & {12} & {20} & {23} \\ \hline y & {2} & {2 \frac{2}{5}} & {4} & {5 \frac{3}{5}} \\ \hline\end{array} $$