91Ó°ÊÓ

Solve each equation. Check each solution. $$ \frac{3}{x}=\frac{12}{x+7} $$

Find the least common multiple of each pair of polynomials. \(12 x^{2}-6 x-126\) and \(18 x-63\)

Find any points of discontinuity for each rational function. $$ y=\frac{x^{3}-8}{x^{3}-8} $$

Draw a graph of each function. Describe properties of the graph. \(y=\frac{-5}{x}\)

\(\boldsymbol{Q}\) and \(\boldsymbol{R}\) are independent events. Find \(\boldsymbol{P}(\boldsymbol{Q} \text { and } \boldsymbol{R})\) $$ P(Q)=0.6, P(R)=0.9 $$

Multiply. State any restrictions on the variables. $$ \frac{4 x^{2}}{5 y} \cdot \frac{7 y}{12 x^{4}} $$

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. $$ \begin{array}{|c|c|c|c|c|}\hline x & {3} & {8} & {10} & {22} \\ \hline y & {15} & {40} & {50} & {110} \\ \hline\end{array} $$

Find any points of discontinuity for each rational function. $$ y=\frac{x^{2}}{x^{2}+1} $$

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. $$ \begin{array}{|c|c|c|c|c|}\hline x & {3} & {5} & {7} & {10.5} \\ \hline y & {14} & {8.4} & {6} & {4} \\ \hline\end{array} $$

Multiply. State any restrictions on the variables. $$ \frac{2 x^{4}}{10 y^{2}} \cdot \frac{5 y^{3}}{4 x^{3}} $$