Chapter 9

A month is selected at random; a number from 1 to 30 is selected at random.

Solve each equation. Check each solution. $$ \frac{x}{5}=\frac{x+3}{8} $$

Simplify each rational expression. State any restrictions on the variable. $$ \frac{2 x}{4 x^{2}-2 x} $$

Find any points of discontinuity for each rational function. $$ y=\frac{2 x^{2}+5}{x^{2}-2 x} $$

The focal length \(f\) of a camera lens is 2 in. The lens equation is \(\frac{1}{f}=\frac{1}{d_{i}}+\frac{1}{d_{o}}\) where \(d_{i}\) is the distance between the lens and the film and \(d_{o}\) is the distance between the lens and the object. The object to be photographed is 10 \(\mathrm{ft}\) away. How far should the lens be from the film?

Make a table of values. Then sketch a graph of each inverse variation. \(y=\frac{2}{x}\)

Suppose that \(x\) and \(y\) vary inversely. Write a function that models each inverse variation. $$ x=1 \text { when } y=11 $$

A month is selected at random; a day of that month is selected at random.

Solve each equation. Check each solution. $$ \frac{1}{5 x}=\frac{1}{9 x} $$

Simplify each rational expression. State any restrictions on the variable. $$ \frac{6 c^{2}+9 c}{3 c} $$

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

Make a table of values. Then sketch a graph of each inverse variation. \(y=\frac{10}{x}\)

Suppose that \(x\) and \(y\) vary inversely. Write a function that models each inverse variation. $$ x=-13 \text { when } y=100 $$

The focal length \(f\) of a camera lens is 2 in. The lens equation is \(\frac{1}{f}=\frac{1}{d_{i}}+\frac{1}{d_{o}}\) where \(d_{i}\) is the distance between the lens and the film and \(d_{o}\) is the distance between the lens and the object. The object to be photographed is 20 \(\mathrm{ft}\) away. How far should the lens be from the film?

A letter of the alphabet is selected at random; one of the remaining letters is selected at random.

Solve each equation. Check each solution. $$ \frac{4}{3 x+3}=\frac{12}{x^{2}-1} $$

Simplify each rational expression. State any restrictions on the variable. $$ \frac{b^{2}-1}{b-1} $$

$$ y=\frac{3 x-3}{x^{2}-1} $$

Make a table of values. Then sketch a graph of each inverse variation. \(y=-\frac{10}{x}\)

Suppose that \(x\) and \(y\) vary inversely. Write a function that models each inverse variation. $$ x=1 \text { when } y=1 $$

Solve each equation. Check each solution. $$ \frac{2}{x-1}=\frac{x+4}{3} $$

Simplify each rational expression. State any restrictions on the variable. $$ \frac{z^{2}-49}{z+7} $$

Find any points of discontinuity for each rational function. $$ y=\frac{6-3 x}{x^{2}-5 x+6} $$

Find the least common multiple of each pair of polynomials. 9\((x+2)(2 x-1)\) and 3\((x+2)\)

Draw a graph of each function. Describe properties of the graph. \(y=\frac{0.2}{x}\)

Suppose that \(x\) and \(y\) vary inversely. Write a function that models each inverse variation. $$ x=28 \text { when } y=-2 $$

\(\boldsymbol{Q}\) and \(\boldsymbol{R}\) are independent events. Find \(\boldsymbol{P}(\boldsymbol{Q} \text { and } \boldsymbol{R})\) $$ P(Q)=\frac{1}{4}, P(R)=\frac{2}{3} $$

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

Simplify each rational expression. State any restrictions on the variable. $$ \frac{2 x+10}{x^{2}+10 x+25} $$

Find any points of discontinuity for each rational function. $$ y=\frac{x^{2}+5 x+6}{x^{2}+6 x+9} $$

Find the least common multiple of each pair of polynomials. \(x^{2}-1\) and \(x^{2}+2 x+1\)

Draw a graph of each function. Describe properties of the graph. \(y=\frac{-3}{x}\)

Suppose that \(x\) and \(y\) vary inversely. Write a function that models each inverse variation. $$ x=1.2 \text { when } y=3 $$

\(\boldsymbol{Q}\) and \(\boldsymbol{R}\) are independent events. Find \(\boldsymbol{P}(\boldsymbol{Q} \text { and } \boldsymbol{R})\) $$ P(Q)=\frac{12}{17}, P(R)=\frac{3}{8} $$

Solve each equation. Check each solution. $$ \frac{4}{2 x-3}=\frac{x}{5} $$

Simplify each rational expression. State any restrictions on the variable. $$ \frac{x^{2}+8 x+16}{x^{2}-2 x-24} $$

Find any points of discontinuity for each rational function. $$ y=\frac{x^{2}+4 x+3}{2 x^{2}+5 x-7} $$

Find the least common multiple of each pair of polynomials. \((x-2)(x+3)\) and 10\((x+3)^{2}\)

Draw a graph of each function. Describe properties of the graph. \(y=\frac{8}{x}\)

Suppose that \(x\) and \(y\) vary inversely. Write a function that models each inverse variation. $$ x=2.5 \text { when } y=100 $$

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

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

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

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

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

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

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

\(\boldsymbol{Q}\) and \(\boldsymbol{R}\) are independent events. Find \(\boldsymbol{P}(\boldsymbol{Q} \text { and } \boldsymbol{R})\) $$ P(Q)=\frac{1}{3}, P(R)=\frac{6}{x} $$

Solve each equation. Check each solution. $$ \frac{10}{6 x+7}=\frac{6}{2 x+9} $$

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