Exam 7: Rational Expressions and Functions

Choose the one alternative that best completes the statement or answers the question. Solve the problem. Round your answer, as needed. -Calculate an average rate of speed for $\mathrm{v}=4.7 \mathrm{mph}$ and $\mathrm{d}=6.4 \mathrm{mph}$ in the formula $A=\frac{2 D}{\frac{D}{d}+\frac{D}{v}}$ .

Multiply or divide. - $\frac{8 x+16}{x-1} \cdot \frac{3 x^{2}-6 x+3}{x^{2}-4}$

Solve the problem. Round your answer, as needed. -Doug and Inga can deliver 50 papers in 2 hours. How long would it take them to deliver 55 papers?

Choose the one alternative that best completes the statement or answers the question. Simplify the complex fraction - $\frac{\frac{y}{4}}{\frac{3}{y-4}}$

Solve the problem. Round your answer, as needed. -Dr. Taylor can see 6 patients in 3 hours. At this rate, how long would it take him to see 18 patients?

Graph the function. Give the equations of its vertical and horizontal asymptotes. - $f(x)=\frac{1}{x-2}$

Perform the indicated operation and express in lowest terms. - $\frac{z^{2}+9 z+14}{z^{2}+13 z+42} \div \frac{z^{2}+2 z}{z^{2}+15 z+54}$

Choose the one alternative that best completes the statement or answers the question. -The volume $\mathrm{V}$ of a given mass of gas varies directly as the temperature $\mathrm{T}$ and inversely as the pressure $\mathrm{P}$ . If $\mathrm{V}=588.0$ in. ${ }^{3}$ when $\mathrm{T}=490^{\circ}$ and $\mathrm{P}=10 \mathrm{lb} / \mathrm{in} .{ }^{2}$ , what is the volume when $\mathrm{T}=220^{\circ}$ and $\mathrm{P}=15 \mathrm{lb} / \mathrm{in} .2$ ?

Assume that the expressions given are denominators of fractions. Find the least common denominator. - $a+b, a-b, a^{2}-b^{2}$

Choose the one alternative that best completes the statement or answers the question. Determine whether the variation between the indicated quantities is direct or inverse. -The weight of a baby in pounds and his age in months

The resistance, in ohms, of a 25 foot piece of wire is given by the function $R(d)=\frac{0.025}{d^{2}}$ , where $d$ is the diameter of the wire in inches. What happens to the resistance of the wire as the diameter of the wire decreases?

Solve the formula for the specified variable. - $\frac{P V}{T}=\frac{p v}{t}$ for $P$

Assume that the expressions given are denominators of fractions. Find the least common denominator. - $15 \mathrm{a}^{3} \mathrm{~b}^{4}, 20 \mathrm{a}^{2} \mathrm{~b}^{5}$

Perform the indicated operation and express in lowest terms. - $\frac{3 x+16}{x^{2}+3 x-10}-\frac{x+6}{x^{2}+3 x-10}$

Solve the problem. Round your answer, as needed. -Mara can type 57 words per minute. How many words would she type in $\frac{1}{3}$ hour (20 minutes)?

Perform the indicated operation and express in lowest terms. - $\frac{m^{2}-7 m}{m-4}+\frac{12}{m-4}$

Tell whether or not the rational expressions are equivalent. - $\frac{\mathrm{a}^{2}-\mathrm{b}^{2}+\mathrm{c}^{2}}{\mathrm{~b}-\mathrm{c}}, \frac{\mathrm{a}^{2}-\mathrm{b}^{2}+\mathrm{c}^{2}}{\mathrm{c}+\mathrm{b}}$

Determine whether the equation represents direct, inverse, joint, or combined variation. - $f$ -stop $=f / D$ , where $f$ -stop is camera setting with a lens with focal length $f$ and diaphragm opening $\mathrm{D}$

Choose the one alternative that best completes the statement or answers the question. -If the height of a rectangular solid is held constant, the volume varies jointly with the length and the width. If the volume is 160 cubic inches when the length is 8 inches and the width is 5 inches, find the volume when the length is 7 inches and the width is 6 inches.

Solve the problem. Round your answer, as needed. -Maria and Charlie can deliver 75 papers in 3 hours. How long would it take them to deliver 90 papers?