Exam 7: Rational Expressions and Functions

Choose the one alternative that best completes the statement or answers the question. -The resistance of a wire varies directly as the length of the wire and inversely as the square of the diameter of the wire. A 20 foot length of wire with a diameter of 0.1 inch has a resistance of $3 \mathrm{ohms}$ . What would the resistance be for a 42 foot length, with diameter $0.01 \mathrm{inch}$ , of the same kind of wire ?

Multiply or divide. - $\frac{x-6}{(x+4)^{2}} \cdot \frac{x^{2}-2 x-24}{(x-6)^{2}}$

Solve the problem. Round your answer, as needed. -Dr. Wong can see 12 patients in 3 hours. At this rate, how long would it take her to see 48 patients?

The speed of a stream is $6 \mathrm{mph}$ . If a boat travels 56 miles downstream in the same time that it takes to travel 28 miles upstream, what is the speed of the boat in still water?

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 number of hours worked by an hourly worker and the amount of her paycheck

State whether the following situation represents direct variation, inverse variation, or neither, and explain why: The weight of a roast and the number of servings obtained from it.

Simplify the expression, using only positive exponents in your answer. - $\frac{x^{-2}-64 y^{-2}}{5 y-40 x}$

Give the first step in solving the given equation for $x$ . $x y+x z=y-z$

Find all numbers not in the domain of the function - $f(x)=\frac{x^{2}-16}{x^{2}+4 x-32}$

Add or subtract as indicated. Write the answer in lowest terms. - $\frac{4}{y^{2}-3 y+2}+\frac{7}{y^{2}-1}$

Simplify the expression, using only positive exponents in your answer. - $\frac{m^{-1}+z^{-1}}{m^{-1}-z^{-1}}$

Choose the one alternative that best completes the statement or answers the question. -If $x$ varies inversely as $v$ , and $x=6$ when $v=6$ , find $x$ when $v=12$ .

Determine whether the equation represents direct, inverse, joint, or combined variation. - $y=8 x^{2}$

Solve the problem. Round your answer, as needed. -If a boat uses 17 gallons of gas to go 67 miles, how many miles can the boat travel on 68 gallons of gas?

For the equation $\frac{p^{2}}{p^{2}+4 p}=1$ , would any numbers have to be rejected if they appeared as potential solutions? Explain.

Add or subtract as indicated. Write the answer in lowest terms. - $\frac{x}{x^{2}-16}-\frac{7}{x^{2}+5 x+4}$

Choose the one alternative that best completes the statement or answers the question. Solve the problem. Round your answer, as needed. -The distance of an object from a fulcrum is given by $d=\frac{D W}{W}$ . Find $D$ if $d=10, w=12$ , and $W=2$ .

Simplify the expression, using only positive exponents in your answer. - $\frac{x^{-9}+y^{-9}}{x^{-1}+y^{-1}}$

Perform the indicated operation and express in lowest terms. - $\frac{\mathrm{k}^{2}+14 \mathrm{k}+48}{\mathrm{k}^{2}+16 \mathrm{k}+64} \cdot \frac{\mathrm{k}^{2}+8 \mathrm{k}}{\mathrm{k}^{2}-2 \mathrm{k}-48}$

Sandi can make a quilt in 9 days and Eva can make a quilt in 6 days. In how many days can they make a quilt working together?