Contents

Practice Test

In the following exercises, simplify.

613.

$\frac{3 a^{2} b}{6 a b^{2}} \frac{3 a^{2} b}{6 a b^{2}}$

614.

$\frac{5 b - 25}{b^{2} - 25} \frac{5 b - 25}{b^{2} - 25}$

In the following exercises, perform the indicated operation and simplify.

615.

$\frac{4 x}{x + 2} \cdot \frac{x^{2} + 5 x + 6}{12 x^{2}} \frac{4 x}{x + 2} \cdot \frac{x^{2} + 5 x + 6}{12 x^{2}}$

616.

$\frac{5 y}{4 y - 8} \cdot \frac{y^{2} - 4}{10} \frac{5 y}{4 y - 8} \cdot \frac{y^{2} - 4}{10}$

617.

$\frac{4}{p q} + \frac{5}{p} \frac{4}{p q} + \frac{5}{p}$

618.

$\frac{1}{z - 9} - \frac{3}{z + 9} \frac{1}{z - 9} - \frac{3}{z + 9}$

619.

$\frac{\frac{2}{3} + \frac{3}{5}}{\frac{2}{5}} \frac{\frac{2}{3} + \frac{3}{5}}{\frac{2}{5}}$

620.

$\frac{\frac{1}{m} - \frac{1}{n}}{\frac{1}{n} + \frac{1}{m}} \frac{\frac{1}{m} - \frac{1}{n}}{\frac{1}{n} + \frac{1}{m}}$

In the following exercises, solve each equation.

621.

$\frac{1}{2} + \frac{2}{7} = \frac{1}{x} \frac{1}{2} + \frac{2}{7} = \frac{1}{x}$

622.

$\frac{5}{y - 6} = \frac{3}{y + 6} \frac{5}{y - 6} = \frac{3}{y + 6}$

623.

$\frac{1}{z - 5} + \frac{1}{z + 5} = \frac{1}{z^{2} - 25} \frac{1}{z - 5} + \frac{1}{z + 5} = \frac{1}{z^{2} - 25}$

624.

$\frac{t}{4} = \frac{3}{5} \frac{t}{4} = \frac{3}{5}$

625.

$\frac{2}{r - 2} = \frac{3}{r - 1} \frac{2}{r - 2} = \frac{3}{r - 1}$

In the following exercises, solve.

626.

If $y y$ varies directly with $x, x,$ and $x = 5 x = 5$ when $y = 30, y = 30,$ find $x x$ when $y = 42 . y = 42 .$

627.

If $y y$ varies inversely with $x x$ and $x = 6 x = 6$ when $y = 20, y = 20,$ find $y y$ when $x = 2 . x = 2 .$

628.

If $y y$ varies inversely with the square of $x x$ and $x = 3 x = 3$ when $y = 9, y = 9,$ find $y y$ when $x = 4 . x = 4 .$

629.

The recommended erythromycin dosage for dogs, is 5 mg for every pound the dog weighs. If Daisy weighs 25 pounds, how many milligrams of erythromycin should her veterinarian prescribe?

630.

Julia spent 4 hours Sunday afternoon exercising at the gym. She ran on the treadmill for 10 miles and then biked for 20 miles. Her biking speed was 5 mph faster than her running speed on the treadmill. What was her running speed?

631.

Kurt can ride his bike for 30 miles with the wind in the same amount of time that he can go 21 miles against the wind. If the wind’s speed is 6 mph, what is Kurt’s speed on his bike?

632.

Amanda jogs to the park 8 miles using one route and then returns via a 14-mile route. The return trip takes her 1 hour longer than her jog to the park. Find her jogging rate.

633.

An experienced window washer can wash all the windows in Mike’s house in 2 hours, while a new trainee can wash all the windows in 7 hours. How long would it take them working together?

634.

Josh can split a truckload of logs in 8 hours, but working with his dad they can get it done in 3 hours. How long would it take Josh’s dad working alone to split the logs?

635.

The price that Tyler pays for gas varies directly with the number of gallons he buys. If 24 gallons cost him $59.76, what would 30 gallons cost?

636.

The volume of a gas in a container varies inversely with the pressure on the gas. If a container of nitrogen has a volume of 29.5 liters with 2000 psi, what is the volume if the tank has a 14.7 psi rating? Round to the nearest whole number.

637.

The cities of Dayton, Columbus, and Cincinnati form a triangle in southern Ohio, as shown on the figure below, that gives the map distances between these cities in inches.

This is an image of a triangle. Clockwise beginning at the top, each vertex is labeled. The top vertex is labeled “Dayton”, the next vertex is labeled “Columbus”, and the next vertex is labeled “Cincinnati”. The distance from Dayton to Columbus is 3.2 inches. The distance from Columbus to Cincinnati is 5.3 inches. The distance from Cincinnati to Dayton is 2.4 inches.

The actual distance from Dayton to Cincinnati is 48 miles. What is the actual distance between Dayton and Columbus?