Exam 7: Rational Expressions and Equations

The first bird can fly about 20 mph faster than the second one. In the same time that the first bird travels 120 miles, the second bird travels 60 miles. Find their flying speeds.

Assume that all variables represent positive numbers. Assume that $d$ varies directly with t . If $d = 24$ when $t = 4$ , find t when $d = 4$ .

Simplify the complex fraction. $\frac { \frac { 7 } { 6 x } } { \frac { 14 } { 3 x y } }$

Simplify the complex fraction. $\frac { \frac { 1 } { 2 } - \frac { 1 } { 4 } } { \frac { 5 } { 6 } + \frac { 3 } { 4 } }$

A jaguar can run 54 mph. How fast is this in kilometers per hour? Round your answer to the nearest tenth. __________ km\h

Convert 6 meters per minute to kilometers per hour.

Change the fraction $\frac { 4 y } { p }$ into an equivalent fraction with the denominator p ² + p .

Write a fraction in simplified form that expresses the ratio of 0.24 to 0.32.

Write the expression in lowest terms. If the expression is already in lowest terms, so indicate. Assume that the denominator does not equal zero. $\frac { x + 3 } { 9 ( x + 3 ) }$

Use similar triangles to help solve the problem. A man places a mirror on the ground and sees the reflection of the top of a flagpole as shown in the figure below. The two triangles in the figure are similar. Find the height h of the flagpole. a = 13, b = 4, c = 34

Solve the proportion for the variable. $\frac { 4 } { y } = \frac { 6 } { 30 }$ y = __________

If the same number is added to both the numerator and the denominator of $\frac { 1 } { 9 }$ , the result is $\frac { 3 } { 11 }$ .Find the number.

Simplify the complex fraction. $\frac { - \frac { 2 } { x } - \frac { 4 } { x + 2 } } { \frac { 7 } { x ^ { 2 } + 2 x } + \frac { 7 } { x } }$

Convert 98 m³ to liters.

Solve the proportion for the variable. $\frac { 5 } { 5 z + 3 } = \frac { 2 z } { 2 z ^ { 2 } + 6 }$ z = __________

A recipe for spaghetti sauce requires 6 bottles of ketchup to make 8 gallons of sauce. How many bottles of ketchup are needed to make 56 gallons of sauce?

Two certificates of deposit (CDs)pay interest at rates that differ by 4%. Money invested for 1 year in the first CD earns $90 interest. The same principal invested in the second CD earns $150. Find the two rates of interest.

Solve the equation and check the solution. $\frac { 3 x - 1 } { 6 } - \frac { x + 3 } { 2 } = \frac { 3 x + 1 } { 3 }$

Simplify the complex fraction: $\frac { \frac { 14 } { 2 } } { \frac { 10 } { 6 } }$

Perform the operation. Simplify the answer, if possible. $\frac { a } { a - 5 } + \frac { 25 + 5 a } { a ^ { 2 } - 25 }$