Exam 6: Rational Expression and Equations

The first bird can fly about 10 mph faster than the second one. In the same time that the first bird travels 120 miles, the second bird travels 70 miles. Find their flying speeds. The first bird: __________ mph The second bird: __________ mph

When a boat travels _________, the speed of the boat is decreased by the current.

Express the verbal model " P varies directly with the square of a and inversely with the cube of j " into symbols.

The equation $y = k x$ defines __________ variation.

It takes a printer 4 hours to print the class schedules for all of the students enrolled in a community college. A faster printer can print the schedules in 3 hours. How long will it take the two printers working together to print $\frac { 7 } { 8 }$ of the class schedules? __________ hr

Divide: $\frac { 80 x ^ { 9 } y ^ { 6 } + 10 x ^ { 3 } y ^ { 3 } } { 20 x ^ { 3 } y ^ { 2 } }$

An equation that states that two ratios are equal, such as $\frac { 1 } { 2 } = \frac { 4 } { 8 }$ , is called a __________.

To divide a polynomial by a monomial, divide each term of the polynomial by the __________.

A monument casts a shadow of 175 feet at the same time as a 6-foot tall person casts a shadow of 1.5 feet. How tall is the monument?

Let $P ( x ) = 4 x ^ { 3 } - 3 x ^ { 2 } + 4 x - 5$ . Evaluate $P ( 1 )$ by substituting the given value of xinto the polynomial and simplifying. Then evaluate the polynomial by using the remainder theorem and synthetic division.

Divide, then simplify if possible. $\frac { 2 r - 3 s } { 14 } \div \left( 4 r ^ { 2 } - 12 r s + 9 s ^ { 2 } \right)$

The table contains algebraic expressions for the rate an object travels, and the time traveled at that rate in terms of a constant. Complete the table by finding a . Rate (mph) Time (hr) Distance (mi) a a = __________

Perform the division. $\left( 16 y - 12 + 28 y ^ { 2 } \right) \div ( 7 y - 3 )$

Two right triangles are similar. The two legs of one triangle have lengths 1 and ( x + 1), and the corresponding legs of the other triangle have lengths $( x - 1 )$ and 1. Find the value of x .

If one printer can complete a job in 32 minutes and a second printer can finish the same print job in 48 minutes, how long will it take to complete the print job if the second printer starts 2 minutes after the first printer started?

Perform the operations and simplify the result when possible. $\frac { x + 3 } { 2 x ^ { 2 } - 5 x + 2 } - \frac { 3 x - 1 } { x ^ { 2 } - x - 2 }$

Divide, then simplify if possible. $16 n ^ { 2 } \div \frac { 10 n ^ { 3 } } { n - 5 }$

A boat can cruise at 35 mph in still water. What is its cruising speed downstream with a current of 5 mph? ______ mph

Perform the division. $x ^ { 2 } - 7$

Solve: $4 x ^ { - 2 } + 5 x ^ { - 1 } + 1 = 0$