91Ó°ÊÓ

For the given polynomial \(P(x)\) and the given \(c,\) use the remainder theorem to find \(P(c)\). $$ P(x)=4 x^{3}+5 x^{2}-6 x-4 ;-2 $$

Write each sentence as an equation and solve. The sum of two consecutive integers is \(147 .\)

The numerator of a fraction is 4 less than the denominator. If both the numerator and the denominator are increased by 2 the resulting fraction is equivalent to \(\frac{2}{3}\). Find the fraction.

In 2 minutes, a conveyor belt can move 300 pounds of recyclable aluminum from the delivery truck to a storage area. A smaller belt can move the same quantity of cans the same distance in 6 minutes. If both belts are used, find how long it takes to move the cans to the storage area.

Simplify. See Sections 5.1 and \(5.2 .\) $$ \frac{3 x^{3} y^{2}}{12 x} $$

Write each sentence as an equation and solve. The length of a rectangle is 5 inches more than the width. Its perimeter is 50 inches. Find the length and width.

Add or subtract as indicated. If possible, simplify your answer. See Examples I through 6. $$ \frac{4}{3 x^{2} y^{3}}+\frac{5}{3 x^{2} y^{3}} $$

For the given polynomial \(P(x)\) and the given \(c,\) use the remainder theorem to find \(P(c)\). $$ P(x)=4 x^{4}+x^{2}-2 ;-1 $$

Write an equation to describe each variation. Use k for the constant of proportionality. See Examples 1 through 7. \(y\) varies inversely as \(x^{3}\)

Write an equation to describe each variation. Use k for the constant of proportionality. See Examples 1 through 7. \(y\) varies inversely as \(a^{4}\)