Chapter 8

Determine whether \(\frac{2 d+5}{3 d+5}=\frac{2}{3}\) is sometimes, always, or never true. Explain.

Find all of the zeros of each function. $$ g(x)=x^{4}-8 x^{2}-9 $$

PREREQUISITE SKILL Solve each proportion. $$ \frac{16}{v}=\frac{32}{9} $$

Identify each function as S for step, C for constant, A for absolute value, or P for piecewise. \(h(x)=|x-2|\)

Find all of the zeros of each function. $$ h(x)=3 x^{3}-5 x^{2}+13 x-5 $$

PREREQUISITE SKILL Solve each proportion. $$ \frac{7}{25}=\frac{a}{5} $$

Identify each function as S for step, C for constant, A for absolute value, or P for piecewise. \(g(x)=-3\)

For what value(s) of \(x\) is \(\frac{4 x}{x^{2}-x}\) undefined? A -1, 1 B -1, 0, 1 C 0, 1 D 0

GARDENS Helene Jonson has a rectangular garden 25 feet by 50 feet. She wants to increase the garden on all sides by an equal amount. If the area of the garden is to be increased by 400 square feet, by how much should each dimension be increased?

PREREQUISITE SKILL Solve each proportion. $$ \frac{6}{15}=\frac{8}{S} $$

Which is the simplified form of \(\frac{4 x^{3} y^{2} z^{-1}}{\left(x^{-2} y^{3} z^{2}\right)^{2}} ?\) F. \(\frac{4 x^{7}}{y^{4} z^{5}}\) G. \(\frac{4 x y}{z^{5}}\) H. \(\frac{4}{y^{3} z^{5}}\) J. \(\frac{4}{x y^{4} z^{5}}\)

Three times a number added to four times a second number is \(22 .\) The second number is two more than the first number. Find the numbers.

PREREQUISITE SKILL Solve each proportion. $$ \frac{b}{9}=\frac{40}{30} $$

Graph each function. State the domain and range. \(y=\sqrt{x-2}\)

Factor each polynomial. $$ x^{2}+3 x+2 $$

Graph each function. State the domain and range. \(y=\sqrt{x}-1\)

Factor each polynomial. $$ x^{2}-6 x+5 $$

Graph each function. State the domain and range. \(y=2 \sqrt{x}+1\)

Factor each polynomial. $$ x^{2}+11 x-12 $$

Determine whether \(f(x)=x-2\) and \(g(x)=2 x\) are inverse functions.

Factor each polynomial. $$ x^{2}-16 $$

Factor each polynomial. $$ 3 x^{2}-75 $$

Factor each polynomial. $$ x^{3}-3 x^{2}+4 x-12 $$

Earth is an average of \(1.496 \times 10^{8}\) kilometers from the Sun. If light travels \(3 \times 10^{5}\) kilometers per second, how long does it take sunlight to reach Earth?

Solve each equation by factoring. \(r^{2}-3 r=4\)

Solve each equation by factoring. \(18 u^{2}-3 u=1\)

Solve each equation by factoring. \(d^{2}-5 d=0\)

Solve each equation. \(|2 x+7|+5=0\)

Solve each equation. \(5|3 x-4|=x+1\)

Solve each equation. \(\frac{2}{3}+x=-\frac{4}{9}\)

Solve each equation. \(x+\frac{5}{8}=-\frac{5}{6}\)

Solve each equation. \(x-\frac{3}{5}=\frac{2}{3}\)

Solve each equation. \(x+\frac{3}{16}=-\frac{1}{2}\)

Solve each equation. \(x-\frac{1}{6}=-\frac{7}{9}\)

Solve each equation. \(x-\frac{3}{8}=-\frac{5}{24}\)