Chapter 1

In Exercises \(29-44\), perform the indicated operations and write the result in standard form. $$ \sqrt{-12}(\sqrt{-4}-\sqrt{2}) $$

In Exercises \(35-46,\) determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. $$ x^{2}-9 x $$

Use interval notation to express solution sets and graph each solution set on a number line. Solve each linear inequality. $$\frac{3 x}{10}+1 \geq \frac{1}{5}-\frac{x}{10}$$

By making an appropriate substitution. $$ x^{4}-13 x^{2}+36=0 $$

Contain rational equations with variables in denominators. For each equation, a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variable. b. Keeping the restrictions in mind , solve the equation. \(\frac{2}{x-2}=\frac{x}{x-2}-2\)

Things did not go quite as planned. You invested \(\$ 12,000\), part of it in stock that paid \(14 \%\) annual interest. However, the rest of the money suffered a \(6 \%\) loss. If the total annual income from both investments was \(\$ 680,\) how much was invested at each rate?

In Exercises \(29-44\), perform the indicated operations and write the result in standard form. $$ (3 \sqrt{-5})(-4 \sqrt{-12}) $$

In Exercises \(35-46,\) determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. $$ x^{2}-\frac{2}{3} x $$

Use interval notation to express solution sets and graph each solution set on a number line. Solve each linear inequality. $$1-\frac{x}{2}>4$$

By making an appropriate substitution. $$ 9 x^{4}=25 x^{2}-16 $$

Contain rational equations with variables in denominators. For each equation, a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variable. b. Keeping the restrictions in mind , solve the equation. \(\frac{3}{2 x-2}+\frac{1}{2}=\frac{2}{x-1}\)

A rectangular swimming pool is three times as long as it is wide. If the perimeter of the pool is 320 feet, what are its dimensions?

In Exercises \(29-44\), perform the indicated operations and write the result in standard form. $$ (3 \sqrt{-7})(2 \sqrt{-8}) $$

Use interval notation to express solution sets and graph each solution set on a number line. Solve each linear inequality. $$7-\frac{4}{5} x<\frac{3}{5}$$

By making an appropriate substitution. $$ 4 x^{4}=13 x^{2}-9 $$

The length of the rectangular tennis court at Wimbledon is 6 feet longer than twice the width. If the court's perimeter is 228 feet, what are the court's dimensions?

In Exercises \(45-50,\) perform the indicated operation(s) and write the result in standard form. $$ (2-3 i)(1-i)-(3-i)(3+i) $$

In Exercises \(35-46,\) determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. $$ x^{2}-\frac{1}{3} x $$

Use interval notation to express solution sets and graph each solution set on a number line. Solve each linear inequality. $$\frac{x-4}{6} \geq \frac{x-2}{9}+\frac{5}{18}$$

By making an appropriate substitution. $$ x-13 \sqrt{x}+40=0 $$

Contain rational equations with variables in denominators. For each equation, a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variable. b. Keeping the restrictions in mind , solve the equation. \(\frac{3}{x+2}+\frac{2}{x-2}=\frac{8}{(x+2)(x-2)}\)

The length of a rectangular pool is 6 meters less than twice the width. If the pool's perimeter is 126 meters, what are its dimensions?

In Exercises \(45-50,\) perform the indicated operation(s) and write the result in standard form. $$ (8+9 i)(2-i)-(1-i)(1+i) $$

In Exercises \(35-46,\) determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. $$ x^{2}-\frac{1}{4} x $$

Use interval notation to express solution sets and graph each solution set on a number line. Solve each linear inequality. $$\frac{4 x-3}{6}+2 \geq \frac{2 x-1}{12}$$

By making an appropriate substitution. $$ 2 x-7 \sqrt{x}-30=0 $$

Contain rational equations with variables in denominators. For each equation, a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variable. b. Keeping the restrictions in mind , solve the equation. \(\frac{5}{x+2}+\frac{3}{x-2}=\frac{12}{(x+2)(x-2)}\)

The rectangular painting in the figure shown measures 12 inches by 16 inches and is surrounded by a frame of uniform width around the four edges. The perimeter of the rectangle formed by the painting and its frame is 72 inches. Determine the width of the frame.

In Exercises \(45-50,\) perform the indicated operation(s) and write the result in standard form. $$ (2+i)^{2}-(3-i)^{2} $$

Solve each equation in Exercises \(47-64\) by completing the square. $$ x^{2}+6 x=7 $$

Use interval notation to express solution sets and graph each solution set on a number line. Solve each linear inequality. $$4(3 x-2)-3 x<3(1+3 x)-7$$

By making an appropriate substitution. $$ x^{-2}-x^{-1}-20=0 $$

Write each English sentence as an equation in two variables Then graph the equation. The \(y\) -value is four more than twice the \(x\) -value.

Contain rational equations with variables in denominators. For each equation, a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variable. b. Keeping the restrictions in mind , solve the equation. \(\frac{2}{x+1}-\frac{1}{x-1}=\frac{2 x}{x^{2}-1}\)

The rectangular swimming pool in the figure shown measures 40 feet by 60 feet and is surrounded by a path of uniform width around the four edges. The perimeter of the rectangle formed by the pool and the surrounding path is 248 feet. Determine the width of the path.

In Exercises \(45-50,\) perform the indicated operation(s) and write the result in standard form. $$ (4-i)^{2}-(1+2 i)^{2} $$

Solve each equation in Exercises \(47-64\) by completing the square. $$ x^{2}+6 x=-8 $$

Use interval notation to express solution sets and graph each solution set on a number line. Solve each linear inequality. $$3(x-8)-2(10-x)>5(x-1)$$

By making an appropriate substitution. $$ x^{-2}-x^{-1}-6=0 $$

Write each English sentence as an equation in two variables Then graph the equation. The \(y\) -value is the difference between four and twice the \(x\) -value.

Contain rational equations with variables in denominators. For each equation, a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variable. b. Keeping the restrictions in mind , solve the equation. \(\frac{4}{x+5}+\frac{2}{x-5}=\frac{32}{x^{2}-25}\)

An automobile repair shop charged a customer \(\$ 448\), listing \(\$ 63\) for parts and the remainder for labor. If the cost of labor is \(\$ 35\) per hour, how many hours of labor did it take to repair the car?

In Exercises \(45-50,\) perform the indicated operation(s) and write the result in standard form. $$ 5 \sqrt{-16}+3 \sqrt{-81} $$

Solve each equation in Exercises \(47-64\) by completing the square. $$ x^{2}-2 x=2 $$

Use interval notation to express solution sets and graph each solution set on a number line. Solve each linear inequality. $$5(x-2)-3(x+4) \geq 2 x-20$$

By making an appropriate substitution. $$ x^{\frac{2}{3}}-x^{\frac{1}{3}}-6=0 $$

Write each English sentence as an equation in two variables Then graph the equation. The \(y\) -value is three decreased by the square of the \(x\) -value.

Contain rational equations with variables in denominators. For each equation, a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variable. b. Keeping the restrictions in mind , solve the equation. \(\frac{1}{x-4}-\frac{5}{x+2}=\frac{6}{x^{2}-2 x-8}\)

A repair bill on a sailboat came to \(\$ 1603,\) including \(\$ 532\) for parts and the remainder for labor. If the cost of labor is S63 per hour, how many hours of labor did it take to repair the sailboat?

In Exercises \(45-50,\) perform the indicated operation(s) and write the result in standard form. $$ 5 \sqrt{-8}+3 \sqrt{-18} $$