Chapter 2

Use a graphing utility to approximate any solutions of the equation. [Remember to write the equation in the form \(f(x)=0.1\) $$2 x^{3}+x+4=0$$

Perform the operation and write the result in standard form. $$(\sqrt{3}+\sqrt{15} i)(\sqrt{3}-\sqrt{15} i)$$

Solve the equation (if possible). $$\frac{6}{x}-\frac{2}{x+3}=\frac{3(x+5)}{x(x+3)}$$

Solving an Equation Involving Rational Exponents Find all solutions of the equation algebraically. Check your solutions. $$\left(x^{2}-5 x-2\right)^{1 / 3}=-2$$

Solve the inequality and sketch the solution on the real number line. Use a graphing utility to verify your solutions graphically. $$\left|\frac{x-3}{2}\right| \geq 5$$

Solve the quadratic equation by completing the square. Verify your answer graphically. $$9 x^{2}-18 x+3=0$$

Use a graphing utility to approximate any solutions of the equation. [Remember to write the equation in the form \(f(x)=0.1\) $$\frac{1}{4}\left(x^{2}-10 x+17\right)=0$$

Perform the operation and write the result in standard form. $$(6+7 i)^{2}$$

Solve for the indicated variable. Area of a Triangle $$\text { Solve for } h: A=\frac{1}{2} b h$$

Solving an Equation Involving Rational Exponents Find all solutions of the equation algebraically. Check your solutions. $$\left(x^{2}-x-22\right)^{4 / 3}=16$$

Solve the inequality and sketch the solution on the real number line. Use a graphing utility to verify your solutions graphically. $$|x+14|+3 \geq 17$$

Solve the quadratic equation by completing the square. Verify your answer graphically. $$4 x^{2}-16 x-5=0$$

Use a graphing utility to approximate any solutions of the equation. [Remember to write the equation in the form \(f(x)=0.1\) $$-\frac{1}{2}\left(x^{2}-6 x+6\right)=0$$

Perform the operation and write the result in standard form. $$(5-4 i)^{2}$$

Solving an Equation Involving Rational Exponents Find all solutions of the equation algebraically. Check your solutions. $$3 x(x-1)^{1 / 2}+2(x-1)^{3 / 2}=0$$

Solve the inequality and sketch the solution on the real number line. Use a graphing utility to verify your solutions graphically. $$10|1-x|<5$$

Solve the quadratic equation by completing the square. Verify your answer graphically. $$2 x^{2}+5 x-8=0$$

Use a graphing utility to approximate any solutions of the equation. [Remember to write the equation in the form \(f(x)=0.1\) $$2 x^{3}-x^{2}-18 x+9=0$$

Perform the operation and write the result in standard form. $$(4+5 i)^{2}-(4-5 i)^{2}$$

Solve for the indicated variable. Investment at Compound Interest $$\text { Solve for } P: A=P\left(1+\frac{r}{n}\right)^{n t}$$

Solving an Equation Involving Rational Exponents Find all solutions of the equation algebraically. Check your solutions. $$4 x^{2}(x-1)^{1 / 3}+6 x(x-1)^{4 / 3}=0$$

Solve the inequality and sketch the solution on the real number line. Use a graphing utility to verify your solutions graphically. $$3|4-5 x|<9$$

Solve the quadratic equation by completing the square. Verify your answer graphically. $$9 x^{2}-12 x-14=0$$

Use a graphing utility to approximate any solutions of the equation. [Remember to write the equation in the form \(f(x)=0.1\) $$4 x^{3}+12 x^{2}-26 x-24=0$$

Solve for the indicated variable. Investment at Simple Interest Solve for \(r: A=P+P r t\)

Perform the operation and write the result in standard form. $$(1-2 i)^{2}-(1+2 i)^{2}$$

Solving an Equation Involving Fractions Find all solutions of the equation. Check your solutions. $$x=\frac{3}{x}+\frac{1}{2}$$

Use a graphing utility to graph the equation and graphically approximate the values of \(x\) that satisfy the specified inequalities. Then solve each inequality algebraically. Equation \(y=|x-3|\) Inequalities (a) \(y \leq 2\) (b) \(y \geq 4\)

(a) use a graphing utility to graph the equation, (b) use the graph to approximate any \(x\) -intercepts of the graph, and (c) verify your results algebraically. $$y=(x+3)^{2}-4$$

Use a graphing utility to approximate any solutions of the equation. [Remember to write the equation in the form \(f(x)=0.1\) $$x^{5}=3 x^{3}-3$$

Solve for the indicated variable. Volume of a Right Circular Cylinder Solve for \(h: \quad V=\pi r^{2} h\)

Write the complex conjugate of the complex number. Then multiply the number by its complex conjugate. $$6-2 i$$

Solving an Equation Involving Fractions Find all solutions of the equation. Check your solutions. $$\frac{4}{x}-\frac{5}{3}=\frac{x}{6}$$

Use a graphing utility to graph the equation and graphically approximate the values of \(x\) that satisfy the specified inequalities. Then solve each inequality algebraically. Equation \(y=\left|\frac{1}{2} x+1\right|\) Inequalities (a) \(y \leq 4\) (b) \(y \geq 1\)

(a) use a graphing utility to graph the equation, (b) use the graph to approximate any \(x\) -intercepts of the graph, and (c) verify your results algebraically. $$y=1-(x-2)^{2}$$

Use a graphing utility to approximate any solutions of the equation. [Remember to write the equation in the form \(f(x)=0.1\) $$x^{5}=3+2 x^{3}$$

Solve for the indicated variable. Volume of a Right Circular Cone $$\text { Solve for } h: \quad V=\frac{1}{3} \pi r^{2} h$$

Write the complex conjugate of the complex number. Then multiply the number by its complex conjugate. $$3+5 i$$

Solving an Equation Involving Fractions Find all solutions of the equation. Check your solutions. $$\frac{20-x}{x}=x$$

(a) use a graphing utility to graph the equation, (b) use the graph to approximate any \(x\) -intercepts of the graph, and (c) verify your results algebraically. $$y=-4 x^{2}+4 x+3$$

Use a graphing utility to approximate any solutions of the equation. [Remember to write the equation in the form \(f(x)=0.1\) $$\frac{2}{x+2}=3$$

Use the following information. The relationship between the length of an adult's femur (thigh bone) and the height of the adult can be approximated by the linear equations $$y=0.386 x-19.20 \quad \text { Female }$$ $$y=0.442 x-29.37 \quad \text { Male }$$ where \(y\) is the length of the femur in centimeters and \(x\) is the height of the adult in centimeters. (See figure.) An anthropologist discovers a femur belonging to an adult human female. The bone is 43 centimeterss long. Estimate the height of the female.

Write the complex conjugate of the complex number. Then multiply the number by its complex conjugate. $$-1+\sqrt{7} i$$

Solving an Equation Involving Fractions Find all solutions of the equation. Check your solutions. $$4 x+1=\frac{3}{x}$$

(a) use a graphing utility to graph the equation, (b) use the graph to approximate any \(x\) -intercepts of the graph, and (c) verify your results algebraically. $$y=x^{2}+3 x-4$$

Use a graphing utility to approximate any solutions of the equation. [Remember to write the equation in the form \(f(x)=0.1\) $$\frac{1}{x-3}=-2$$

Use the following information. The relationship between the length of an adult's femur (thigh bone) and the height of the adult can be approximated by the linear equations $$y=0.386 x-19.20 \quad \text { Female }$$ $$y=0.442 x-29.37 \quad \text { Male }$$ where \(y\) is the length of the femur in centimeters and \(x\) is the height of the adult in centimeters. (See figure.) From the foot bones of an adult human male, an anthropologist estimates that the person's height was 175 centimeters. A few feet away from the site where the foot bones were discovered, the anthropologist discovers a male adult femur that is 48 centimeters long. Is it likely that both the foot bones and the thigh bone came from the same person?

Write the complex conjugate of the complex number. Then multiply the number by its complex conjugate. $$-4-\sqrt{3} i$$

Solving an Equation Involving Fractions Find all solutions of the equation. Check your solutions. $$\frac{1}{x}-\frac{1}{x+1}=3$$

Use a graphing utility to determine the number of real solutions of the quadratic equation. $$x^{2}-4 x+4=0$$