Chapter 2

Write the complex number in standard form. $$-i-(\sqrt{-23})^{2}$$

Determine whether the equation is an identity, a conditional equation, or a contradiction. $$\frac{5}{x}+\frac{3}{x}=24$$

Find all solutions of the equation algebraically. Check your solutions. $$\sqrt{x-10}-4=0$$

Solve the inequality and sketch the solution on the real number line. Use a graphing utility to verify your solution graphically. $$4 x+7<3+2 x$$

Use a graphing utility to graph the equation and approximate any \(x\) - and \(y\) -intercepts. Verify your results algebraically. $$y=20-(3 x-10)$$

Write the complex number in standard form. $$\sqrt{-0.09}$$

Solve the equation using two methods. Then explain which method you prefer. $$\frac{3 x}{8}-\frac{4 x}{3}=4$$

Solve the inequality and sketch the solution on the real number line. Use a graphing utility to verify your solution graphically. $$3 x+1 \geq 2+x$$

Find all solutions of the equation algebraically. Check your solutions. $$\sqrt{2 x+5}+3=0$$

Solve the quadratic equation by factoring. Check your solutions in the original equation. $$x^{2}+2 a x+a^{2}=0$$

Use a graphing utility to graph the equation and approximate any \(x\) - and \(y\) -intercepts. Verify your results algebraically. $$y=10+2(x-2)$$

Write the complex number in standard form. $$\sqrt{-0.0004}$$

Solve the equation using two methods. Then explain which method you prefer. $$\frac{3 z}{8}-\frac{z}{10}=6$$

Solve the inequality and sketch the solution on the real number line. Use a graphing utility to verify your solution graphically. $$2(1-x)<3 x+7$$

Find all solutions of the equation algebraically. Check your solutions. $$\sqrt[3]{6 x}+9=0$$

Solve the equation by extracting square roots. List both the exact solutions and the decimal solutions rounded to the nearest hundredth. $$x^{2}=49$$

The zero(s) of the function are given. Verify the zero(s) both algebraically and graphically. \(Function\) \(f(x)=4(3-x)\) \(Z e r o(s)\) \(x=3\)

Perform the addition or subtraction and write the result in standard form. $$(4+i)-(7-2 i)$$

Solve the equation using two methods. Then explain which method you prefer. $$\frac{2 x}{5}+5 x=\frac{4}{3}$$

Solve the inequality and sketch the solution on the real number line. Use a graphing utility to verify your solution graphically. $$2 x+7<3(x-4)$$

Find all solutions of the equation algebraically. Check your solutions. $$2 \sqrt[3]{x}-10=0$$

Solve the equation by extracting square roots. List both the exact solutions and the decimal solutions rounded to the nearest hundredth. $$x^{2}=144$$

Perform the addition or subtraction and write the result in standard form. $$(11-2 i)-(-3+6 i)$$

Solve the equation using two methods. Then explain which method you prefer. $$\frac{4 y}{3}-2 y=\frac{16}{5}$$

Solve the inequality and sketch the solution on the real number line. Use a graphing utility to verify your solution graphically. $$\frac{3}{4} x-6 \leq x-7$$

Find all solutions of the equation algebraically. Check your solutions. $$\sqrt[3]{2 x+1}+8=0$$

Solve the equation by extracting square roots. List both the exact solutions and the decimal solutions rounded to the nearest hundredth. $$3 x^{2}=81$$

The zero(s) of the function are given. Verify the zero(s) both algebraically and graphically. \(Function\) \(f(x)=x^{3}-6 x^{2}+5 x\) \(Z e r o(s)\) \(x=0,5,1\)

Perform the addition or subtraction and write the result in standard form. $$13 i-(14-7 i)$$

Solve the equation (if possible). $$3 x-5=2 x+7$$

Solve the inequality and sketch the solution on the real number line. Use a graphing utility to verify your solution graphically. $$3+\frac{2}{7} x>x-2$$

Find all solutions of the equation algebraically. Check your solutions. $$\sqrt[3]{4 x-3}+2=0$$

Solve the equation by extracting square roots. List both the exact solutions and the decimal solutions rounded to the nearest hundredth. $$9 x^{2}=36$$

The zero(s) of the function are given. Verify the zero(s) both algebraically and graphically. \(Function\) \(f(x)=x^{3}-9 x^{2}+18 x\) \(Z e r o(s)\) \(x=0,3,6\)

Perform the addition or subtraction and write the result in standard form. $$22+(-5+8 i)-9 i$$

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

Solve the inequality and sketch the solution on the real number line. Use a graphing utility to verify your solution graphically. $$1 \leq 2 x+3 \leq 9$$

Find all solutions of the equation algebraically. Check your solutions. $$\sqrt{5 x-26}+4=x$$

Solve the equation by extracting square roots. List both the exact solutions and the decimal solutions rounded to the nearest hundredth. $$x^{2}+12=112$$

The zero(s) of the function are given. Verify the zero(s) both algebraically and graphically. \(Function\) \(f(x)=\frac{x+1}{2}-\frac{x-2}{7}+1\) \(Z e r o(s)\) \(x=-5\)

Perform the addition or subtraction and write the result in standard form. $$\left(\frac{3}{2}+\frac{5}{2} i\right)+\left(\frac{5}{3}+\frac{11}{3} i\right)$$

Solve the equation (if possible). $$3(y-5)=3+5 y$$

Solve the inequality and sketch the solution on the real number line. Use a graphing utility to verify your solution graphically. $$-8 \leq-3 x+5<13$$

Find all solutions of the equation algebraically. Check your solutions. $$x-\sqrt{8 x-31}=5$$

Solve the equation by extracting square roots. List both the exact solutions and the decimal solutions rounded to the nearest hundredth. $$x^{2}-3=78$$

The zero(s) of the function are given. Verify the zero(s) both algebraically and graphically. \(Function\) \(f(x)=x-3-\frac{10}{x}\) \(Z e r o(s)\) \(x=-2,5\)

Perform the addition or subtraction and write the result in standard form. $$\left(\frac{3}{4}+\frac{7}{5} i\right)-\left(\frac{5}{6}-\frac{1}{6} i\right)$$

Solve the equation (if possible). $$4(z-3)+3 z=1+8 z$$

The following ordered pairs \((t, T)\) represent the Olympic year \(t\) and the winning time \(T\) (in minutes) in the women's 400 -meter freestyle swimming event. $$\begin{aligned} &(1956,4.91)\\\ &(1960,4.84)\\\ &(1964,4.72)\\\ &(1968,4.53)\\\ &(1972,4.32)\\\ &(1976,4.16)\\\ &(1980,4.15)\\\ &(1984,4.12) \end{aligned}$$ $$\begin{aligned} &(1988,4.06)\\\ &(1992,4.12)\\\ &(1996,4.12)\\\ &(2000,4.10)\\\ &(2004,4.09)\\\ &(2008,4.05)\\\ &(2012,4.02) \end{aligned}$$ (a) Use the regression feature of a graphing utility to find a linear model for the data and to identify the correlation coefficient. Let \(t\) represent the year, with \(t=0\) corresponding to 1950 (b) What information is given by the sign of the slope of the model? (c) Use the graphing utility to plot the data and graph the model in the same viewing window. (d) Create a table showing the actual values of \(y\) and the values of \(y\) given by the model. How closely does the model fit the data? (e) How can you use the value of the correlation coefficient to help answer the question in part (d)? (f) Would you use the model to predict the winning times in the future? Explain.

Solve the inequality and sketch the solution on the real number line. Use a graphing utility to verify your solution graphically. $$-8 \leq 1-3(x-2)<13$$