Chapter 2

Find all solutions of the equation algebraically. Check your solutions. $$\sqrt{x+1}-3 x=1$$

Solve the equation by extracting square roots. List both the exact solutions and the decimal solutions rounded to the nearest hundredth. $$(x-12)^{2}=16$$

Solve the equation algebraically. Then write the equation in the form \(f(x)=0\) and use a graphing utility to verify the algebraic solution. $$2.7 x-0.4 x=1.2$$

Perform the addition or subtraction and write the result in standard form. $$(1.6+3.2 i)+(-5.8+4.3 i)$$

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

In a study, 60 colts were measured every 14 days from birth. The ordered pairs \((d, l)\) represent the average length \(l\) (in centimeters) of the 60 colts \(d\) days after birth. (Spreadsheet at LarsonPrecalculus.com) $$\begin{aligned} &(14,81.2)\\\ &(56,98.3)\\\ &(98,110.0) \end{aligned}$$ $$\begin{aligned} &(28,87.1)\\\ &(70,102.4) \end{aligned}$$ $$\begin{aligned} &(42,93.7)\\\ &(84,106.2) \end{aligned}$$ (a) Use the regression feature of a graphing utility to find a linear model for the data and to identify the correlation coefficient. (b) According to the correlation coefficient, does the model represent the data well? Explain. (c) Use the graphing utility to plot the data and graph the model in the same viewing window. How closely does the model fit the data? (d) Use the model to predict the average length of a colt 112 days after birth.

Solve the inequality and sketch the solution on the real number line. Use a graphing utility to verify your solution graphically. $$0 \leq 2-3(x+1)<20$$

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

Solve the equation by extracting square roots. List both the exact solutions and the decimal solutions rounded to the nearest hundredth. $$(x-5)^{2}=25$$

Solve the equation algebraically. Then write the equation in the form \(f(x)=0\) and use a graphing utility to verify the algebraic solution. $$3.6 x-8.2=0.5 x$$

Perform the addition or subtraction and write the result in standard form. $$-(-3.7-12.8 i)-(6.1-16.3 i)$$

Solve the equation (if possible). $$\frac{3 x}{4}+\frac{x}{2}=-5$$

Determine whether the statement is true or false. Justify your answer. A linear regression model with a positive correlation will have a slope that is greater than \(0 .\)

Solve the inequality and sketch the solution on the real number line. Use a graphing utility to verify your solution graphically. $$-4<\frac{2 x-3}{3}<4$$

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

Solve the equation by extracting square roots. List both the exact solutions and the decimal solutions rounded to the nearest hundredth. $$(3 x-1)^{2}+6=0$$

Solve the equation algebraically. Then write the equation in the form \(f(x)=0\) and use a graphing utility to verify the algebraic solution. $$12(x+2)=15(x-4)-3$$

Perform the addition or subtraction and write the result in standard form. $$(5+\sqrt{-27})-(-12+\sqrt{-48})$$

Solve the equation (if possible). $$\frac{5 x-4}{5 x+4}=\frac{2}{3}$$

Solve the inequality and sketch the solution on the real number line. Use a graphing utility to verify your solution graphically. $$0 \leq \frac{x+3}{2}<5$$

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

Solve the equation by extracting square roots. List both the exact solutions and the decimal solutions rounded to the nearest hundredth. $$(2 x+3)^{2}+25=0$$

Solve the equation algebraically. Then write the equation in the form \(f(x)=0\) and use a graphing utility to verify the algebraic solution. $$1200=300+2(x-500)$$

Perform the addition or subtraction and write the result in standard form. $$(7+\sqrt{-18})+(3+\sqrt{-32})$$

Solve the equation (if possible). $$\frac{10 x+3}{5 x+6}=\frac{1}{2}$$

Use your school's library, the Internet, or some other reference source to locate data that you think describe a linear relationship. Create a scatter plot of the data and find the least squares regression line that represents the points. Interpret the slope and \(y\) -intercept in the context of the data. Write a summary of your findings.

Use a graphing utility to approximate the solution. $$5-2 x \geq 1$$

Find all solutions of the equation algebraically. Check your solutions. $$2 x+9 \sqrt{x}-5=0$$

Solve the equation by extracting square roots. List both the exact solutions and the decimal solutions rounded to the nearest hundredth. $$(x-7)^{2}=(x+3)^{2}$$

Solve the equation algebraically. Then write the equation in the form \(f(x)=0\) and use a graphing utility to verify the algebraic solution. $$\frac{3 x}{2}+\frac{1}{4}(x+2)=10$$

Perform the operation and write the result in standard form. $$\sqrt{-6} \cdot \sqrt{-2}$$

Solve the equation (if possible). $$\frac{2}{5}(z-4)+\frac{3 z}{10}=4 z$$

Find all solutions of the equation algebraically. Check your solutions. $$6 x-7 \sqrt{x}-3=0$$

Solve the equation by extracting square roots. List both the exact solutions and the decimal solutions rounded to the nearest hundredth. $$(x+5)^{2}=(x+4)^{2}$$

Solve the equation algebraically. Then write the equation in the form \(f(x)=0\) and use a graphing utility to verify the algebraic solution. $$\frac{2 x}{3}+\frac{1}{2}(x-5)=6$$

Perform the operation and write the result in standard form. $$\sqrt{-5} \cdot \sqrt{-10}$$

Solve the equation (if possible). $$\frac{3 x}{2}+\frac{1}{4}(x-2)=10$$

Evaluate the function at each value of the independent variable and simplify. \(f(x)=2 x^{2}-3 x+5\) (a) \(f(-1)\) (b) \(f(w+2)\)

Use a graphing utility to approximate the solution. $$3(x+1)

Find all solutions of the equation algebraically. Check your solutions. $$\sqrt{x}-\sqrt{x-5}=1$$

Solve the quadratic equation by completing the square. Verify your answer graphically. $$x^{2}+4 x-32=0$$

Solve the equation algebraically. Then write the equation in the form \(f(x)=0\) and use a graphing utility to verify the algebraic solution. $$0.60 x+0.40(100-x)=1.2$$

Perform the operation and write the result in standard form. $$(\sqrt{-10})^{2}$$

Solve the equation (if possible). $$\frac{17+y}{y}+\frac{32+y}{y}=100$$

Evaluate the function at each value of the independent variable and simplify. \(g(x)=5 x^{2}-6 x+1\) (a) \(g(-2)\) (b) \(g(z-2)\)

Use a graphing utility to approximate the solution. $$4(x-3)>8-x$$

Find all solutions of the equation algebraically. Check your solutions. $$\sqrt{x}+\sqrt{x-20}=10$$

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

Solve the equation algebraically. Then write the equation in the form \(f(x)=0\) and use a graphing utility to verify the algebraic solution. $$0.75 x+0.2(80-x)=3.9$$

Perform the operation and write the result in standard form. $$(\sqrt{-75})^{2}$$