Chapter 1

What is the rectangular coordinate system?

Solve absolute value inequality. \(|x+3| \leq 4\)

In Exercises \(55-74\), solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? $$ V-\pi r^{2} h \text { for } h $$

Solve each equation in Exercises \(47-64\) by completing the square. $$2 x^{2}-4 x-1=0$$

Explain how to divide complex numbers. Provide an example with your explanation.

Explain how to plot a point in the rectangular coordinate system. Give an example with your explanation.

Solve absolute value inequality. \(|2 x-6|<8\)

Solve each equation in Exercises \(47-64\) by completing the square. $$3 x^{2}-2 x-2=0$$

Explain why \((5,-2)\) and \((-2,5)\) do not represent the same point. CAN'T COPY THE GRAPH

Solve absolute value inequality. \(|3 x+5|<17\)

Solve each equation in Exercises \(47-64\) by completing the square. $$3 x^{2}-5 x-10=0$$

A stand-up comedian uses algebra in some jokes, including one about a telephone recording that announces "You have just reached an imaginary number. Please multiply by \(i\) and dial again." Explain the joke.

Explain how to graph an equation in the rectangular coordinate system.

Solve absolute value inequality. \(|2(x-1)+4| \leq 8\)

Solve each equation in Exercises \(65-74\) using the quadratic formula. $$x^{2}+8 x+15=0$$

Explain the error. $$ \sqrt{-9}+\sqrt{-16}-\sqrt{-25}-i \sqrt{25}-5 i $$

What does a \([-20,2,1]\) by \([-4,5,0.5]\) viewing rectangle mean?

Solve absolute value inequality. \(|3(x-1)+2| \leq 20\)

Solve each equation in Exercises \(65-74\) using the quadratic formula. $$x^{2}+8 x+12=0$$

Explain the error. $$ (\sqrt{-9})^{2}-\sqrt{-9} \cdot \sqrt{-9}-\sqrt{81}-9 $$

What does a \([-20,2,1]\) by \([-4,5,0.5]\) viewing rectangle mean?

Solve absolute value inequality. \(\left|\frac{2 x+6}{3}\right|<2\)

Solve each equation in Exercises \(65-74\) using the quadratic formula. $$x^{2}+5 x+3=0$$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. The rectangular coordinate system provides a geometric picture of what an equation in two variables looks like.

Solve absolute value inequality. \(\left|\frac{3(x-1)}{4}\right|<6\)

Solve each equation in Exercises \(65-74\) using the quadratic formula. $$x^{2}+5 x+2=0$$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. The word imaginary in imaginary numbers tells me that these numbers are undefined.

Solve absolute value inequality. \(|x|>3\)

Solve each equation in Exercises \(65-74\) using the quadratic formula. $$3 x^{2}-3 x-4=0$$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. There is something wrong with my graphing utility because is not displaying number; I used I used the ordered pairs and (-2,2) and (0,0)(2,2) to graph a straight line.

Solve each absolute value equation or indicate that the equation has no solution. $$7|5 x|+2-16$$

Solve absolute value inequality. \(|x|>5\)

Solve each equation in Exercises \(65-74\) using the quadratic formula. $$5 x^{2}+x-2=0$$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. When I add or subtract complex numbers, I am basically combining like terms.

Solve each absolute value equation or indicate that the equation has no solution. $$7|3 x|+2-16$$

Solve absolute value inequality. \(|x-1| \geq 2\)

Solve each equation in Exercises \(65-74\) using the quadratic formula. $$4 x^{2}=2 x+7$$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. Some irrational numbers are not complex numbers.

Solve each absolute value equation or indicate that the equation has no solution. $$2\left|4-\frac{5}{2} x\right|+6-18$$

Solve absolute value inequality. \(|x+3| \geq 4\)

Solve each equation in Exercises \(65-74\) using the quadratic formula. $$3 x^{2}=6 x-1$$

Solve each absolute value equation or indicate that the equation has no solution. $$4\left|1-\frac{3}{4} x\right|+7-10$$

Solve absolute value inequality. \(|3 x-8|>7\)

Solve each equation in Exercises \(65-74\) using the quadratic formula. $$x^{2}-6 x+10=0$$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$ \frac{7+3 i}{5+3 i}-\frac{7}{5} $$

Solve absolute value inequality. \(|5 x-2|>13\)

Solve each equation in Exercises \(65-74\) using the quadratic formula. $$x^{2}-2 x+1=0$$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. In the complex number system, \(x^{2}+y^{2}\) (the sum of two squares) can be factored as \((x+y i)(x-y i)\)

Solve each absolute value equation or indicate that the equation has no solution. $$|x+1|+6-2$$

Solve absolute value inequality. \(\left|\frac{2 x+2}{4}\right| \geq 2\)