Chapter 2

For the following exercises, perform the indicated operation and express the result as a simplified complex number. $$ (-2+4 i)(8) $$

For exercises 17 and 18, use this scenario: A retired woman has $$\$ 50,000$$ to invest but needs to make $$\$ 6,000$$ a year from the interest to meet certain living expenses. One bond investment pays \(15 \%\) annual interest. The rest of it she wants to put in a CD that pays \(7 \%\). Paul has $$\$ 20,000$$ to invest. His intent is to earn \(11 \%\) interest on his investment. He can invest part of his money at \(8 \%\) interest and part at \(12 \%\) interest. How much does Paul need to invest in each option to make get a total \(11 \%\) return on his $$\$ 20,000 ?$$

For the following exercises, find the equation of the line using the point- slope formula. Write all the final equations using the slope-intercept form. (1, 2) with a slope of \(-\frac{4}{5}\)

For each of the following exercises, find the coordinates of the midpoint of the line segment that joins the two given points. (-1,1) and (7,-4)

For the following exercises, describe all the \(x\) -values within or including a distance of the given values. Distance of 5 units from the number 7

For the following exercises, solve the radical equation. Be sure to check all solutions to eliminate extraneous solutions. $$ \sqrt{t+1}+9=7 $$

For the following exercises, solve the quadratic equation by using the square root property. $$ (x-5)^{2}=4 $$

For the following exercises, perform the indicated operation and express the result as a simplified complex number. $$ (2+3 i)(4-i) $$

For the following exercises, use this scenario: A truck rental agency offers two kinds of plans. Plan A charges $$\$ 75 / w$$ k plus $$\$.10 / \mathrm{mi}$$ driven. Plan \(\mathrm{B}\) charges $$\$ 100 / \mathrm{wk}$$ plus $$\$ .05 / \mathrm{mi}$$ driven. Write the model equation for the cost of renting a truck with plan \(\mathrm{A} .\)

For each of the following exercises, find the coordinates of the midpoint of the line segment that joins the two given points. $$(-5,-3) \text { and }(-2,-8)$$

For the following exercises, describe all the \(x\) -values within or including a distance of the given values. Distance of 3 units from the number 9

For the following exercises, solve the radical equation. Be sure to check all solutions to eliminate extraneous solutions. $$ \sqrt{12-x}=x $$

For the following exercises, solve the quadratic equation by completing the square. Show each step. $$ x^{2}-9 x-22=0 $$

For the following exercises, perform the indicated operation and express the result as a simplified complex number. $$ (-1+2 i)(-2+3 i) $$

For the following exercises, use this scenario: A truck rental agency offers two kinds of plans. Plan A charges $$\$ 75 / w$$ k plus $$\$.10 / \mathrm{mi}$$ driven. Plan \(\mathrm{B}\) charges $$\$ 100 / \mathrm{wk}$$ plus $$\$ .05 / \mathrm{mi}$$ driven. Write the model equation for the cost of renting a truck with plan B.

For the following exercises, find the equation of the line using the point- slope formula. Write all the final equations using the slope-intercept form. \(y\) -intercept is \(2,\) and (4,-1)

For each of the following exercises, find the coordinates of the midpoint of the line segment that joins the two given points. $$(0,7) \text { and }(4,-9)$$

For the following exercises, describe all the \(x\) -values within or including a distance of the given values. Distance of 10 units from the number 4

For the following exercises, solve the radical equation. Be sure to check all solutions to eliminate extraneous solutions. $$ \sqrt{2 x+3}-\sqrt{x+2}=2 $$

For the following exercises, solve the quadratic equation by completing the square. Show each step. $$ 2 x^{2}-8 x-5=0 $$

For the following exercises, perform the indicated operation and express the result as a simplified complex number. $$ (4-2 i)(4+2 i) $$

For the following exercises, use this scenario: A truck rental agency offers two kinds of plans. Plan A charges $$\$ 75 / w$$ k plus $$\$.10 / \mathrm{mi}$$ driven. Plan \(\mathrm{B}\) charges $$\$ 100 / \mathrm{wk}$$ plus $$\$ .05 / \mathrm{mi}$$ driven. Find the number of miles that would generate the same cost for both plans.

For the following exercises, find the equation of the line using the point- slope formula. Write all the final equations using the slope-intercept form. (-3,10) and (5,-6)

For each of the following exercises, find the coordinates of the midpoint of the line segment that joins the two given points. $$(-43,17) \text { and }(23,-34)$$

For the following exercises, describe all the \(x\) -values within or including a distance of the given values. Distance of 11 units from the number 1

For the following exercises, solve the radical equation. Be sure to check all solutions to eliminate extraneous solutions. $$ \sqrt{3 x+7}+\sqrt{x+2}=1 $$

For the following exercises, solve the quadratic equation by completing the square. Show each step. $$ x^{2}-6 x=13 $$

For the following exercises, perform the indicated operation and express the result as a simplified complex number. $$ (3+4 i)(3-4 i) $$

For the following exercises, use this scenario: A truck rental agency offers two kinds of plans. Plan A charges $$\$ 75 / w$$ k plus $$\$.10 / \mathrm{mi}$$ driven. Plan \(\mathrm{B}\) charges $$\$ 100 / \mathrm{wk}$$ plus $$\$ .05 / \mathrm{mi}$$ driven. If Tim knows he has to travel \(300 \mathrm{mi},\) which plan should he choose?

For the following exercises, find the equation of the line using the point- slope formula. Write all the final equations using the slope-intercept form. (1,3)\(\quad\) and \(\quad(5,5)\)

For each of the following exercises, identify the information requested. What are the coordinates of the origin?

For the following exercises, solve the compound inequality. Express your answer using inequality signs, and then write your answer using interval notation. $$ -4<3 x+2 \leq 18 $$

For the following exercises, solve the radical equation. Be sure to check all solutions to eliminate extraneous solutions. $$ \sqrt{2 x+3}-\sqrt{x+1}=1 $$

For the following exercises, solve the quadratic equation by completing the square. Show each step. $$ x^{2}+\frac{2}{3} x-\frac{1}{3}=0 $$

For the following exercises, perform the indicated operation and express the result as a simplified complex number. $$ \frac{3+4 i}{2} $$

For the following exercises, use the formula given to solve for the required value. \(A=P(1+r t)\) is used to find the principal amount \(P\) deposited, earning \(r \%\) interest, for \(t\) years. Use this to find what principal amount \(P\) David invested at a \(3 \%\) rate for 20 yr if $$A=\$ 8,000$$.

For the following exercises, find the equation of the line using the point- slope formula. Write all the final equations using the slope-intercept form. parallel to \(y=2 x+5\) and passes through the point (4,3)

For each of the following exercises, identify the information requested. If a point is located on the \(y\) -axis, what is the \(x\) -coordinate?

For the following exercises, solve the compound inequality. Express your answer using inequality signs, and then write your answer using interval notation. $$ 3 x+1>2 x-5>x-7 $$

For the following exercises, solve the equation involving absolute value. $$ |3 x-4|=8 $$

For the following exercises, solve the quadratic equation by completing the square. Show each step. $$ 2+z=6 z^{2} $$

For the following exercises, perform the indicated operation and express the result as a simplified complex number. $$ \frac{6-2 i}{3} $$

For the following exercises, find the equation of the line using the point- slope formula. Write all the final equations using the slope-intercept form. perpendicular to \(3 y=x-4\) and passes through the point (-2,1).

For each of the following exercises, identify the information requested. If a point is located on the \(x\) -axis, what is the \(y\) -coordinate?

For the following exercises, solve the compound inequality. Express your answer using inequality signs, and then write your answer using interval notation. $$ y<5-2 y<7+y $$

For the following exercises, solve the equation involving absolute value. $$ |2 x-3|=-2 $$

For the following exercises, solve the quadratic equation by completing the square. Show each step. $$ 6 p^{2}+7 p-20=0 $$

For the following exercises, perform the indicated operation and express the result as a simplified complex number. $$ \frac{-5+3 i}{2 i} $$

For the following exercises, use the formula given to solve for the required value. \(F=m a\) indicates that force \((F)\) equals mass \((m)\) times acceleration (a). Find the acceleration of a mass of \(50 \mathrm{~kg}\) if a force of \(12 \mathrm{~N}\) is exerted on it.

For the following exercises, find the equation of the line using the given information. (-2,0) and (-2,5)