Chapter 2

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

Solve the quadratic equation by using the square root property. $$ (x-5)^{2}=4 $$

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. $$ \sqrt{12-x}=x $$

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 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 \(\$ 75 / \mathrm{wk}\) . plus \(\$ .10 / \mathrm{mi}\) driven. Plan B charges \(\$ 100 / \mathrm{wk}\) plus \(\$ .05 \mathrm{mi}\) driven. Write the model equation for the cost of renting a truck with plan B.

Solve the quadratic equation by completing the square. Show each step. $$ x^{2}-9 x-22=0 $$

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. $$ \sqrt{2 x+3}-\sqrt{x+2}=2 $$

Distance of 10 units from the number 4

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

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 \(\$ 75 / \mathrm{wk}\) . plus \(\$ .10 / \mathrm{mi}\) driven. Plan B charges \(\$ 100 / \mathrm{wk}\) plus \(\$ .05 \mathrm{mi}\) driven. Find the number of miles that would generate the same cost for both plans.

Solve the quadratic equation by completing the square. Show each step. $$ 2 x^{2}-8 x-5=0 $$

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. $$ \sqrt{3 x+7}+\sqrt{x+2}=1 $$

Distance of 11 units from the number 1

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

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. $$ (1,3) \text { and }(5,5) $$

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 \(\$ 75 / \mathrm{wk}\) .plus \(\$ .10 / \mathrm{mi}\) driven. Plan 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?

Solve the quadratic equation by completing the square. Show each step. $$ x^{2}-6 x=13 $$

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. $$ \sqrt{2 x+3}-\sqrt{x+1}=1 $$

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

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 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 \(\operatorname{point}(4,3)\)

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

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

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

\(A=P(1+r t)\) is used to fi \(\mathrm{d}\) the principal amount \(P\) deposited, earning \(r \%\) interest, for \(t\) years. Use this to fi \(\mathrm{d}\) what principal amount \(P\) David invested at a \(3 \%\) rate for 20 yr if \(A=\$ 8,000\).

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. $$ |3 x-4|=8 $$

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

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 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 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 slope of the lines that pass through each pair of points and determine whether the lines are parallel or perpendicular. The formula \(F=\frac{m v^{2}}{R}\) relates force \((F),\) velocity \((v)\), \(\operatorname{mass}(m),\) and resistance \((R) .\) Find \(R\) when \(m=45, \) \(v=7,\) and \(F=245\).

Solve the quadratic equation by completing the square. Show each step. $$ 2+z=6 z^{2} $$

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

The formula \(F=\frac{m v^{2}}{R}\) relates force \((F),\) velocity \((v)\) \(\operatorname{mass}(m),\) and resistance \((R) .\) Find \(R\) when \(m=45\), \(v=7,\) and \(F=245\)

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

Solve the compound inequality. Express your answer using inequality signs, and then write your answer using interval notation. $$ 3 y<5-2 y<7+y $$

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