91Ó°ÊÓ

In Exercises \(1-12\), plot the given point in a rectangular coordinate system. $$ (-3,-5) $$

In Exercises \(1-8,\) add or subtract as indicated and write the result in standard form. $$7-(-9+2 i)-(-17-i)$$

Graph each equation in Exercises \(13-28\). Let \(x=-3,-2,-1,0\) \(1,2,\) and 3 $$ y=x+2 $$

Solve and check linear equation. \(45-[4-2 y-4(y+7)]=\) \(-4(1+3 y)-[4-3(y+2)-2(2 y-5)]\)

Check all proposed solutions. $$ x-\sqrt{2 x+5}=5 $$

A new car worth \(\$ 45,000\) is depreciating in value by \(\$ 5000\) per year. a. Write a formula that models the car's value, \(y,\) in dollars, after \(x\) years. b. Use the formula from part (a) to determine after how many years the car's value will be \(\$ 10,000\). c. Graph the formula from part (a) in the first quadrant of a rectangular coordinate system. Then show your solution to part (b) on the graph.

In Exercises \(35-46,\) determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. $$ x^{2}-10 x $$

Use interval notation to express solution sets and graph each solution set on a number line. Solve each linear inequality. $$7-\frac{4}{5} x<\frac{3}{5}$$

In Exercises \(35-46,\) determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. $$ x^{2}-\frac{1}{3} x $$

The length of a rectangular pool is 6 meters less than twice the width. If the pool's perimeter is 126 meters, what are its dimensions?