91Ó°ÊÓ

A club swimming pool is \(30 \mathrm{ft}\) wide and \(40 \mathrm{ft}\) long. The club members want an exposed aggregate border in a strip of uniform width around the pool. They have enough material for \(296 \mathrm{ft}^{2}\). How wide can the strip be?

A rectangular piece of sheet metal has a length that is 4 in. less than twice the width. A square piece 2 in. on a side is cut from each corner. The sides are then turned up to form an uncovered box of volume 256 in. \(^{3}\). Find the length and width of the original piece of metal.

Find the discriminant. Use it to determine whether the solutions for each equation are A. two rational numbers B. one rational number C. two irrational numbers D. two nonreal complex numbers. Tell whether the equation can be solved using the zero-factor property, or if the quadratic formula should be used instead. Do not actually solve. $$ 25 x^{2}+70 x+49=0 $$

Find the discriminant. Use it to determine whether the solutions for each equation are A. two rational numbers B. one rational number C. two irrational numbers D. two nonreal complex numbers. Tell whether the equation can be solved using the zero-factor property, or if the quadratic formula should be used instead. Do not actually solve. $$ 4 x^{2}-28 x+49=0 $$

Find the constant that must be added to make each expression a perfect square trinomial. Then factor the trinomial. \(x^{2}+6 x+\) _______ It factors as __________.

Find the discriminant. Use it to determine whether the solutions for each equation are A. two rational numbers B. one rational number C. two irrational numbers D. two nonreal complex numbers. Tell whether the equation can be solved using the zero-factor property, or if the quadratic formula should be used instead. Do not actually solve. $$ 9 x^{2}-12 x-1=0 $$

Find the discriminant. Use it to determine whether the solutions for each equation are A. two rational numbers B. one rational number C. two irrational numbers D. two nonreal complex numbers. Tell whether the equation can be solved using the zero-factor property, or if the quadratic formula should be used instead. Do not actually solve. $$ 4 x^{2}=4 x+3 $$

Solve each problem using a quadratic equation. Use the formula \(A=P(1+r)^{2}\) to find the interest rate \(r\) at which a principal \(P\) of \(\$ 10,000\) will increase to \(\$ 10,920.25\) in 2 yr.

A model rocket is projected vertically upward from the ground. Its distance s in feet above the ground after t seconds is given by the quadratic function $$ s(t)=-16 t^{2}+256 t $$ to see how quadratic equations and inequalities are related. At what times will the rocket be less than 624 ft above the ground? (Hint: Let \(s(t)<624,\) solve the quadratic inequality, and observe the solutions in to determine the least and greatest possible values of \(t .)\)

Solve each equation. (All solutions for these equations are nonreal complex numbers.) \(x^{2}=-12\)