91Ó°ÊÓ

Use a graphing calculator to graphically solve the radical equation. Check the solution algebraically. $$\sqrt{3 x-2}=4-x$$

The relationship between a roller coaster's velocity \(v(\text { in feet per second })\) at the bottom of a drop and the height of the drop \(h\) (in feet) can be modeled by the formula \(v=\sqrt{2 g h}\) where \(g\) represents acceleration due to gravity. a. Use the fact that \(g=32 \mathrm{ft} / \mathrm{sec}^{2}\) to show that \(v=\sqrt{2 g h}\) can be simplified to \(v=8 \sqrt{h}\) b. Sketch the graph of \(v=8 \sqrt{h}\) c. Writing Use the formula or the graph to explain why doubling the height of a drop does not double the velocity of a roller coaster.

$$\text { Simplify } \sqrt{5}(6+\sqrt{5})^{2}$$ $$\begin{array}{llllll} \text { (A) } 41+2 \sqrt{5} & \text { (B) } 53 \sqrt{5} & \text { (C) } 41 \sqrt{5}+60 & \text { (D } 101 \sqrt{5} \end{array}$$

Find the x-intercepts of the graph of the equation. $$y=-x^{2}+4 x+1$$

Which of the following is the difference \(\sqrt{3}-5 \sqrt{9} ?\) $$\begin{aligned} &\begin{array}{llll} \text { A) } \sqrt{3}-3 & \text { (B) } \sqrt{3}-15 & \text { (C) }-4 \sqrt{3} \end{array}\\\ &\text { (D) } \sqrt{3}-45 \end{aligned}$$

Use a graphing calculator to graphically solve the radical equation. Check the solution algebraically. $$\sqrt{15-4 x}=2 x$$

Solve the quadratic equation. $$4 p^{2}-12 p+5=0$$

Find the domain of \(y=\frac{3}{\sqrt{x}-2}\)

Factor the expression. $$x^{2}-64$$

Factor the expression completely. \(3 x^{3}+12 x^{2}-15 x\)