The length of a rectangle is three times its width. The area of the rectangle is $192 \mathrm{cm}^{2}$. Find the perimeter of the rectangle.

Explain how you solve each problem. Show all your work. Erin owns 48 movies on DVD. Three eighths of the movies are comedies, $\frac { 1 } { 3 }$ are dramas, $\frac { 1 } { 4 }$ are action adventure, and the rest are science fiction. What part of her movie collection is science fiction?

For which value of $m$ does the graph of $y=18x^2+mx+2$ have exactly one $x$-intercept?

For which positive integers k can the number $5 + 2 ^ { - k }$ be represented exactly (with no rounding error) in double precision floating point arithmetic?

Which equation is $y = –6x^2 + 3x + 2$ rewritten in vertex form?

Differentiate the given function. $L(x)=\ln \left[\frac{x^{2}+2 x-3}{x^{2}+2 x+1}\right]$

Solve each equation. a. $x^2 - 9 = 0$ b. $(x - 3)^2 - 16 = 0$ c. $\bigg(x- \dfrac{3}{2}\bigg)^2 - \dfrac{1}{4} =0$ d. Express $x$ in terms of $a$ and $b$ if $(x - a)^2 - b^2 = 0.$

Change the percent to a decimal number. 21.7%

Simplify each root. $\sqrt[3]{m^{9}}$

If the discriminant of a quadratic equation is $4$, which statement describes the roots?

$a$. There are two complex roots.

$b$. There are two real roots.

$c$. There is one real root.

$d$. There is one complex root.

If the discriminant of a quadratic equation is $4$, which statement describes the roots?

Define joint, or articulation. Name and describe the differences among the three major classes of joints.

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I solved a formula for one of its variables, so now I have a numerical value for that variable.

The Latin root-vis-means "see." The root appears in the word improvised, which literally means "not seen before." It also appears in these words and phrases:

$$\begin{array}{ll}{\text { visitor }} & {\text { revise }} \\ {\text { supervisor }} & {\text { visual aid }} \\ {\text { invisible }} & {\text { envision }}\end{array}$$

Identify the word or phrase above that matches each clue. Not able to be seen