Use the Distributive Property to multiply. Explain why

$$5 x + 15 = 5 ( x + 3 )$$

Write the absolute value function as a piecewise function.

$$y = | x - 2 |$$

Does the inverse of each function pass the vertical line test? Choose all for which the answer is yes. A. $f(x)=\frac{x+2}{2}$ B. $f(x)=3 \sqrt{x}+9$ C. $2 y^{2}=x$ D. $x=\frac{\sqrt{y}}{2}$ E. $y=\frac{x+3}{3}$

Find the start, elapsed, or end time. Start time: 11:00 A.M. Elapsed time: 4 hours 5 minutes. End time: ________

Solve the equation. 4x + 11 = 4x - 24

Write two inequalities using the number pairs. Use the symbols < or >. -6 and -2

Consider the following costs for a certain chemical product: Fixed cost: $2.045 million/year. Variable costs: Material cost: 62 cents per gallon of product. Energy cost: 24 cents per gallon of product. Labor cost: 16 cents per gallon of product. Assume that we produce only what we sell. Let P be the selling price in dollars per gallon. Suppose that the selling price and the sales quantity$Q$are interrelated as follows:$Q=6\times 10^6-1.1\times 10^6P$. Accordingly, if we raise the price, the product becomes less competitive and sales drop. Use this information to plot the fixed and total variable costs versus$Q$, and graphically determine the breakeven point(s). Fully label the plot and mark the breakeven points. For what range of$Q$is production profitable? For what value of$Q$ is profit a maximum?

Apply the methods of this and the previous section to graph each function. Be sure to label key points and show at least two periods $y=-\tan \left(3 x+\frac{\pi}{2}\right)$

Write each of the following in terms only of sin

$$\theta$$

and cos

$$\theta$$

. (Hint: A sketch will be useful.)

$$\sin \left( 180 ^ { \circ } + \theta \right)$$

find the limit (if it exists). If the limit does not exist, then explain why. Use a graphing utility to verify your result graphically. lim x→0 √x+4 - 2 / x

Find the derivative of the function. r = In(cosˉ¹ x)

The ____ states that for all real numbers a and b, if ab = 0, then either a = 0 or b = 0. completing the square, discriminant, Product Property of Square Roots, quadratic equation, quadratic formula, standard form of a quadratic equation, Zero-Product Property, zeros of a function

Solve the system using the elimination method.

$$\left. \begin{array} { l } { x + 3 y - z = 2 } \\ { x + y - z = 0 } \\ { 3 x + 2 y - 3 z = - 1 } \end{array} \right.$$

The point P is on the unit circle. Find P(x, y) from the given information. The x-coordinate of P is

$$\frac { 5 } { 13 }$$

, and the y-coordinate is negative.