A music store is offering a Frequent Buyers Club membership. The membership costs $22 per year, and then a member can buy CDs at a reduced price. If a member buys 17 CDs in one year, the cost is$111.25. Write a linear equation to represent the total cost y of a one year membership, if x CDs are purchased.

Position and label the triangle on the coordinate plane. isosceles ΔABC with base ¯AB that is a units long

Solve the equation. Check your solution.

$$5 = 7 w + 8 w + 2$$

Fill in the blanks. If f(x) becomes arbitrarily close to a unique number L as x approaches c from either side, then the _______ of f(x) as x approaches c is L.

Compute the derivative of the following functions.

$$f ( x ) = 15 e ^ { 3 x }$$

Factor.

$$x ^ { 2 } + 4 x + 4 - 4 p ^ { 4 }$$

Simplify. Express your answer in lowest terms. $8 \frac { 1 } { 2 } \div 2 \frac { 1 } { 8 }$

Use an identity to solve each equation on the interval

$$[ 0,2 \pi )$$

$$\cos 2 x + \cos x + 1 = 0$$

Verify that

$$y(x) = e^x \sin x$$

is a solution to the differential equation

$$2 y \cot x - \frac { d ^ { 2 } y } { d x ^ { 2 } } = 0.$$

(a) If v and w are nonzero vectors in an inner product space V, show that

$$- 1 \leq \frac { \langle \mathbf { v } , \mathbf { w } \rangle } { \| \mathbf { v } \| \| \mathbf { w } \| } \leq 1$$

, and hence that a unique angle

$$\theta$$

exists such that

$$\frac { \langle \mathbf { v } , \mathbf { w } \rangle } { \| \mathbf { v } \| \| \mathbf { w } \| } = \cos \theta$$

and

$$0 \leq \theta \leq \pi$$

. This angle

$$\theta$$

is called the angle between v and w. (b) Find the angle between v=(1, 2, -1, 1, 3) and w=(2, 1, 0, 2, 0) in

$$\mathbb { R } ^ { 5 }$$

with the dot product. (c) If

$$\theta$$

is the angle between v and w, show that the law of cosines is valid:

$$\| \mathbf { v } - \mathbf { w } \| ^ { 2 } = \| \mathbf { v } \| ^ { 2 } + \| \mathbf { w } \| ^ { 2 } - 2 \| \mathbf { v } \| \| \mathbf { w } \| \cos \theta$$

.

Graph each equation.

A hexose was obtained after (+)-glyceraldehyde underwent three successive Kiliani–Fischer syntheses. Identify the hexose from the following experimental information: oxidation with nitric acid forms an optically active aldaric acid; a Wohl degradation followed by oxidation with nitric acid forms an optically inactive aldaric acid; and a second Wohl degradation forms erythrose.

Solve each problem. Round to the nearest tenth, if necessary. Use 3.14 for

$$\pi.$$

What is the length of a rectangle with width 10 in. and area

$$45\ in.^2?$$

Given that ΔABC ≅ ΔDEF, m∠ A = 70°, m∠ B = 60°, m∠ C = 50°, m∠ D = (3x + 10)°, m∠ E = (y/3 + 20)°, and m∠ F = (z² + 14)°, find the values of x, y, and z.