Sketch each parabola using the given information. vertex (3,6), y-intercept 2

Write the rational number as a decimal.

$$\frac{4}{7}$$

Use the matrix capabilities of a graphing utility to find the inverse of the matrix (if it exists).

$$\left[\begin{array}{rrr}{-\frac{5}{6}} & {\frac{1}{3}} & {\frac{11}{6}} \\ {0} & {\frac{2}{3}} & {2} \\ {1} & {-\frac{1}{2}} & {-\frac{5}{2}}\end{array}\right]$$

Let y = f(x) be a cubic polynomial with leading coefficient a = -1 and f(2) = f(i) = 0.Write an equation for f.

Based on the graph, determine the domain and the range of the quadratic function. $f(x)=3 x^{2}-12 x+4$

Starting with $2,3,5,7 , \ldots ,$ construct the positive integers $1 + 2 \cdot 3$ , $1 + 2 \cdot 3 \cdot 5,1 + 2 \cdot 3 \cdot 5 \cdot 7 , \ldots .$ Do you always get a prime number this way?

Simplify. State any restrictions on the variables. a)

$$\frac { 1 } { 3 } + \frac { 5 } { 4 }$$

b)

$$\frac { 2 x } { 5 } + \frac { 6 x } { 2 }$$

c)

$$\frac { 5 } { 4 x ^ { 2 } } + \frac { 1 } { 7 x ^ { 3 } }$$

d)

$$\frac { 2 } { x } + \frac { 6 } { x ^ { 2 } }$$

D. Read the following conversation. Circle the verb in each question. Then, write the appropriate form of that same verb in the blank. The first one has been done for you.

1. JUAN ¿Buscaste una camisa nueva? EMILIO: Si, yo ____________ una camisa nueva. Tere ____________ zapatos.

A flat wooden frame of uniform width, with outside dimensions of 8 inches by 10 inches, surrounds a rectangular photograph. If

$$15 \mathrm { in. } ^ { 2 }$$

of the photograph is visible, how wide is the material from which the frame is made?

Find the slope of the line described by each equation. y+2=7x

In a maternity ward, four babies become accidentally mixed up. The ABO types of the four babies are known to be O, A, B, and AB. The ABO types of the four sets of parents are determined. Indicate which baby belongs to each set of parents:

$$\text { (a) } A B \times O , ( b ) A \times O , ( c ) A \times A B \text { (d) } \mathrm { O } \times \mathrm { O }$$

A bottle of wine contains 12.5% ethanol by volume. The density of ethanol $\left( \mathrm { C } _ { 2 } \mathrm { H } _ { 5 } \mathrm { OH } \right)$ is 0.789 $\mathrm { g } / \mathrm { cm } ^ { 3 } .$ Calculate the concentration of ethanol in wine in terms of mass percent and molality.

Sketch the surface.

$$z = y ^ { 2 } - 1$$

Replace the circle with the proper comparison symbol: 3 - 4 O 4 - 3