Factor the trinomial. x²-2x-63

Find the center, vertices, foci, and asymptotes of the hyperbola, and sketch its graph using the asymptotes as an aid. Use a graphing utility to verify your graph. $\frac{(x-2)^{2}}{4}-\frac{(y+5)^{2}}{25}=1$

Use the Binomial Theorem to expand the expressions

$$\left( 2 x + \frac { 1 } { 3 } \right) ^ { 3 }$$

The table shows ordered pairs that satisfy the equation $y=-x^{2}+2 x+15.$

$$\begin{array}{|c|c|c|c|c|c|}\hline x & {-3} & {0} & {2} & {3} & {5} \\ \hline y & {0} & {15} & {15} & {12} & {0} \\ \hline\end{array}$$

Based on this table, what is the solution set of the equation $-x^{2}+2 x+15=0 ?$ F. {0, 15} G. {-3, 15} H. {5, 0} I. {-3, 5}

An 8 foot ladder leaning against a house touches 7 feet above the ground. Draw a diagram and determine the measure of the angle created by the ladder and the ground.

A jogger travels a route that has two parts. The first is a displacement

$$\vec { \mathrm { A } }$$

of 2.50 km due south, and the second involves a displacement

$$\vec { \mathrm { B } }$$

that points due east. (a) The resultant displacement

$$\vec { \mathbf { A } } + \vec { \mathbf { B } }$$

has a magnitude of 3.75 km. What is the magnitude of

$$\vec { \mathrm { B } }$$

and what is the direction of

$$\vec { \mathbf { A } } + \vec { \mathbf { B } }$$

relative to due south? (b) Suppose that

$$\vec { \mathbf { A } } - \vec { \mathbf { B } }$$

had a magnitude of 3.75 km. What then would be the magnitude of

$$\vec { \mathrm { B } }$$

, and what is the direction of

$$\vec { \mathbf { A } } - \vec { \mathbf { B } }$$

relative to due south?

Determine whether y varies directly with x. If so, find the constant of variation. $5 x+y=0$

La papalera esta ______________________________________ de la puerta.

Find all solutions of the given system of equations and check your answer graphically.

$$\begin{array}{l}{2 x+y=2} \\ {-2 x+y=2}\end{array}$$

Simplify each expression.

$$7^{-2}$$

The formula for calcium oxide is CaO. What are the formulas for magnesium oxide and strontium oxide?

Instead of arranging dots into squares,suppose we extend our thinking to consider squares of side length x cm. Create a formula for the area $A(x) \mathrm{cm}^{2}$ of a square if side length x cm: A(x) = _______.

The line y = (5/9)x + 6 is graphed on a coordinate plane. A second line is drawn on the same plane with a slope of -(5/9) and y-intercept (0, -6). Write the equation of the second line. Describe the relationship between these two graphs.

Use natural logarithms to solve each equation. $e^x = 18$