Solve the equation by completing the square. Round to the nearest tenth if necessary.

$$x^2 + 4x = 6$$

draw a scatter diagram

$$\begin{array}{ccccccc}{X} & {0} & {1.2} & {1.8} & {2.3} & {3.5} & {4.1} \\ \hline Y & {2} & {6.4} & {7} & {7.3} & {4.5} & {2.4} \\ \hline\end{array}$$

Evaluate each determinant.

$$\left| \begin{array} { c c } { - 5 } & { - 1 } \\ { - 2 } & { - 7 } \end{array} \right|$$

Find the value of k that would make the left side of each equation a perfect square trinomial. $25 x^{2}-k x+1=0$

Use Pascal’s Triangle to find the binomial coefficient. $_7C_2$

Use the Intermediate Value Theorem and Rolle’s Theorem to prove that the equation has exactly one real solution. 2x² + 7x - 1 = 0

Find the first five terms of each sequence described.

$$a _ { 1 } = 6 , a _ { n + 1 } = 3 a _ { n } - n$$

Suppose A is an orthogonal matrix. Then show that $\mathbf{A}^{-1}$ is orthogonal.

Work cooperatively. Use a graphing calculator to solve each system of inequalities.

$$\begin{array}{l}{y \geq 2 x+1} \\ {y \leq-x-1}\end{array}$$

For the reaction at 298 K,

$$2 \mathrm { NO } _ { 2 } ( g ) \rightleftharpoons \mathrm { N } _ { 2 } \mathrm { O } _ { 4 } ( g )$$

the values of $\Delta H ^ { \circ }$ and $\Delta S ^ { \circ }$ are $- 58.03\ \mathrm { kJ }$ and $- 176.6\ \mathrm { J/K }$ respectively. What is the value of $\Delta G ^ { \circ }$ at 298$\mathrm { K }$? Assuming that $\Delta H ^ { \circ }$ and $\Delta S ^ { \circ }$ do not depend on temperature, at what temperature is $\Delta G ^ { \circ } = 0 ?$ Is $\Delta G ^ { \circ }$ negative above or below this temperature?

Find a polynomial function that has the given zeros. (There are many correct answers.) $-7,4-\sqrt{6}, 4+\sqrt{6}$

Distinguish between essential and nonessential amino acids.

Write the number in scientific notation. Show the steps you used to get the answer. 12.4 × 10^-5

Add or subtract.

$$\left[\begin{array}{ccc}{0} & {-1} & {5} \\ {6} & {10} & {12}\end{array}\right]+\left[\begin{array}{rrr}{9} & {-5} & {7} \\ {-4} & {10} & {0}\end{array}\right]$$