Write the form of the partial fraction decomposition of the rational expression. Do not solve for the constants. $\frac{6 x+5}{(x+2)^{4}}$

Choose the letter of the correct term or concept below to complete the sentence. a. ACT b. SAT c. forensic psychologist d. industrial/organizational psychologist e. sports psychology f. visualization g. gerontology h. crisis intervention program i. clinical psychologist j. school psychologist. A(n) __________ is often self-employed, practicing some form of psychotherapy.

Evaluate the expression.

$$\frac{(1 + 6)9}{5^2 - 4}$$

Solve the equation. Check your solution.

$$24 + x ^ { 2 } = 10 x$$

Evaluate each expression for a = -5 and b = -2. Write in simplest form.

$$\frac { b } { a }$$

A lottery game is set up so that each player chooses six different numbers from 1 to 15. If the six numbers match the six numbers drawn in the lottery, the player wins (or shares) the top cash prize. What is the probability of winning the prize with 50 different lottery tickets?

Sketch the graph of all complex numbers z satisfying the given condition. $|z| = 6$

Find the x- and y-intercepts of the graph of the linear equation. 3y = 6x - 9

The building for the headquarters for the United States Department of Defense is In the shape of a regular polygon with five sides. What is the measure of one of the interior angles of the building?

Fix any labelling of the vertices of a square and use this to identify $D_8$ as a subgroup of $S_4$. Prove that the elements of

$$D_8$$

and $\langle (1\ 2\ 3) \rangle$ do not commute in $S_4$.

Powers of trigonometric functions are rewritten to be useful in calculus. Verify the identity. $\sec ^{4} x \tan ^{2} x=\left(\tan ^{2} x+\tan ^{4} x\right) \sec ^{2} x$

We know that for an adiabatic process

$$pV^γ = a$$

constant. Evaluate “a constant” for an adiabatic process involving exactly 2.0 mol of an ideal gas passing through the state having exactly p = 1.0 atm and T = 300 K. Assume a diatomic gas whose molecules rotate but do not oscillate.

Fill in each blank so that the resulting statement is true. Sums of money that reduce federal income tax by the full dollar-for-dollar amount are called _____.

Let

$$\begin{equation*}V=\begin{pmatrix}\begin{bmatrix}v_1\\v_2\end{bmatrix}\in R^2:v_1=0 \end{pmatrix}\end{equation*}$$

and

$$\begin{equation*}W=\begin{pmatrix}\begin{bmatrix}v_1\\v_2\end{bmatrix}\in R^2:v_2=0 \end{pmatrix}.\end{equation*}$$

(a) Prove that both $V$ and $W$ are subspaces of $R^n$. (b) show that $V\cup W$ is not a subspace of $R^2.$