Solve the equation.

$$( a - 5 ) ^ { 2 } - 4 ( a - 5 ) - 21 = 0$$

Simplify the quotient. Answer the following correctly.

$$\left(\frac{3}{4}\right)^2$$

Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. ∫ sin² 2x cos 2x dx = 1/3sin³ 2x + C

Use the data in the accompanying table and express all results in decimal form.

$$\begin{matrix} \text{ } & \text{Driver Killed} & \text{Driver Not Killed}\\ \text{Seatbelt used} & \text{3655} & \text{7005}\\ \text{Seatbelt not used} & \text{4402} & \text{3040}\\ \end{matrix}$$

Fi nd the probability of randomly selecting a driver and getting one who was

not ki lled given that the driver was using a seatbelt.

If $p \geqslant 5$ and $p$ is prime, prove that $[p] = [1]$ or $[p] = [5]$ in $\mathbb{Z}_6$.

Find the standard matrix of the linear transformation T, and use it to determine whether T is onto. $T:R^3\to R$ defined by

$$\begin{equation*}T\begin{pmatrix}\begin{bmatrix}x_1\\x_2\\x_3\end{bmatrix}\end{pmatrix} =2x_1-5x_2+4x_3.\end{equation*}$$

Consider the sequence {A$_n$}whose nth term is given by
$A_n=P\left(1+\frac{r}{12}\right)^n$
where P is the principal, $A_n$ is the account balance after n months, and r is the annual interest rate (in decimal form). Write the first 10 terms of the sequence when P=$1000 and r=0.03.

Determine whether each statement is true or false. If the statement is falsey make the necessary change(s) to produce a true statement. The functions

$$f ( x ) = 3 ^ { - x } \text { and } g ( x ) = - 3 ^ { x }$$

have the same graph.

a.

$$( 9 \sqrt { x - 5 } ) ^ { 2 }$$

b.

$$( 9 + \sqrt { x - 5 } ) ^ { 2 }$$

In this exercise, find, to the nearest hundredth, the radian measures of all $\theta$ in the interval $0 \leq \theta<2 \pi$ that make the equation true.

$$10 \sin \theta+1=3-2 \sin \theta$$

The function f is defined by $f : x \mapsto-10 \sin 2 x \cos 2 x, 0 \leqslant x \leqslant \pi$. Write down an expression for f(x) in the form k sin 4x.

Simplify.

$$\frac { 3 x ^ { - 2 } y ^ { 5 } } { 9 x ^ { 3 } y ^ { 5 } }$$

Use prime factorization to subtract these fractions: 1/18 - 1/30

Solve each equation.

$$7x + 5 = 5(x + 3) + 2x$$