Find the equation of the line passing through the points $\left(5\,,7\right)$ and $\left(-2\,,\,8\right)$. Write the final equation in slope-intercept form.

Teresa bought a pair of shoes on sale for $\$\Va $. The sale price was $\VqSubOneSub 0\%$ of the regular price. Find the regular price $n$ of the shoes.

Evaluate the following expression
$$\frac{\VaSubOneSub \VPlusbSubOneSub i}{\VaSubTwoSub \VPlusbSubTwoSub i}\,$$

Describe all values $x$ within a distance of $7$ from the number $5$ in interval notation.

Given $$f\left(x\right)\,=\,\frac{5}{x^{2}-4}$$ and $$g\left(x\right)=\frac{2}{x-1}$$, find the domains of both $f\left(g\left(x\right)\right)$ and $g\left(f\left(x\right)\right)$ as a union of intervals written in natural order.

Solve $$\left|x-27\right|-4=-6$$

A couple plans to go on a month-long vacation to Singapore (assume that one month is four weeks). They set aside $\$87,500$ for the trip and are planning to spend $\$28,000$ each week. 

1. Write a linear model for the amount of money $M$ they have remaining after $w$ weeks.
2. Will they be able to afford their entire trip to paid for from their savings?

Give all the possible rational zeros for $f(x)=3x^5 - 5x^3 + 4$. 

Enter your answers in the increasing order.

Identify the multiplicity of the zeros of $$f\left(x\right)=\Va x\left(x\VMinusb \right)^{\VnSubOneSub }\left(x\VMinusc \right)^{\VnSubTwoSub }\left(x\VMinusd \right)^{\VnSubThreeSub }$$

Are $f(x)=\frac{1}{x-4}$ and $g(x)=\frac{1}{x}+4$  inverses of each other for $x\neq 0, 4$?

The volume $V$ of a gas in a container varies inversely with the pressure of the gas $p$. If a container of gas has a volume of $\VV \uL$ when the pressure is $\Vp $ atm.

• Write an equation that relates the volume to the pressure
• If the pressure is $\VpSubOneSub $ atm, what will the volume of the gas be?

Write the following exponential equation in logarithmic form  $$3^{4}=81$$

Expand the following logarithmic expression
$$\log_{2}\left(\frac{100x\left(x+2\right)^{3}}{x-8}\right)$$

Solve for $x$.$4\log_{2}x-6=14$

The following data represent the growth of a bacteria population over time $t$.

Determine:

• The equation that represents the bacteria population $y$ at a time $t$
  
  
• The doubling time

Find the cosine of $\angle X$.

Given the following right angle triangle, determine the $\csc \theta,\sec \theta,\;\text{and}\;\cot \theta$

Which of the following is a periodic function.

If $\sin\theta=\frac{9}{10}$ in Quadrant II, find $\sin(2\theta)$, $\cos(2\theta)$, and $\tan(2\theta)$ using the double angle identities.

Given a triangle with $a=2$, $b=3$, and $c=4$, find the angles.

A vector $\vec{u}$ starts at $(30,20)$ and ends at $(6,13)$. Another vector $\vec{v}$ starts at $(-1,-2)$ and ends at $(-21,-17)$. Are the magnitudes the same? Are the directions the same?

An amusement park sold three kinds of tickets to its latest concert. The adult ticket sold for $\$20$, the student ticket for $\$18$, and the child ticket for $\$10$. The amusement park sold $300$ tickets and earned $\$5220$ in one night. The number of adult tickets sold is twice the number of child tickets sold. How many of each type did the amusement park sell?

Let $x$ be the number of adult tickets, $y$ be the number of student tickets, and $z$ be the number of child tickets.

Find the partial fraction decomposition of $$\frac{x^{2}+2x+5}{(x+1)^{3}}$$

Set $A=\begin{bmatrix} {5}&{-3}\\ {-1}&{7}\\ \end{bmatrix},\,B=\begin{bmatrix} {2}&{1}\\ {-4}&{3}\\ \end{bmatrix}$. Compute $AB$ and $BA$.

Find the sum of the arithmetic series below.

$2+6+10+\dots+62$

Use Pascal's Triangle to expand $$(2x-y)^{5}$$