Determine whether $a=\frac{4}{3}$ and $b=\frac{1}{3}$ are solutions to the following equation $$3\left(3x-1\right)=6x-2$$

Solve the following linear equation$$\VqSubOneSub (d\VPlusqSubTwoSub )-(d\VPlusqSubThreeSub )=\VqSubFourSub (d\VPlusqSubFiveSub )$$

One number is $\Va $ more than $\Vb $ times another. Their sum is $\Vc $. Find the two numbers. Assume $n$ is the first number.

Without graphing, determine the number of solutions and then classify the two-variable system of linear equations $\begin{cases} {y=2x+3}&{\,}\\ {4x-2y=8\,}&{\,}\\ \end{cases}$

Caleb has a pet sitting business. He charges $\$\Va /\uhr$. His monthly expenses are $\$\Vb $. How many full hours $n$ does he have to work in order to have a profit of at least $\$\Vc $?

Henry is mixing pistachios and almonds to make $12.5$ pounds of trail mix. Pistachios cost $\$16$ per pound and almonds cost $\$6$ per pound. How many pounds $x$ of pistachios and how many pounds of almonds should Henry use for the trail mix to cost $\$10$ per pound?

Lily has an assignment to design a traffic cone, the dimensions of which are shown in the figure below. Given that $a=20\,\ucm\,\text{and}\,c=101\ucm$, use Pythagorean Theorem to find the height of the traffic cone $b$ in$\ucm$.

Matt drove two hours from Austin towards Houston and stopped at a gas station to fill his tank. At the gas station, he met Neal, who had driven three hours from Houston towards Austin. The distance between Austin and Houston is $162\,\umi$, and Matt's speed was nine miles per hour faster than Neal's speed. Find the speed of the two truckers.

Let $s$ be Neal's speed.

Determine the $x$-intercept for this linear equation

Find the slope-intercept equation of the line with slope $-3$ and $y$-intercept $\left(0,-1\right)$. Assume the equation of the line is $y=mx+b$.

Find the slope-intercept equation of the line shown below, using the given information. Assume the equation of the line is $y=mx+b$.

Anna and her family want to go to this year's fair. She heard from a group that it cost $\$\Vh $ for $\Vg $ children and $\Vd $ adults. Her mother also heard from another group that it cost $\$\Vb $ for $\Ve $ children and $\Vf $ adults. If her family has $\Vi $ children and $\Vj $ adults (including her), how much will their tickets cost.

Use $c$  for the cost of children ticket and $a$ for the cost of adult ticket.

Solve the following system of equations by substitution
\begin{lalign*} &{\left(1\right)\,x+3y=7}\\ &{\left(2\right)\,4x-2y=0}\\ \end{lalign*}

Priam has a collection of nickels and quarters, with a total value of $\$\Vv $. The number of nickels $n$ is $\Vb $ less than $\Va $ times the number of quarters $q$. How many nickels and how many quarters does he have?

The tiles in this model represent a quadratic expression $y$. Determine the factored form. Red is positive and blue is negative.

Factor using the "$ac$" method$$\VA x^{2}\VPlusB x\VPlusC $$

Factor

$$\VA w^{2}\VPlusB wu\VPlusC u^{2}$$

Given a rectangle with the area $A\,=\,12x^{2}+4x-21$, determine the dimensions$\,l,w$ of the rectangle where $l>w$ for large enough $x$ values.

Add and simlify$$\frac{7}{3xy+y^{2}}+\frac{4}{9x^{2}-y^{2}}\,$$

Solve the following rational equation for $x$.
$$1+\frac{4}{x}=\frac{5}{x^{2}}$$

Given that the two solids below are similar, what is the height, $h$, of the smaller solid to two decimal places?

Simplify $${\sqrt[\Va ]{\frac{\Vc x^{\Vd }}{y^{\Vf }}}}$$

Determine the equation of the quadratic function given its vertex $\left(\VxSubOneSub ,\VySubOneSub \right)$ and a point on the parabola  $\left(\VxSubTwoSub ,\VySubTwoSub \right)$. 

A rancher wants to construct a rectangular fence with a partition. He buys $100\um$ of fencing to create the fence and partition.

1. Find a formula for the area enclosed by the fence.
2. What is the length $L$ that will give the rancher the most area?
3. What is the maximum area?