Express the equation of the given line in the form $A x+B y+C=0$. Then find the distance from the given point $P\left(x_1, y_1\right)$ to that line. Round answers to the nearest hundredth.

$$x=3 ; P(5,7)$$

For each point, determine another point that satisfies the specified symmetry.

$(-1,3)$; origin

Show that $P(1,1), Q(5,4), R(9,1)$, and $S(5,-2)$ are the vertices of a rhombus.

To rent a car from the RENT-ME Car Rental Company costs $\$ 25$ per day plus $\$ 0.07$ per mile. For the number of days indicated, find a linear function for the cost $C$ of renting the car as a function of the number of miles driven $d$.

The car is rented for five days.

Solve each quadratic equation by an appropriate method.

$$x^2-10 x+70=0$$

Using the given information, find the equation of the line.

The line passes through the points $(6,1)$ and $(-3,2)$.

Express each quadratic function in the form $f(x)=a(x-h)^2+k$. Then use transformations of the graph of $f(x)=x^2$ to graph each function.

$$f(x)=\frac{1}{4} x^2-2 x+3$$

Determine the symmetries of each equation and then graph.

$$x^2 y=2$$

Solve each polynomial equation. If a solution occurs more than once, state its multiplicity.

$$x^3+x^2-9 x-9=0$$

Determine the equation of the line satisfying the given conditions:

Passes through the point $(-2,-4)$ and has slope of $-2$

A ball thrown in space where there is virtually zero gravity would travel in a straight line at a constant speed. The data below was collected.

$$\begin{array}{c|c} \text{Time (s)} & \text{Distance (ft)} \\ \hline 10 & 5.70 \\ 0.2& 8.5 \\ 0.5& 16.6 \\ 0.7& 22.0 \\ 1.5& 43.6 \end{array}$$

Determine the slope of the line that contains the points.

In the derivation of the formula for the distance from a point to a line, the slope of the line $\ell$ is given as $-\frac{A}{B}$. Explain why this is true.

Solve each polynomial equation.

$$3 x^3+17 x^2-28 x=0$$

A swimming pool manufacturer makes rectangular pools so that the sides are in the ratio $1: 2: 3$. If the pool holds $2058 \mathrm{ft}^3$ of water when filled to the top, find the dimensions of the pool.