Prove that the diagonals of a parallelogram bisect each other.

Use a graphing utility to graph each pair of equations on the same set of axes. Determine how the two equations are related.

$y_1=x^3-3 x^2$ and $y_2=x^3+3 x^2-4$

Engineers are designing a stretch of highway in a valley. They want to install a storm drain at its lowest point. The equation for the transition curve is $y=0.00004 x^2-0.05 x+1100$. Determine the coordinates of the storm drain, to the nearest unit.

Solve each polynomial equation.

$$x^3-4 x^2+4 x-16=0$$

How could rounding affect your answer to the Exercise earlier?

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.

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

Find an equation giving the distance traveled as a function of time.

Marketing A company determines that it can sell $100$ calculators per month if the selling price is $\$ 25$. For each $\$ 2$ decrease in the price, the number of calculators sold per month increases by $20$ . Find the revenue function and determine the price the company should sell the calculators for if they want a revenue of $\$ 3000$ for the month.

Solve each polynomial equation.

$$x^3-2 x^2-48 x=0$$

Express the equation of the given line in standard form. Then find the distance from the given point $P\left(x_1, y_1\right)$ to that line. Round answers to the nearest hundredth.

The line is perpendicular to the line $2 y=3 x-4$ and passes through the origin; $P(2,-5)$.

How would you determine the cubic polynomial that has the solutions $-3,-2$, and $7$ ?

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.

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

Determine the symmetries of each equation. Then use the properties of symmetry to graph each equation.

$$y=|x-2|$$

Determine the remainder on dividing $x^4+x^3+x^4+x^2+x+1$ by $x-1$.

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.