A car sharing service charges your account once a month according to how much you use their cars. The graph shows the amount charged for the month in dollars as a function of the number of miles driven.

1. Use this information to predict how many miles a customer would need to drive so that the monthly charge is $100.
2. Is the monthly charge a linear function of miles driven? Explain your reasoning.

In science class, Jada uses a graduated cylinder with water in it to measure the volume of some marbles. After dropping in 4 marbles so they are all under water, the water in the cylinder is at a height of 10 milliliters. After dropping in 6 marbles so they are all under water, the water in the cylinder is at a height of 11 milliliters.

1. What is the volume of 1 marble?
2. How much water was in the cylinder before any marbles were dropped in?
3. What should the height of the water be after 13 marbles are dropped in?
4. Is the relationship between volume of water and number of marbles a linear relationship? If so, what does the slope of a line representing this relationship mean? If not, explain your reasoning.

Solve each of these equations. Explain or show your reasoning.

The school designed their vegetable garden to have a perimeter of 32 feet, with the length measuring 2 feet more than twice the width.

1. Using \(\ell\) to represent the length of the garden and \(w\) to represent its width, write and solve a system of equations that describes this situation.

2. What are the dimensions of the garden?