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Use the formula for the area of a rectangle and the Pythagorean Theorem to solve A small television has a picture with a diagonal measure of 10 inches and a viewing area of 48 square inches. Find the length and width of the screen. (IMAGE CAN NOT COPY)

When a small plane flies with the wind, it can travel 800 miles in 5 hours. When the plane flies in the opposite direction, against the wind, it takes 8 hours to fly the same distance. Find the average velocity of the plane in still air and the average velocity of the wind.

Between 1990 and 2013 , there was a drop in violent crime and a spike in the prison population in the United States. The bar graph shows the number of violent crimes per \(100,000\) people and the number of imprisonments per \(100,000\) people for six selected years from 1990 through 2013. (GRAPH CAN NOT COPY) a. Based on the information in the graph, it appears that there was a year when the number of violent crimes per \(100,000\) Americans was the same as the number of imprisonments per \(100,000\) Americans. According to the graph, between which two years did this occur? b. The data can be modeled by quadratic and linear functions. Violent erime rate \(\quad y=0.6 x^{2}-28 x+730\) Imprisonment tate \(-15 x+y=300\) In each function, \(x\) represents the number of years after 1990 and \(y\) represents the number per \(100,000\) Americans. Solve a nonlinear system to determine the year described in part (a). Round to the nearest year. How many violent crimes per \(100,000\) Americans and how many imprisonments per \(100,000\) Americans were there in that year?

What is a system of nonlinear equations? Provide an example with your description.

Write sentence as an inequality in two variables. Then graph the inequality. The \(y\)-variable is at least 2 more than the product of \(-3\) and the \(x\)-variable.

With the current, you can canoe 24 miles in 4 hours. Against the same current, you can canoe only \(\frac{3}{4}\) of this distance in 6 hours. Find your average velocity in still water and the average velocity of the current.

With the current, you can row 24 miles in 3 hours. Against the same current, you can row only \(\frac{3}{4}\) of this distance in 4 hours. Find your average rowing velocity in still water and the average velocity of the current.

The graphs of solution sets of systems of inequalities involve finding the intersection of the solution sets of two or more inequalities. By contrast, you will be graphing the union of the solution sets of two inequalities. Graph the union of \(y>\frac{3}{2} x-2\) and \(y<4\).

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. A system of two equations in two variables whose graphs are two circles must have at least two real ordered-pair solutions.

Use the exponential growth model, \(A=A_{0} e^{k t},\) to solve this exercise. In \(1975,\) the population of Europe was 679 million. By \(2015,\) the population had grown to 746 million. a. Find an exponential growth function that models the data for 1975 through 2015 b. By which year, to the nearest year, will the European population reach 800 million?