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Chapter 7: Problem 89
What is a half-plane?
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Use a system of linear equations to solve Exercises. A hotel has 200 rooms. Those with kitchen facilities rent for \(\$ 100\) per night and those without kitchen facilities rent for \(\$ 80\) per night. On a night when the hotel was completely occupied, revenues were \(\$ 17,000 .\) How many of each type of room does the hotel have?
a. Graph the solution set of the system: $$\left\\{\begin{array}{c}x \geq 0 \\\y \geq 0 \\\3 x-2 y \leq 6 \\\y \leq-x+7\end{array}\right.$$ b. List the points that form the corners of the graphed region in part (a). c. Evaluate \(2 x+5 y\) at each of the points obtained in \(\operatorname{part}(\mathrm{b})\)
What is a solution of a system of linear inequalities?
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)
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?
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