91Ó°ÊÓ

A football team plays in a large stadium. With a ticket price of \(\$ 20,\) the average attendance at recent games has been \(30,000.\) A market survey indicates that for each \(\$ 1\) increase in the ticket price, attendance decreases by 500 . a. Express the number of spectators at a football game, \(N\), as a function of the ticket price, \(x\). b. Express the revenue from a football game, \(R\), as a function of the ticket price, \(x\)

Find \(f(g(x))\) and \(g(f(x))\) and determine whether each pair of functions \(f\) and \(g\) are inverses of each other. $$f(x)=-x \text { and } g(x)=-x$$

In Exercises \(1-18\), find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimals places. $$(0,-2) \text { and }(4,3)$$

A baseball team plays in a large stadium. With a ticket price of \(\$ 15,\) the average attendance at recent games has been \(20,000 .\) A market survey indicates that for each \(\$ 1\) increase in the ticket price, attendance decreases by \(400 .\) a. Express the number of spectators at a baseball game, \(N\), as a function of the ticket price, \(x\). b. Express the revenue from a baseball game, \(R\), as a function of the ticket price, \(x\).

In Exercises \(1-18\), find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimals places. $$(3.5,8.2) \text { and }(-0.5,6.2)$$

On a certain route, an airline carries 9000 passengers per month, each paying \(\$ 150 .\) A market survey indicates that for each \(\$ 1\) decrease in the ticket price, the airline will gain 50 passengers. a. Express the number of passengers per month, \(N,\) as a function of the ticket price, \(x\) b. Express the monthly revenue for the route, \(R\), as a function of the ticket price, \(x\).

Use the given conditions to write an equation for each line in point-slope form and general form. Passing through \((4,-7)\) and perpendicular to the line whose equation is \(x-2 y-3=0\)

Find the average rate of change of the function from \(x_{1}\) to \(x_{2}.\) $$f(x)=3 x \text { from } x_{1}=0 \text { to } x_{2}=5$$

Graph each equation . Let \(x=-3,-2,-1,0\) \(1,2,\) and 3. $$y=x+2$$

The sum of two numbers is \(66 .\) Express the product of the numbers, \(P,\) as a function of one of the numbers, \(x\).