Atheater manager graphed weekly profits as a function of the number of patrons and found that the relationship was linear. one week the profit was  $10,229   when  1374 patrons attended. another week  1595 patrons produced a profit of  $12,107.50 a. find a formula for weekly profit,  y, as a function of the number of patrons,  x. b. what is the break-even point (the number of patrons for which there is zero profit)? round your answer to the nearest integer. c. find a formula for the number of patrons as a function of profit. d. if the weekly profit was  $15,558.50,   how many patrons attended the theater?

Given that profit is a linear function of number patrons.

Let p be the profit and x be the number of patrons.

Let the linear relation be p=mx+b  ( equation of straight line having slope m)

A)Given profit p=10229$, for x=1374

That is 10229 =m(1374)+b

For x= 1595, profit p=12,107.50

That is 12107.5 = m(1595)+b

Subtracting first equation from second equation

12107.5-10229 = m*1595+b -(m*1374+b)

1878.5 = m*(1595-1374)

221m = 1878.5

To find b, we will plugin m=8.5 in first equation.

10229 = 8.5*1374+b

b= 10229-8.5*1374

b=10229-11679= -1450

Hence equation is profit = 8.5x-1450

B) Let us equate profit to 0 and solve for x.

8.5x-1450 = 0

8.5x = 1450

 ≈ 171

Hence break even point is (171,0)

C) p= 8.5x-1450

p+1450 = 8.5x

D)Given weekly profit = 15558.5

So, number of patrons x =

                                        ≈2001 patrons

its an acute right triangle

step-by-step explanation: