Task 1: 6.4 Application of Linear Systems A community theater is putting on a performance. ⦁ An adult ticket sells for a dollars.

⦁ A child’s ticket sells for c dollars.

System A - adults 600, children 200
System B - adults 700, children 100
System C - adults 500, children 300

⦁ The manager needs to collect $5000 in revenue to cover the theater’s expenses.

⦁ The theater can seat 800 people, and the manager expects to sell out.

⦁ The manager wants to price the adult ticket at three times the cost of a child’s ticket.

The manager wants to find the break-even point where the theater’s income equals its expenses. You need to determine the price of each ticket given the number of tickets sold for the three Systems below.

f(x) is going down by 4

step-by-step explanation:

(its either that or its going left by 4)

69.64%

step-by-step explanation:

let f (x ) is a function and c be a positive real number,   the graph of the function g (x ) = f (cx ) is represented as follows.

when, c > 1,   the function compresses it in the x - direction.

when, 0 < c < 1, the function stretches it.

the function is g ( x ) = (9x )2.

the heighest power of x in g ( x ) = (9x )2 is 2, so the parent function is square function.

the equation of parent function is f ( x ) = x 2 .

the function is g ( x ) = (9x )2 and the parent function is f ( x ) = x 2 .

so, the functions f and g have the following relationship.

g ( x ) = f ( 9x ).

compare the function g ( x ) = f ( 9x ) with g (x ) = f (cx ).

c = 9 ( > 1 ).

so, the function g (x ) = (9x )2 compresses it in the x - direction.

step-by-step explanation: