A local gym sells monthly memberships. The function f(x) = −x2 + 18x − 72 models the daily profit in dollars, where x is the number of memberships sold.

Determine the zeros, and explain what these values mean in the context of the problem.

x = 9, x = 18; The zeros represent the number of monthly memberships that produces a maximum profit.
x = 9, x = 18; The zeros represent the number of monthly memberships where no profit is made.
x = 6, x = 12; The zeros represent the number of monthly memberships that produces a maximum profit.
x = 6, x = 12; The zeros represent the number of monthly memberships where no profit is made.

A:

Complete the square for the vertex

f(x) = -(x - 18x) - 72

f(x) = -(x - 18x + 81) - 72 + 81

f(x) = -(x - 9)^2 + 9

so the vertex is (9, 9).  The vertex is the point where the maximum amount of profit is made.

B:

f(x) = x^2 - 18x + 72 (this makes the factoring easier and doesn't change the x-intercepts)

f(x) = (x - 12)(x - 6) = 0

set both factors equal to 0

x - 12 = 0                        x - 6 = 0

x = 12                             x = 6

These are the number of memberships where the gym will break even meaning neither make a profit nor take a loss.

answer:

total cost for tiles and paints is $924.  

step-by-step explanation:

we have been given that a community hall is in the shape of a cuboid. the hall is 40m long 15m high and 3m wide.

the paint will be required for 4 walls and ceiling.

let us find area of walls and ceiling.

therefore, the area of walls and ceiling is 1410 square meters.

given: cost for 10 litre of paint is $10 and 10 litre paint covers 25 square meter. therefore,

therefore, the total painting cost is $564.

tiles will be required for floor. let us find the area of floor.

given: 1m squared floor tiles costs $3. so,

therefore, the total tiles cost is $360.

now let us find combined total cost of tiles and paint.

therefore, the combined total cost of tiles and paint is $924.