Question

The attendances y for two movies can be modeled by the following equations, where x is the number of days since the movies opened.



y=-x^2+35x+100 Movie A

y=-5x+275 Movie B



When is the attendance for each movie the same?
After ___ days and after ___ days.

Answer 1

Answer:

After

days and after

days.

Answer 2

By solving a quadratic equation, we will see that the attendance will be the same after 5 days and after 35 days.

When is the attendance for each movie the same?

This will happen for the values of x such that:

y = -x^2 +35x + 100 = y = -5x+275

There says that the attendance for movie A is the same as the one for movie B. So we just need to solve that.

We can write the equation as:

-x^2 +35x + 100 = -5x+275

If we simplify this, we get:

-x^2 + 35x + 100 + 5x - 275 = 0

-x^2 + 40x - 175 = 0

This is a quadratic equation, the two solutions are given by Bhaskara's formula, we will get:

$x = \frac{-40 \pm \sqrt{(40ft)^2 - 4*(-1)*-175)} }{2*-1} \\\\x = \frac{-40 \pm 30}{-2}$

So the two solutions are:

x = (-40 + 30)/-2 = 5

x = (-40 - 30)/-2 = 35

So, the attendance will be the same after 5 days and after 35 days.

If you want to learn more about quadratic equations, you can read:

https://brainly.com/question/1214333