MATH SOLVE

4 months ago

Q:
# WILL GIVE BRAINLIESTSince opening night, attendance at Play A has increased steadily, while Play B first rose then fell. Equations modeling the daily attendance y at each play are shown below, where x is the number of days since opening night. On what day(s) was the attendance the same at both plays and what was the attendance?Play A: y=15x+76Play B: y=-x^2 +36x-4Option A) the attendance was the same on day 5. The attendance was 151 at both plays on that day.Option B) the attendance was the same on day 16. The attendance was 316 at both plays on that day.Option C) the attendance was the same on day 5 and 16. The attendance at both plays on that day was 151 and 316 respectively.Option D) the attendance was never the same at both plays.

Accepted Solution

A:

Play A: y=15x+76

Play B: y=-x^2 +36x-4

set them equal:

15x+76=-x^2 +36x-4

80=-x^2+21x

x^2-21x+80=0

-> solve for x

for example with the quadratic equation formula or solving the square

factorized:

(x-16)(x-5)=0

so x1=5 and x2=16

insert them into y=15x+76

y1=151, y2=316

so (5,151) and (16,316) are days with equal attendance for both plays which is option C

Play B: y=-x^2 +36x-4

set them equal:

15x+76=-x^2 +36x-4

80=-x^2+21x

x^2-21x+80=0

-> solve for x

for example with the quadratic equation formula or solving the square

factorized:

(x-16)(x-5)=0

so x1=5 and x2=16

insert them into y=15x+76

y1=151, y2=316

so (5,151) and (16,316) are days with equal attendance for both plays which is option C