Since the opening night, attendance at Play A has
increased steadily, while attendance at Play B first rose and then fell.
Equations modeling the daily attendance y at each play are shown below,
where x is the number of days since the opening night. On what day(S)
was the attendance the same at both plays? what was the attendance?
Play A: y = 16x + 150
Play B: y = -x^2 60x - 10
answer choices:
The attendance was the same on day 40. The attendance was 790 at both plays that day.
The attendance was the same on day 4. The attendance was 214 at both plays that day.
The attendance was the same on days 4 and 40. The attendance at both plays on those days was 214 and 790 respectively.
The attendance was never the same at both plays.
plus or minus 60 x
plus
thankks
To find the day(s) on which the attendance was the same at both plays, we need to set the equations for Play A and Play B equal to each other and solve for x.
Setting the equations equal:
16x + 150 = -x^2 + 60x - 10
Rearranging the equation:
x^2 - 44x + 160 = 0
To solve this quadratic equation, we can factor it or use the quadratic formula. Let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this equation, a = 1, b = -44, and c = 160.
Applying the quadratic formula:
x = (-(-44) ± √((-44)^2 - 4(1)(160))) / (2(1))
x = (44 ± √(1936 - 640)) / 2
x = (44 ± √1296) / 2
x = (44 ± 36) / 2
Simplifying:
x = (44 + 36) / 2 or x = (44 - 36) / 2
x = 80 / 2 or x = 8 / 2
x = 40 or x = 4
Therefore, the attendance was the same on days 4 and 40. To find the attendance on these days, we can substitute these values back into one of the equations.
For day 4:
Play A: y = 16(4) + 150 = 214
Play B: y = -(4)^2 + 60(4) - 10 = 214
For day 40:
Play A: y = 16(40) + 150 = 790
Play B: y = -(40)^2 + 60(40) - 10 = 790
So, the correct answer is:
The attendance was the same on days 4 and 40. The attendance at both plays on those days was 214 and 790, respectively.
私たちに物を売ろうとしないでください。そのクソ迷惑
just find when the two are equal:
16x+150 = -x^2+60x-10
x^2 - 44x + 160 = 0
(x-40)(x-4) = 0
Now the answer should be clear.