The drama club is selling tickets to their play to raise money for the show's expenses. each student ticket sells for $5 and each adult ticket sells for $9. the auditorium can hold no more than 90 people. the drama club must make a minimum of $610 from ticket sales to cover the show's costs. if 57 student tickets were sold, determine the minimum number of adult tickets that the drama club must sell in order to meet the show's expenses. if there are no possible solutions, submit an empty answer.

  NO SOLUTION

Step-by-step explanation:

The maximum number of adult tickets that can be sold is ...

  90 -57 = 33

The revenue from sale of 57 student and 33 adult tickets is ...

  57×$5 + 33×$9 = $285 +297 = $582

The drama club cannot meet expenses by selling available seats.

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1