Tickets for a dance recital cost $12 for adults and $8 for children. The dance company sold 257 tickets, and the total receipts were $2,576. How many adult tickets and how many child
tickets were sold? Set up a system of equations, state both variables, and solve. Write your
answer in a complete sentence and make sure to write the units.

Step-by-step explanation:

a + c = 257

12a + 8c = 2576

-12a - 12c = -3084

12a  + 8c = 2576

-4c = -508

c =  127 children tickets

a + 127 = 257

a = 130 adult tickets

if the eqn of the parabola is f(x) = (x-4)(x+2), we need to mult. this out to find the coordinates of the vertex.

then f(x) = x^2 + 2x - 4x - 8, and f(x) = x^2 - 2x - 8.

one way in which you can find the vertex is to calculate x = -b / (2a).   here, that comes to

        )

x = = 1.   f(1) = 1^2 - 2(1) - 8 = - 9.   vertex is at (1, -9).

        2(1) 

find another point on the curve:   let x=0, for which y=-8.   then (0, -8) is on the curve.   plot the vertex and this point and draw a smooth parabola thru both.

hope this

765238725478629038640962136509762139056074

step-by-step explanation:

64087235609746097215074621039754021037