An amphitheater charges $74 for each seat in Section A, $59 for each seat in Section B, and $28 for each lawn seat. There are three times as many seats in Section B as in Section A. The revenue from selling all 13,000 seats is $503,000. Let x be the number of seats in A, y be the number of seats in B, and z be the number of lawn seats. Which system of equations represents the situation?

Step-by-step explanation:

let x be the number of seats in A,

y be the number of seats in B, and

z be the number of lawn seats.

y=3x

the total number of seats is given by

(x+y+z)=13000

put y=3x

(x+3x+z)=13000

(4x+z)=130001

also

(4x+z)13000=5030002

hence the systems of equation is

(4x+z)=130001

(4x+z)13000=5030002

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

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