David is running a concession stand at a soccer game. He sells nachos and sodas. Nachos cost $2.50 each and sodas cost $1.50each. At the end of the game, David made a total of $120 and sold a total of 72 nachos and sodas combined. Which system of equations represents this situation? (x value represents nachos and y value represents sodas) (12, 60)

(57, 15)

(61, 26)

(15, 57)

it is (12,60)

Step-by-step explanation:

12x2.50= 30.00

60x1.50= 90.00

30+90= 120

1. when "a" is a root of a polynomial, (x -a) is a factor of it. for the three roots given, the factors of the desired polynomial are (x +2)(x -1/2)(x -3).

in order to make the leading coefficient be negative, we need to multiply this product by a negative number. any negative number will do, but we choose a small (magnitude) value that will eliminate the fraction: -2.

then

f(x) = -2(x +2)(x -1/2)(x -3) = -(x +2)(2x -1)(x -3)

= -(2x² +3x -2)(x -3)

= -(2x³ -3x² -11x +6)

f(x) = -2x³ +3x² +11x -6

2. a graph created by the desmos on-line graphing calculator is shown, and the zeros are highlighted.

3. as indicated in part 1, the multiplier of this equation can be anything and the zeros will remain the same. you want a negative leading coefficient, so the "anything" is restricted to any of the infinite number of numbers that will make that be the case.

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