Melinda and paul shovel driveways and sidewalks in the winter as a way to earn extra money. together they shoveled 450 square feet of sidewalk in 30 minutes. then melinda shoveled for 20 minutes while paul shoveled for 25 minutes to complete 345 square feet of driveway. how much more can paul shovel in 1 minute than melinda?

30x + 30y = 450

20x + 25y = 345

3 square ft per minute

yes

step-by-step explanation:

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.