Will mark also 99 if a train is scheduled to go 87 and 1 half miles in 2 and 1 half hours, what average speed must it travel? answer options with 5 options a. 37 and 1 fourth miles per hour b. 43 and 3 fourths miles per hour c. 35 miles per hour d. 25 miles per hour e. 2.5 miles per hour

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.

the furthest the dog can be is 508 meters away from the house, and the closest he can be is 492 meters away from the house.