Mrs. Heid needs repairs on her car. She took her car to two different repair shops to get a
quote. Both shops told her there would be a charge for the parts and then a charge per hour.
With x being the number of hours her car is worked on and f(x) the total cost, her quotes are
summarized in the two equations:
Al’s Auto: f(x) = .75 + 15x
Service Place: f(x) = 35 + 35x
Which of the following statements best summarizes Mrs. Heid’s options?

A.
If Mrs. Heid’s car repair takes less than 2
hours she should go with Al's Auto.

C.
If Mrs. Heid’s car repair takes more than 2
hours she should go with Service Palace.

answer: the four apples you took away.

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.

answer: the correct option is d.

explanation:

it is given that the triangle j'k'l' shown on the grid below is a dilation of triangle jkl using the origin as the center of dilation.

from the given graph it is noticed that k(4,8) and k'(2,4). let origin is defined by o and scale factor is defined by k, then

    (1)

distance formula,

put these values in equation (1).

therefore scale factor is     and option d is correct.