Which of the following situations is best represented by the equation 27 = 3 + 4X2 А
Hillary hod x amount of dollars before she bought 4 necklaces with her allowance. Each necklace costs $3. If
she has $27 left how much was her allowance?
B
Jack had 27 trading cards. He gave his brother 3 of them and then he divided the rest evenly between himself
and three friends. How many cards, x, did Jack have left?
C
Susan completed 4 homework assignments. She completed her science homework in x minutes and her reading
log in 3 minutes. If she spends a total of 27 minutes on her science and reading homework, how long did it take
her to complete the science homework
D
Cory cams money every week by raking leaves in his neighbor's yard. Cory is paid $4 for every yard he rakes
and he charges a $3 fee for bagging up the leaves. If he makes a $27 profit, what is x, the number of yards he
mowed?
a
a
b
b

C

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x is the total time in minutes for the free response

you are given number of questions as 15 - m and time per item as 8 minutes

to find x multiply the two givens together:

x = 8 * (15-m) = 8(15-m)

the equation is not included but the answer is (1.50, 2.00, 2.75)

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.