Question

Two linear functions are combined with addition, and then the same two linear functions are combined by multiplication.

Answer 1

Answer:

Step-by-step explanation:

We can eliminate options C and D quite quickly because factoring either one would have one equation be y = x and the other either y = 72x - 96 or y = 72x + 108. Neither of these added to x will give either option A or B

so that leaves E.

72x² – 204x + 144 = 0

we can find the zeros

x = (204 ± √(204² - 4(72)(144))) / (2(72))

x = (204 ± 12) / 144

x = 1.5

x = 4/3

so the equation has factors

(x - 1.5)(x - 4/3)

and therefore also a factor in their product

x² - ($\frac{17}{6}$)x + 2

which is 1/72 of the original quadratic

so all factors of E are

72(x - 1.5)(x - 4/3)

now we need to distribute factors of 72 among the other two factors so that when we add them together the x¹ terms are either 16 or 17  and the x⁰ terms sum to -12. let "a" and "b" be the factors of 72.

ab = 72

a = 72/b

-1.5a - 4b/3 = -12

1.5a + 4b/3 = 12

1.5(72/b) + 4b/3 = 12

108/b + 4b/3 = 12

 324/b + 4b = 36

   324 + 4b² = 36b

        81 + b² = 9b

b² - 9b + 81 = 0

b = (9 ±√(9² - 4(1)(81))) / 2(1))

b = (9 ± √-243) / 2

as both of these roots are imaginary numbers

there is no valid solution to this problem as posed

IF we allow a slight edit to answer B, we can factor 72 into 9•8

y = 8(x - 1.5)    y = 9(x - 4/3)

y = 8x - 12       y = 9x - 12

so the sum of the two would be 17x - 24