Darren and quincy wanted to justify that the expression 1/6 (6×+12)-1/2(4x+2) is equivalent to -x+1. their justifications are shiwn below.

Option C is correct!

Step-by-step explanation:

Both are correct because after substituting the same value into both expressions, the result is the same.

Option D. is the correct option.

Step-by-step explanation:

To get the correct option we will plug in the values of x and y in each option.

For (x, y)→(-4, 42)

Option A.

Which is not true because at x = -4 value of y is given as 42.

So its not the correct option.

Option B.

0.34x²+ 3.4x + 8.60 = (0.34)(-4)² + (3.4).(-4) + 8.6 = 5.44 - 13.6 + 8.60 = 0.44

Again incorrect option.

Option. C

y = 1.62x² + 2.30x + 9.20

Now we put x = -4

y = (1.62)(-4)² + (2.30)(-4) + 09.20 = 25.92- 9.20 + 9.20 = 25.92

Incorrect option.

Option D.

y = 2.38x² + 0.90x + 9.90

Now we put x = -4

y = (2.38)(-4)² + (.90)(-4) + 9.90 = 38.08 - 3.60 + 9.90 = 44.38

And this value is same as given in the table.

Therefore Option D. is the correct option.