Which of the following shows that mnop is a parallelogram for s=1 and t=2?

(C)

Step-by-step explanation:

Plug in 1 for s, and 2 for t:

5t - 2 = 5(2) - 2 = 10 - 2 = 8

t + 6 = (2) + 6 = 8

2s + 3 = 2(1) + 3 = 2 + 3 = 5

3s + 2 = 3(1) + 2 = 3 + 2 = 5

NM = PO = 8 ; NO = MP = 5 ∴ (C) is your answer

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choice A

NO = MP = 5 and PO = MN = 8, so MNOP is a parallelogram

A parallelogram has opposite sides that are congruent. So if we can show that MN and PO are the same length, then...

MN = PO

5t - 2 = t+6

5t-t = 6+2

4t = 8

t = 2

Meaning that

MN = 5t - 2 = 5*2-2 = 10-2 = 8

PO = t+6 = 2+6 = 8

Both MN and PO are 8 units, so we can say PO = MN = 8

A similar thing happens when we solve MP = NO

MP = NO

2s+3 = 3s+2

3-2 = 3s-2s

1 = 1s

1 = s

s = 1

If s = 1, then,

MP = 2s+3 = 2*1+3 = 2+3 = 5

NO = 3s+2 = 3*1+2 = 3+2 = 5

Both are 5 units, so NO = MP = 5

We've shown the opposite sides are the same length (aka congruent), therefore MNOP is a parallelogram.

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step-by-step explanation:

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