Ab = 3x
dc = x + 4
ad = y + 2
bc = 2y

quadrilateral abcd is a parallelogram if both pairs of opposite sides are congruent. show that quadrilateral abcd is a parallelogram by finding the lengths of the opposite side pairs.

see explanation

Step-by-step explanation:

If a parallelogram then AB = DC and AD = BC

Equating AB = DC, then

3x = x + 4 ( subtract x from both sides )

2x = 4 ( divide both sides by 2 )

x = 2

Thus

AB = 3x = 3(2) = 6 and DC = x + 4 = 2 + 4 = 6 ⇒ AB = DC

Equating AD and BC, then

2y = y + 2 ( subtract y from both sides )

y = 2

Thus AD = y + 2 = 2 + 2 = 4 and BC = 2y = 2(2) = 4 ⇒ AD = BC

Since opposite sides are congruent then ABCD is a parallelogram

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step-by-step explanation:

27/4x^6 y^8

step-by-step explanation:

4(3x^2y^4)^3 (2x^3y^5)^4

=

108x^6 y^12 /16x^12 y^20

=

108 /16x^6 y^8

=

27 /4x^6 y^8