What is the value of x?

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x=11

Step-by-step explanation:

Since the lines in the middle are parallel, we know that both sides are proportional to each other.

6:48 can be simplified to 1:8

Since we know the left side ratio is 1:8, we need to match the right side with the same ratio

We can multiply the ratio by 5 to match 5:3x+7

5:40

5:3x+7

Now we can set up the equation: 40=3x+7

Subtract 7 from both sides

3x=33

x=11

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.