3. which expression is equivalent to the expression shown below?
7/2x-3(5x-1/2)
a. -23/2x+3/2
b. -23/2x-3/2
c. 37/2x+3/2
d. 37/2x-3/2

option a

Step-by-step explanation:

we have:

7/2x-3(5x-1/2)

apply distributive property we have:

7/2x-3*5x-3*(-1/2)

7/2x-15x+3/2

7/2-15=-23/2

so we have:

-23/2x+3/2

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.