What is the maximum profit that the band could make from the show? how many purchased tickets will produce that maximum profit? about 15% of ticket buyers will also buy a t-shirt giving the band $5 profit for each sale. about 5% of ticket buyers will buy a poster giving the band $3.50 profit for each sale. all the bands other expenses for each show will average about $300 p(x)= 0.10(-0.04x+30)x+ 5(0.15x) + 3.50(0.05x) - 300

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.