A banquet hall has three rooms available for events. One room holds 252 people, another room holds 180 people, and the smallest room holds 75 people . If each room is filled to capacity, how many people can the banquet hall serve?

507 people

Step-by-step explanation:

If each room is filled to capacity, the banquet hall can serve the sum of the number of people in each room put together

That’s

252 + 180 + 75 = 507 people

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.

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step-by-step explanation: