The cold faucet in my bath let’s the water in at the rate of 5 liters per minute. the hot faucet fills the bath at the rate of 10 liters per minute. the plug lets the water out of the bath at the rate of 12 liters per minute. the bath holds a maximum of 520 liters. i turn both faucets on, but forget to put the plug in. how many minutes does it take for the bath to overflow?

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.

the answer on ed. is:

c. "the graph of f(x) has exactly two x-intercepts."

hope i could someone! : )