Blake operates a hot air balloon business. The relationship between the height of the hot air balloon and the time spent to reach that height is given by the function H(t) = 100t where t is the number of minutes. Additionally, the relationship between the height of the hot air balloon and the atmospheric pressure, inHg, being applied to the balloon is given by the function P(H) = 29.9 − 0.5H 500 . Which function can be used to determine the pressure on the hot air balloon based on the time it spends rising in height? A) t(P(H)) B) t(H(P)) C) H(P(t)) D) P(H(t))

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.

v = 1/3 a^2h

step-by-step explanation:

the volume is 1/3 a^2h.

16 is the absolute value

step-by-step explanation:

i think the answer is true

step-by-step explanation: