A large explosion causes wood and metal debris to rise vertically into the air with an initial velocity of 96 feet per second. The quadratic function h(t)=96t−16t2 gives the height h (in feet) of the debris at time t (in seconds) after the explosion. How many seconds will it take before the debris falls back to the ground?

6 seconds

Step-by-step explanation:

We have to find the t-intercepts of the function. To do so, let's set h(t) = 0.

0 = 96t - 16t²

0 = 16t(6 - t)  -- Factor 96t - 16t²

16t = 0 or 6 - t = 0  -- Use Zero Product Property

t = 0 or t = 6 -- Solve for t

We're not looking for the solution t = 0 because that represents when the debris was launched. Therefore, the answer is 6 seconds.

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.

what? ?

what type of question is thiss

step-by-step explanation: