Alicia watched a drone take off from a bridge. The height of the drone (in meters above the ground) minutes after takeoff is modeled by h(t)=−3t2+12t+96h(t)=-3t^2+12t+96h( t)=−3t2+12t+96h, left parenthesis, t, right parenthesis, equals, minus, 3, t, squared, plus, 12, t, plus, 96 Alicia wants to know when the drone will land on the ground. 1) Rewrite the function in a different form (factored or vertex) where the answer appears as a number in the equation. h(t)=h(t)=h(t)=h, left parenthesis, t, right parenthesis, equals 2) How many minutes after takeoff does the drone land on the ground?

Step-by-step explanation:

Given the height of the drone modelled by the equation:

h(t)=-3t^2+12t+96

a) Rewriting this in a factored form.

From the equation, we can see that -3 is the greatest common factor. The equation therefore becomes:

h(t)= -3(t^2-4t-32)

Hence the function can also be written as h(t)= -3(t^2-4t-32)

b) The drone landed on the ground at when h(t) = 0. Substitute h(t) = 0 into the expression  h(t)= -3(t^2-4t-32)

0 = -3(t^2-4t-32)

Divide through by -3

(t^2-4t-32) = 0

Factorize

t²+8t-4t-32 = 0

t(t+8)-4(t+8) = 0

(t-4)(t+8) = 0

t-4 = 0 and t+8 = 0

t = 4 and t = -8

Time can't be negative:

t = 4minutes

Hence it took the drone 4 minutes take off to land on the ground

10 glasses of juice could be made with 5 carrots, 1,500 orange juice, 2,000 papaya juice.

d. $180

step-by-step explanation:

if the dimensions of the room is 9ft by 12 ft, we have the area of the floor as,

so the area of the floor is 108 square feet, converting that into square yards we get,

the cost of carpet is $15 per square yard, therefore the cost of carpet for 12 square yards is,

hence, the cost of carpet is $180.

assuming the dimensions of the room be,

15 ft by 12 ft

so, the area of the floor of that room is,

we can convert 180 square feet into square yards, we know that,

1 sq ft = 0.111 sq yard

so, 180 square feet is,

so the area of floor is 20 square yards.

now, the cost of carpet is 15 dollars per square yard, therefore the cost of carpet for 20 square yards is,

so, it will cost $300.