A rock is thrown from the top of a tall building. The distance, in feet, between the rock in the ground T seconds after it is thrown it is given by d=-16t-4t+462. How long after the rock is thrown is 450 feet from the ground

0.75 seconds

Step-by-step explanation:

We simply set the distance d to 450 feet

Thus, we have

450 = -16t^2 - 4t + 462

= 16t^2 + 4t - 462 + 450

0 = 16t^2 + 4t - 12

divide through by 4

4t^2 + t - 3 = 0

4t^2 + 4t - 3t - 3 = 0

4t(t + 1) -3( t + 1) = 0

(4t-3)(t + 1) = 0

t + 1 = 0 or 4t-3 = 0

t = -1 or 3/4

t = -1 or 0.75

Since time cannot be negative , we have 0.75 as our only answer

Thus, it will take the rock 0.75 seconds to reach a distance of 450 feet after it is thrown from the ground

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3

step-by-step explanation: