Jack is standing on the roof of his house in kicked a rubber ball in the air for it to land on the ground for his dog Henry to fetch. The ball is launched into the air from a height of 12 feet at time t=0. The function that models the situation is h(f) = -2t^2 + 10t +12, where T is measured in seconds and H is the height in feet When will the ball hit the ground

Please help me with all the steps for this problem. Giving 100 PTS

6 seconds

Step-by-step explanation:

h(t) = -2t² + 10t +12

On the ground, h = 0

-2t² + 10t + 12 = 0

t² - 5t - 6 = 0

t² - 6t + t - 6 = 0

t(t - 6) + (t - 6) = 0

(t - 6)(t + 1) = 0

t = 6, -1

time can not be negative

So, t = 6

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!

10.416 m/s

step-by-step explantion:

distance=100m

time= 9.6s

average speed=100/9.6

=10.416 m/s