Nate tosses a ball up a hill for his dog to chase. The path of the ball is modeled by the function y=-1/4x^2 + 33/5x, where x is
the ball's horizontal distance from Nate in feet and y is the ball's
height in feet. The hill is modeled by the line y
2. How far
does the ball travel horizontally before it hits the ground? (in
feet, round to tenth place if necessary)

26.4 m

Step-by-step explanation:

The path the ball follows is given by the function

Before it hits the ground means y will be zero.

There are two points where the vertical displacement is zero the point at which Nate tosses the ball and the point where it lands.

So, the ball travels 26.4 m horizontally before it hits the ground.

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!

a thesis statement is not a fact or a question

step-by-step explanation:

a thesis statement is a topic it is not a fact or a question