A penny is thrown straight down from a height of 200 feet. The polynomial - 16t2 – 25t + 200 represents the height of the penny after t seconds. At the same time, a paintbrush is dropped from
a height of 100 feet. The binomial – 16t2 + 100 represents the height of the paintbrush after
t seconds.
a. Write a polynomial that represents the distance between the penny and the paintbrush after t
seconds.
The polynomial is
b. Interpret the coefficients of the polynomial in part (a) by filling in the blanks.
The constant term is
which indicates that the distance between the penny and the paintbrush
is
feet when they begin to fall. The coefficient of the linear term is
which indicates that the
penny and the paintbrush become
feet closer to each other each second.

d

step-by-step explanation:

the solution is in the picture

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 natural event such as a flood, earthquake, or hurricane that causes great damage or loss of life.

step-by-step explanation:

77

step-by-step explanation: