Between 1990 and 1999, the number of movie screens in the united states increased by about 1500 each year. in 1996, there were 29,690 movie screens. write an equation of a line in slope-intercept form, to find the total number of screens y for any year x.

predict the number of movie screens in the united states in 2005.

Part a)

Part b) see the explanation

Step-by-step explanation:

Part a) Write an equation of a line in slope-intercept form, to find the total number of screens y for any year x

we know that

The linear equation in slope intercept form is equal to

where

m is the slope or unit rate of the linear equation

b is the y-intercept or initial value of the linear equation

Let

x ----> the number of years between 1990 and 1999

y ----> the number of movie screens in the United States

In this problem we have that

The unit rate or slope is equal to

we have the ordered pair

(6,29,690)

The x-coordinate is 6 because

1996-1990=6 years ---> is the number of years since 1990

substitute the given values in the equation

Solve for b

The linear equation is

Part b) Predict the number of movie screens in the United States in 2005

we know that

The domain of the linear equation are the years between 1990 and 1999

so

2005 not belong to the domain of the linear equation

therefore

The number of movies in 2005 cannot be predicted with the given linear equation

b) well because you get well

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!