When the survey results came back employees indicated that the lighting in the building is too low. There are 50 lights in the building it will cost 50 to replace each light the new lights are led lights that are brighter and more efficient and last 10 years it will save the company 305 per year in energy cost plus make a brighter more productive work space making employees happier how many years will it take for the new lights to pay for themselves round to the nearest year

8 years

Step-by-step explanation:

There are 50 lights present in the building and each light cost $50. Therefore the cost of changing all the bulbs is:

Cost = number of lights * cost per light = 50 lights * $50 = $2500

Changing the lights in the building save the company $305 per year in energy cost. Therefore, the number of years required for the new lights to pay for themselves is:

number of years = cost of changing bulbs / money saved per year

number of years = $2500 / $305 per year = 8.2

number of years = 8 years to the nearest year

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!