Three friends each have some ribbon. carl has 54 inches of ribbon, tino has 13.5 feet of ribbon, and baxter has 3.5 yards of ribbon. express the total length of ribbon the three friends have in inches, feet, and yards?

  342 inches, or 28.5 feet, or 9.5 yards

Step-by-step explanation:

It is perhaps easiest to start with all the dimensions in inches.

  13.5 ft = (13.5 ft)(12 in/ft) = 162 in

  3.5 yd = (3.5 yd)(36 in/yd) = 126 in

Then the total of the lengths of ribbon is ...

  54 in + 162 in + 126 in = 342 in

Converting to feet, we get ...

  (342 in)/(12 in/ft) = 28.5 ft

And converting to yards, we get ...

  (342 in)/(36 in/yd) = 9.5 yd

The total length of ribbon is 342 inches, or 28.5 feet, or 9.5 yards.

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!