A picture frame has a perimeter of 100 centimeters. Its width is 4 centimeters less than twice its length. What is the width of the picture frame?

32 cm

Step-by-step explanation:

Let the length = L.

The width is 2L - 4.

perimeter = 2 * length + 2 * width

perimeter = 2 * L + 2 * (2L - 4)

perimeter = 2L + 4L - 8

perimeter = 6L - 8

perimeter = 100

6L - 8 = 100

6L = 108

L = 18

width = 2L - 4 = 2(18) - 4 = 36 - 4 = 32

The width is 32 cm.

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!

i think 5 miles per hour

step-by-step explanation: