You are going to make three shelves for your father and have one piece of lumber 20 feet long. Your plan is to make the top shelf half a foot shorter than the middle shelf and to have the bottom shelf half a foot shorter than twice the length of the top shelf. How long is each shelf? t= length of the top shelf t=m-1/2 m = length of middle shelf b = length of bottom shelf. B=2t-1/2 t+m+b=20

The top shelf is 5 feet, the middle shelf is 5.5 feet and the bottom shelf is 9.5 feet

Step-by-step explanation:

Let t= length of the top shelf, m = length of middle shelf and b = length of bottom shelf.

Therefore:

t = m - 1/2; m = t  + 1/2

Also, b = 2t - 1/2

The total of the three shelves is 20 feet, therefore:

t + m + b = 20

Substituting:

t + t + 1/2 + 2t - 1/2 = 20

4t = 20

t = 20/4

t = 5 feet

m = t + 1/2 = 5 + 1/2 = 5.5 feet

b = 2t - 1/2 = 2(5) - 1/2 = 9.5 feet

The top shelf is 5 feet, the middle shelf is 5.5 feet and the bottom shelf is 9.5 feet

step-by-step explanation:

i think you should think about the question and not look online.

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!