Which equation shows the result of substituting and expression for y from the first equation into the second equation for the
given system?
ly=x+5
ly-2x=2
(5 – x) – 2x = 2
(x + 5) - 2x = 2
(x + 5) + 2x = 2
(x + 5)-2x = 0

(b) After substitution: the givens system is  (x + 5) -  2 x  =  2 .

Step-by-step explanation:

Here, the system of equations is:

y = x + 5

y - 2 x = 2

Now, substituting the value of y   = x + 5 in the second equation, we get

y - 2 x = 2

⇒   (x + 5) -  2 x  =  2

Hence, after substitution: the givens system is  (x + 5) -  2 x  =  2 .

(a) the volume of the cone is 20/3 in3

hence, option a is correct.

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!