From the following figure, how can you conclude that lines l and m are parallel? a) corresponding angles postulate b) alternate exterior angles theorem c) alternate interior angles theorem d) same side interior angles theorem

C) Alternate interior angles theorem.

Step-by-step explanation:

Given : Figure with two line l and m ans alternates interior angle 70°

To find : how can you conclude that lines l and m are parallel.

Solution : We have given that two line l and m ans alternates interior angle 70°.

Two angle are alternate and interior to the line l and m .

Hence they are congruent to each other .

By the alternates interior angle theorem :   if two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.

Therefore, C) Alternate interior angles theorem.

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!

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

eventually after a few more steps, your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x