PLEASE HELP ME 20 POINTS In the plane shown in the figure below, lines land mare cut by the transversal line n. The eight angles at the intersections of these lines are labeled. Which of the following statements, when it is true, CANNOT always be used
to prove that lines land mare parallel?

Option (4)

Step-by-step explanation:

Since, lines l and m are the parallel lines and line 'n' is intersecting these parallel lines,

Option (1)

∠c ≅ ∠y

True.

[Corresponding interior angles]

Option (2)

∠a ≅ ∠w

True.

[Corresponding interior angles]

Option (3)

∠b ≅ ∠x

True.

[Corresponding interior angles]

Option (4)

∠b ≅ ∠z

False.

[Since, ∠b + ∠Z = 180°, consecutive exterior angles]

Option (5)

∠a ≅ ∠z

True.

[Alternate exterior angles]

Therefore, Option (4) will be the answer.

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!