Which is the graph of linear inequality 2x-3y< 12 ?

Option 3

Step-by-step explanation:

Given : Inequality

To find : Which is the graph of linear inequality ?

Solution :

Inequality

Solve for y,

Now, We plot the graph of the equation using x-intercept and y-intercept,

x-intercept is when y=0,

y-intercept is when x=0,

So, Graph passing through (0,-4) and (6,0).

Now, The area of the graph is

Put x=0 and y=0

It is true. So, The region is towards origin.

The inequality is not have equal sign so the line is dotted.

From the given graph Option 3 is correct.

Refer the attached figure below.

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.