Which graph represents the system 3x + 5y ≤ 9 and 2x + y ≥ 5?

Answer with Step-by-step explanation:

we are given system of inequalities:

3x + 5y ≤ 9 and

2x + y ≥ 5

We have to determine the graph of the above system

In Second and third graph point (0,6) lies in shaded region

Putting (0,6) in 3x + 5y ≤ 9

3×0+5×6≤9

⇒ 30≤9 which is incorrect

Hence, second and third are not its graph

In fourth graph (0,3) lies in shaded region

Putting (0,3) in 3x + 5y ≤ 9

3×0+5×3≤9

⇒ 15≤9 which is incorrect

Hence, fourth is not its graph

Hence, the only option we are left is graph first

Hence, first graph is the correct representation of 3x + 5y ≤ 9 and

2x + y ≥ 5

45

step-by-step explanation:

30+15

∠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.