Evaluate f(x)=12 for the function f(x)=5(x-3)+17

x = 5

Step-by-step explanation:

We are given the function;

f(x) = 5(x-3) + 17

And f(x) = 12

Thus;

5(x-3) + 17 = 12

Expanding the bracket gives;

5x - 15 + 17 = 12

5x + 2 = 12

5x = 12 - 2

5x = 10

x = 10/2

x = 5

Thus,for f(x) = 12, x has to be 5

∠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.