4. A function consists of the pairs (2,3), (x, y) and (5,6). If the inverse is also a function what values can y NOT be? Explain.

In a nutshell, cannot be 3 or 6 in the inverse function for all distinct from 2 and 5.

Step-by-step explanation:

From Functional Theory we remember that a function is a relation in which all elements of its domain has an unique and different element from range. If is the image of the inverse, which is a function, then . Otherwise, the inverse could not be a function when .

In a nutshell, cannot be 3 or 6 in the inverse function for all distinct from 2 and 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.

the answer is 13

step-by-step explanation:

5*5=25

12*12=144

25+144=169

169^2=13