Determine for what numbers, if any, the given function is discontinuous. f(x) = {x−5 if x≤5x2−10 if x> 5

x = 5

Step-by-step explanation:

Discontinuities arise in function definitions from several sources. One of them is the boundary of the piecewise definition. Here, the boundary is at x=5.

The function is defined to be f(5) = 0, but the limit from above as x approaches 5 is 5²-10 = 15. This value is not equal to zero (the value of f(5)), so there is a discontinuity at that point.

∠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.