Manuel is hiking up a mountain. after 3 hours, he is 2500 feet from the summit. after 5 hours, he is 1300 feet from the summit. what is the height, in feet, of the mountain?

 Height of summit = 4300 ft

Explanation:

 Let the height of summit be h.

 After 3 hours, he is 2500 feet from the summit,

 Height traveled = (h - 2500)

 Time taken = 3 hours

  Speed = (h-2500)/3

 After 5 hours, he is 1300 feet from the summit

  Height traveled = (h - 1300)

  Time taken = 5 hours

  Speed = (h-1300)/5

Here speed is same, so we have

  Height of summit = 4300 ft

4

step-by-step explanation:

∠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.