3. a running track has the shape of a rectangle capped with a semicircle on each end, as shown below. if
the track is 80 feet wide, and the rectangular portion of the track is 90 feet tall, estimate the length
around the outside of the track.

Step-by-step explanation:

We want to determine the perimeter of the track. Perimeter is the distance around the entire track.

The diameter of each semicircle is 80 feet.

Radius = diameter/2 = 80/2 = 40 feet

Since the semicircles are 2, the perimeter of the outside of both semi circles would be

Perimeter = 2 × π × r

Perimeter = 2 × 3.14 × 40 = 251.2 feet.

Therefore, the distance around the outside of the track would be

251.2 + 90 + 90 = 431.2 feet

function 2 has a greater rate of change than function 1

function 2 has a greater y-intercept than function 1

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.