7. Bill took a trip to see a friend. His friend lives 225 miles away. He drove in town at an average of 30mph, then he drove on the interstate at an average of 70 mph. The trip took three-and-a-half hours total. How far did Bill drive on the interstate?

Bill drove 210 miles on the interstate.

Step-by-step explanation:

The total distance of his travel was 225 miles and there were two types of road in the course, the town roads at which he drove "x" miles and the interestate road at which he drove "y" miles. Therefore:

x + y = 225

On the town he drove at 30 mph on average and on the interestate he drove at 70 mph on average. Therefore:

x/30 + y/70 = 3.5

We can now build a system of equations shown below:

x + y = 225

x/30 + y/70 = 3.5

Multiplying second equation by -30, we have:

x + y = 225

-x - (3/7)*y = -105

(4/7)*y = 120

y = 120*(7/4) = 210

x + 210 = 225

x = 225 - 210 = 15

Bill drove 210 miles on the interstate.

∠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.

g

step-by-step explanation: