Mrs. hall has a balance of $450 in her student account. she spends $15 each week on snacks for the after school meetings. if mrs. hall has $180 remaining in the account at the end of the semester, how many weeks are in the semester?

18 weeks

Step-by-step explanation:

Let the number of weeks be represented by a variable x;

Beginning balance = 450

Ending balance=  180

Amount spent per week= 15

Amount spent in x weeks = 450-180= $270

Total amount spent in x weeks = 15*x = 15x

Equate the above equations to the corresponding dollar amount;

15x=270

Next, solve for x by dividing both sides by 15

x=270/15

x= 18

Therefore, there are 18 weeks in the semester.

∠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.