Awoman has $500 in a bank account. every week she writes out a check for $50. if she doesn't make any deposits, what will be in her bank account x weeks from now a. $500 + 50x b. $500 - x c. $500 - $50 + x d. $500 - 50x

Solution:

we are given that

A woman has $500 in a bank account.

Every week she writes out a check for $50.

It mean after one week , remaining balance in her account

It mean after Two week , remaining balance in her account

...........................................................................................................................................

............................................................................................................................,...............

It mean after x week , remaining balance in her account

Hence the correct option is D

∠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.