Compound $35.000 is invested at 5% compound interest. What is the interest at the end of three years?

$40,516.86

Step-by-step explanation:

start by taking 35,000 and multiplying it by 0.05 to get 5% of the number. then add that number (1,750) to the original 35,000 and you should get 36,750. this would be the first year. Then multiply 36,750 by 0.05 again and add that number (1837.5) to the original 36,750 and you should get 38,587.5. Finally multiply that by 0.05 and add that number (1,929.375) to the original 38,587.5 and you should get 40516.875. Round to the hundredths since it is money.

∠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.