Simon borrowed $1,000 for 3 years at 5% compound interest rate. How much did he owe after 3 years? Enter your numeric answer, (without the $ sign), to the nearest cent below

Total amount after 3 year = 1,157.625

Step-by-step explanation:

Given:

Amount deposit P = $1,000

Number of year n = 3 year

Interest rate r = 5% = 0.05

Find:

Total amount after 3 year

Computation:

Amount = P[1+r]ⁿ

Total amount after 3 year = 1,000[1+0.05]³

Total amount after 3 year = 1,000[1.05]³

Total amount after 3 year = 1,157.625

∠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.