Suki invested $20,000, some at 5% interest and the rest at 10%. How much did she invest at each rate if she received $1,400 in interest in one year?

Suki invested $12,000 at 5% and $8,000 at 10%

Step-by-step explanation:

Let the amount invested at R1 be P1 and that invested at R2 be 20000 - P1

⇒ Total Interest = P1×R1×T/100 + (20000 - P1)×R2×T/100 (since Simple Interest = PRT/100)

⇒ Total Interest = T/100 [P1R1 + (20000 - P1)R2] (Taking out the common factors)

⇒ 1400 = 1/100 (5P1 + 20,000 × 10 - 10P1)

⇒ 140,000 = -5P1 + 200,000

⇒ 5P1 = 60,000

⇒ P1 = 60,000/5 = $12,000

⇒ P2 = 20,000 - P1 = $8,000

answer: d. $20

step-by-step explanation:

just took the test

∠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.