Given the kite below, if NO = 5 and OM = 12, what is the value of NM?

Mathematics

1 answer:

tester [92]3 years ago

6 0

Answer:

NM = 13

Step-by-step explanation:

pythagorean theorem: $a^{2} + b^{2} = c^{2}$

a or NO = 5

b or OM = 12

c or NM = ?

plug in what is known:

⇒ $5^{2} + 12^{2} = c^{2}$

⇒ $25 + 144 = c^{2}$

⇒ 169 = $c^{2}$

square root each side of the equation:

⇒ $\sqrt{169} = \sqrt{c^{2} }$

solve:

⇒ 13 = c

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Steve has $25,000 to invest and wishes to earn an overall annual rate of return of 8%. His financial advisor recommends that h

Alexeev081 [22]

Answer:

Steve should place $6,250 in the 5-year CD and $18,750 in the corporate bond

Step-by-step explanation:

System of Equations

We need to find how Steve will distribute his investments between two possible options: one of them will pay 5% per annum and the other will pay 9% per annum. We know Steve has $25,000 to invest and wants to have an overall annual rate of return of 8%.

Let's call x to the amount Steve will invest in the CD paying 5% per annum and y to the amount he will invest in a corporate bond paying 9% per annum.

The total investment is $25,000 which leads to the first equation

$x+y=25,000$

If x dollars are invested at 5%, then the interest return is 0.05x. Similarly, y dollars at 9% return 0.09y. The overall return is 8% on the total investment, thus

$0.05x+0.09y=0.08(x+y)$