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2 years ago

What is the interest rate if the principal is $25,000, the interest is $10,875, and the time is 15 years?

Mathematics

1 answer:

mel-nik [20]2 years ago

8 0

Answer:

interest rate = 2.9%

Step-by-step explanation:

the principal is $25,000, the interest is $10,875

Number of years = 15

We use simple interest formula

I = P*r*t

Where I is the interest amount=10,875

P is the principal amount= 25000

r is the interest rate = r

t is the number of years = 15

Plug in all the value in the formula

I = P*r*t

10875 = 25000 * r * 15

10875 = 375000 * r

Divide both sides by 375000

r=0.029

We always write rate of interest in percentage so we multiply by 100

0.029 * 100= 2.9%

So interest rate = 2.9%

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A: What are the solutions to the quadratic equation x2+9=0? B: What is the factored form of the quadratic expression x2+9? Selec

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Answer:

A. The solutions are $x=3i,\:x=-3i$ .

B. The factored form of the quadratic expression $x^2+9=(x-3i)(x+3i)$

Step-by-step explanation:

A. To find the solutions to the quadratic equation $x^2+9=0$ you must:

$\mathrm{Subtract\:}9\mathrm{\:from\:both\:sides}\\\\x^2+9-9=0-9\\\\\mathrm{Simplify}\\\\x^2=-9\\\\\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\\\\x=\sqrt{-9},\:x=-\sqrt{-9}$

$x=\sqrt{-9} = \sqrt{-1}\sqrt{9}=\sqrt{9}i=3i\\\\x=-\sqrt{-9}=-\sqrt{-1}\sqrt{9}=-\sqrt{9}i=-3i$

The solutions are:

$x=3i,\:x=-3i$

B. Two expressions are equivalent to each other if they represent the same value no matter which values we choose for the variables.

To factor $x^2+9$ :

First, multiply the constant in the polynomial by $i^2$ where $i^2$ is equal to -1.

$x^2+9i^2$

Since both terms are perfect squares, factor using the difference of squares formula

$a^2-i^2=(a+i)(a-i)$

$x^2+9=x^2+9i^2=\left(-3i+x\right)\left(3i+x\right)$

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