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MArishka [77]
3 years ago
15

Ernesto has $70 in a savings account. The interest rate is 5%, compounded annually. To the nearest cent, how much will he have i

n 3 years?
Mathematics
1 answer:
Paul [167]3 years ago
3 0

Answer: $81.03

Step-by-step explanation:

The interest is compounded annually which means that the future value formula applies:

Future value = Amount * ( 1 + rate) ^ number of years

Amount = $70

Rate = 5%

Number of years = 3 years

In 3 years, Ernesto will have:

= 70 * ( 1 + 5%)³

= $81.03

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Sam puts $500 in the bank and does not put any more money in or take any out for elght years. He receives 6% Interest
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Which graph represents the function of f(x) = the quantity of 9 x squared plus 9 x minus 18, all over 3 x plus 6
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Answer:

The answer is the option C

graph of 3x minus 3, with discontinuity at negative 2, negative 9

Step-by-step explanation:

we have

f(x)=\frac{9x^{2}+9x-18}{3x+6}

Simplify

f(x)=9\frac{(x^{2}+x-2)}{3(x+2)}

f(x)=3\frac{(x^{2}+x-2)}{(x+2)}

Step 1

Convert to a factored form the numerator

x^{2}+x-2=0    

Group terms that contain the same variable, and move the constant to the opposite side of the equation

x^{2}+x=2

Complete the square. Remember to balance the equation by adding the same constants to each side.

x^{2}+x+0.25=2+0.25

x^{2}+x+0.25=2.25

Rewrite as perfect squares

(x+0.5)^{2}=2.25

Square root both sides

x+0.5=(+/-)1.5

x=-0.5(+/-)1.5

x=-0.5+1.5=1

x=-0.5-1.5=-2

so

x^{2}+x-2=(x-1)(x+2)  

Step 2

Simplify the function f(x)

f(x)=3\frac{(x^{2}+x-2)}{(x+2)}=3\frac{(x-1)(x+2)}{(x+2)}

The domain of the function f(x) is all real numbers except the number x=-2

Because the denominator can not be zero

f(x)=3\frac{(x-1)(x+2)}{(x+2)}=3(x-1)=3x-3  

f(x)=3x-3  ------> with a discontinuity at x=-2

f(-2)=3(-2)-3=-9

The discontinuity is at point (-2,-9)

the answer in the attached figure

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Now, for the second pattern, we have 4 times as many in each row, so we have 4*2 = 8 drummers in each row, then we have 16/8 = 2 rows.

You can see that in each pattern we have the same number of drummers, but a different number of rows.

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