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wolverine [178]
3 years ago
11

G(x) = -3/2x-9, if G(x) = -48, find x

Mathematics
1 answer:
Svetlanka [38]3 years ago
6 0

Answer:

x=26

Step-by-step explanation:

first rewrite the problem since u know that G(x)=-48

-48=-3/2x-9

second you want to add the 9 to -48 which gives u -39

-39=-3/2x

third you want to times the reciprocal so it would be

-2/3 times -39/1

u can cross out the negatives and turn them into a positive

fourth you can cross cancel 3 and 39 which now the problem looks like this

2/1 times 13/1

which you would times 2 and 13 which your answer would be

26

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How long does it take for an investment to quadruple in value if it is invested at 11% compounded
defon

Let's assume we have $100 and an interest rate of 7%. For the $100 to quadruple it means that the future value would be $400. Thus, because we are talking about compounding daily we will set us the equation as follows:

100 * (1+1.07)x = 400

Then we will take 400 and divide it by 100 getting:

1.07X = 4

Now we have encountered a problem where we do not know exponent, so we will use logarithm to calculate such and transform our equation to: Log1.07(4)=X

Using our calculator we will find that it takes about 20.4895 days to quadruple the money invested under 7% interest rate compounded daily.

2nd: Using the same $100 but with the rate of 5.5% compounded continuously we will be using A=PERT formula

where:

P (principal) is equal to hypothetical $100

E (e) is a mathematical constant, which is approximately 2.718

R (rate) is the interest rate, in our case it is 5.5%

T (time) is the time required for money to grow

A (amount) is the final amount desired, which is 4 times larger of $100, thus $400

We have the following:

400 = 100 * e0.055t

400/100 = e0.055t

4 = e0.055t

Then we will apply natural log to both sides of the equations and get the following:

ln(4) = ln(e0.055t)

Since e is the base of ln(x) the equation simplifies to:

ln(4) = 0.055t

Using the calculator to find ln(4) we are getting:

1.38629 = 0.055t

Lastly find t

t = 1.38629/0.055

t = 25.20535202

Plug the answers back to the original equation to verify the answers.

1st part of the question answer: t = 20.4895

2nd part of the question answer: t = 25.20535202

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The commutative property of addition lets you rewrite this to ...

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Subtracting 2.6 from both sides of the equation gives its solution:

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