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Leokris [45]
2 years ago
12

What is 6 7/9 as an improper fraction? Explain your answer.

Mathematics
1 answer:
miskamm [114]2 years ago
4 0

Answer:

Step-by-step explanation:

6\dfrac{7}{9}=\dfrac{(6*9)+7}{9}=\dfrac{54+7}{9}\\\\\\=\dfrac{61}{9}

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You need a 30-year, fixed-rate mortgage to buy a new home for $225,000. your bank will lend you the money at an apr of 5.5 perce
bulgar [2K]
Loan amount, P = 225000
interest = 5.5%/12  per month
Monthly payment, A = 1000

At the end of 30 years, 
Future value of loan (with zero repayment)
F1=225000*(1+.055/12)^(30*12)
=1167162.264

Future value of repayment, A=1000 per month
F2=\frac{A((1+i)^n-1)}{i}
=\frac{1000((1+.055/12)^{360}-1)}{.055/12}
=913611.893

Therefore balloon payment
= F1-F2
=1167162.264-913611.893
=253550.37   (to the nearest cent)
6 0
3 years ago
Log_(5)(x-4)=1-log_(5)(x-8)
hjlf

Answer:

x = 3, x = 9

Step-by-step explanation:

When solving this problem, keep the general format of a logarithm in mind:

b^x=y\\log_b(y)=x

Where, (b) represents the base, (x) is the exponent, and (y) is the evalutaor. Please note that others might use slightly different terminotoly than what is used in this answer.

One is given the following expression, and is asked to solve for the parameter (x);

log_5(x-4)=1-log_5(x-8)

First, manipulate the exquestion such that all of the logarithmic expressions are on one side. Use inverse operations to do this.

(log_5(x-4))+(log_5(x-8))=1

Now use the Logarithmic Base Change rule to simplify. The Logarithmic Base Change rule states the following;

log_b(x)=\frac{log(x)}{log(b)}

Remember, if no base is indicated in a logarithm, then the logarithm's base is (10). Apply the Logarithmic Base Change rule to this problem;

\frac{log(x-4)}{log(5)}+\frac{log(x-8)}{log(5)}=1

Now remove the denominator. Multiply all terms in the equation by the least common denominator; (log(5)) to remove it from the denominator on the left side.

(\frac{log(x-4)}{log(5)}+\frac{log(x-8)}{log(5)}=1)*(log(5))

log(x-4)+log(x-8)=log(5)

All logarithms have the same base, the left side of the equation has the addition of logarithms. This means that one can apply the Logarithm product rule. The logarithm product rules the following;

log_b(x*y)=(log_b(x))+(log_b(y))

This rule can be applied in reverse to simplify the left side of the equation. Rather than rewriting the product of logarithms as two separate logarithms being added, one can rewrite it as one logarithm getting multiplied.

log(x-4)+log(x-8)=log(5)

log((x-4)(x-8))=log(5)

Now used inverse operations to bring all of the terms onto one side of the equation:

log((x-4)(x-8))=log(5)

log((x-4)(x-8))-log(5)=0

Similar to the Logarithm product rule, the Logarithm quotient rule states the following;

log_b(x/y)=(log_b(x))-(log_b(y))

One can apply this rule in reverse here to simplify the logarithms on the left side:

log((x-4)(x-8))-log(5)=0

log(\frac{(x-4)(x-8)}{5})=0

The final step in solving this equation is to use the Logarithm of (1) property. This property states the following:

log_b(1)=0

When applying this property here, one can conclude that the evaluator must be equal to (1), therefore, the following statements can be made.

log(\frac{(x-4)(x-8)}{5})=0

\frac{(x-4)(x-8)}{5}=1

Inverse operations,

\frac{(x-4)(x-8)}{5}=1

(x-4)(x-8)=5

(x-4)(x-8)-5=0

Simplify,

(x-4)(x-8)-5=0

x^2-12x+32-5=0

x^2-12x+27=0

Factor, rewrite the quadratic expression as the product of two linear expressions, such that when the linear expressions are multiplied, the result is the quadratic expression:

x^2-12x+27=0

(x-3)(x-9)=0

Now use the zero product property to solve. The zero product property states that any number times (0) equals (0).

x=3,x=9

7 0
3 years ago
Read 2 more answers
2x-4y=28 solve for y
max2010maxim [7]

Answer:

y=7+1/2x

Step-by-step explanation:

Hope this helps

7 0
3 years ago
A new computer can complete a complex biochemistry calculation in 11 hours less than an older-model computer. Working together,
AlekseyPX

Answer:

New computer will take 33.28 hours to complete the calculation by itself.

Step-by-step explanation:

Let the time taken by the new computer to complete the calculation = x hours

Per hours work done by the new computer = \frac{1}{x}

Time taken by the older computer to complete the calculation = (x + 11) hour

Per hour work done by old computer = \frac{1}{(x+11)}

When both the computers work together they complete the work in 19 hours.

Therefore, per hour work done by both together = \frac{1}{19}

We per hour work done by both individually = per hour work done by both together

\frac{1}{x}+\frac{1}{x+11}=\frac{1}{19}

\frac{x+x+11}{x(x+11)}=\frac{1}{19}

\frac{2x+11}{x(x+11)}=\frac{1}{19}

38x + 209 = x² + 11x

x² - 27x - 209 = 0

By quadratic formula,

x = \frac{27\pm \sqrt{(-27)^{2}-4\times 1\times (-209)}}{2}

x = \frac{27\pm \sqrt{729+836}}{2}

x = \frac{27\pm \sqrt{1565}}{2}

x = \frac{27\pm 39.56}{2}

x = 33.28 hours

Therefore, new computer will take 33.28 hours to complete the calculation by itself.

3 0
3 years ago
HELP FAST
ddd [48]

Answer:

D. $5688

Step-by-step explanation:

good luck

4 0
3 years ago
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