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nekit [7.7K]
3 years ago
8

Last year, Manuel deposited $7000 into an account that paid 11% interest per year and $1000 into an account that paid 5% interes

t per year. No withdrawals were made from the accounts. Answer the questions below. Do not do any rounding. (a) What was the total interest earned at the end of year? (b) What was the percent interest for the total deposited?
Mathematics
1 answer:
Westkost [7]3 years ago
5 0

Answer:

The total interest earned at the end of the year was $ 820, and the interest generated by the total deposited was 10.25%.

Step-by-step explanation:

Given that last year, Manuel deposited $ 7000 into an account that paid 11% interest per year and $ 1000 into an account that paid 5% interest per year, and no withdrawals were made from the accounts, to determine what was the total interest earned at the end of year and what was the percent interest for the total deposited, the following calculations must be performed:

7000 x 0.11 + 1000 x 0.05 = X

770 + 50 = X

820 = X

8000 = 100

820 = X

820 x 100/8000 = X

82,000 / 8,000 = X

10.25 = X

Therefore, the total interest earned at the end of the year was $ 820, and the interest generated by the total deposited was 10.25%.

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Find the inverse when f(x)=3x^2-3x-2
Vikentia [17]

Answer:

The inverse of f(x) is f^{-1}(x) =  ± \sqrt{\frac{x+\frac{11}{4}}{3}} + \frac{1}{2}

Step-by-step explanation:

To find the inverse of the quadratic function f(x) = ax² + bx + c, you should put it in the vertex form f(x) = a(x - h)² + k, where

  • h = \frac{-b}{2a}
  • k is the vlue f at x = h

∵ f(x) = 3x² - 3x - 2

→ Compare it with the 1st form above to find a and b

∴ a = 3 and b = -3

→ Use the rule of h to find it

∵ h = \frac{-(-3)}{2(3)} = \frac{3}{6} = \frac{1}{2}

∴ h =  \frac{1}{2}

→ Substitute x by the value of h in f to find k

∵ k = 3( \frac{1}{2})² - 3( \frac{1}{2}) - 2

∴ k = -\frac{11}{4}

→ Substitute the values of a, h, and k in the vertex form above

∵ f(x) = 3(x -  \frac{1}{2})² + -\frac{11}{4}

∴ f(x) = 3(x -  \frac{1}{2})² - \frac{11}{4}

Now let us find the inverse of f(x)

∵ f(x) = y

∴ y = 3(x -  \frac{1}{2})² - \frac{11}{4}

→ Switch x and y

∵ x = 3(y -  \frac{1}{2})² - \frac{11}{4}

→ Add \frac{11}{4} to both sides

∴ x + \frac{11}{4} = 3(y - \frac{1}{2})²

→ Divide both sides by 3

∵ \frac{x+\frac{11}{4}}{3} = (y - \frac{1}{2})²

→ Take √ for both sides

∴ ± \sqrt{\frac{x+\frac{11}{4}}{3}} = y - \frac{1}{2}

→ Add  \frac{1}{2} to both sides

∴ ± \sqrt{\frac{x+\frac{11}{4}}{3}} + \frac{1}{2} = y

→ Replace y by f^{-1}(x)

∴ f^{-1}(x) =  ± \sqrt{\frac{x+\frac{11}{4}}{3}} + \frac{1}{2}

∴ The inverse of f(x) is f^{-1}(x) =  ± \sqrt{\frac{x+\frac{11}{4}}{3}} + \frac{1}{2}

       

4 0
3 years ago
Help with this question !
Genrish500 [490]
Statements                                           Reasons
1. Write all the given as you did            1. Given
2. <DBA and <DBC are right angles     2. Def of perpendicular lines
3. m<DBA = 90                                     3. Def of right angle
    m<DBC = 90
4. m<DBA = m<DBC                             4. Substitution
5. m<DBA = m<1 + m<3                       5. Angle addition postulate
    m<DBC = m<2 + m<4
6. m<1 + m<3 = m<2 + m<4                  6. Substitution
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5 0
4 years ago
Help please ;-;
anzhelika [568]

Answer:

could be either b or d

Step-by-step explanation:

3 0
3 years ago
At the local bookstore, 4 paperback books cost $20. The table below represents the amount of books compared to the cost. Which o
Sindrei [870]

<em>Answer:</em>

<em>80 books = $400</em>

<em>Step-by-step explanation:</em>

<em />

3 0
3 years ago
Adalynn planted 20 peach trees over 400 feet.Dwight planted 18 plum trees over 270 feet.Is it proportional relationship.Explain
docker41 [41]

As the ratio 0.050:1 for Adalynn and the ratio 0.067:1 for Dwight are not equivalent, it shows that this is not a proportional relationship.

What is a proportional relationship?

Proportional relationships can be described as relationships between two variables that have equivalent ratios.

The ratio of Adalynn that planted 20 peach trees over 400 feet can be expressed as follows:

20:400

Divide through by 400, we have:

0.050:1

The ratio of Dwight that planted 18 plum trees over 270 feet can be expressed as follows:

Divide through by 270, we have:

0.067:1

Since the ratio 0.050:1 for Adalynn and the ratio 0.067:1 for Dwight are not equivalent, this implies that this is not a proportional relationship.

Learn more about the proportional relationship here: brainly.com/question/12917806.

#SPJ1

8 0
2 years ago
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