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4 years ago

Algebra 2 Simplify 3+i/2-i

Mathematics

1 answer:

Evgesh-ka [11]4 years ago

4 0

3-i/2
Pls mark me brainliest

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When Mai turned 21, she invested $2000 in an Individual Retirement Account (IRA) that has grown at a rate of 10% compounded annu

Brrunno [24]

well, Mai is 21 today and when she's 25 is 4 years from now, so

$~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$2000\\ r=rate\to 10\%\to \frac{10}{100}\dotfill &0.10\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &4 \end{cases} \\\\\\ A=2000\left(1+\frac{0.10}{1}\right)^{1\cdot 4}\implies A=2000(1.1)^4\implies A=2928.2$

3 0

3 years ago

Eliot opens a savings account with $5,000. He deposits $50 every month into the account that compounds annually and has a 0.95%

lbvjy [14]

Answer:

$8,328.65

Step-by-step explanation:

First we need take the number of deposits and add the amount to the initial amount in the account.

$50 x 12Months = $600

Initial Amount = $5,000

Now we convert the interest rate into decimal to make things easier.

0.95% = 0.0095

Now that we have the principal amount, we can then use the formula $A = P (1 + r)^{t}$ .

We need to keep in mind that the value for time will have to stay in a constant value as the total deposits each year will affect the amount.

Now let's begin with the amount for the first year:

$A = P (1 + r)^{t}$ .

$A = 5,600 (1 + 0.0095)^{1}$

A = 5,600 ( 1.0095 )

A = 5,653.20 Year 1

Now let's proceed to the next year. Remember that the deposits that Eliot make total at $600 each year.

P = 5,653.20 + 600

P = 6,253.20

Now we can proceed to calculate for the amount of the second year:

[tex]A = 6253.2 (1.0095)^{1}[/text]

A = 6,253.2 ( 1.0095 )

A = 6,312.61 Year 2

Now let's proceed doing the same process until the 5th year.

Year 3 Computation:

P = 6,312.61 + 600

P = 6,912.61

[tex]A = 6912.61 (1.0095)^{1}[/text]

A = 6978.28 Year 3

Year 4 Computation:

P = 6,978.28 + 600

P = 7,578.28

[tex]A = 7,578.28 (1.0095)^{1}[/text]

A = 7,650.27 Year 4

Last but no the least year 5.

P = 7,650.27 + 600

P = 8,250.27

[tex]A = 8,250.27 (1.0095)^{1}[/text]

A = 8,328.65 Year 5

So now we can conclude that at the end of year 5, Eliot will have a total of:

$8,328.65 in his account.

6 0

3 years ago

Which products result in a difference of of squares? check all that apply.

igomit [66]

Answer:

B, D

Step-by-step explanation:

The product of a sum and a difference results in a difference of squares.

The product must be of the form (a + b)(a - b) to work.

Answer: B, D

6 0

3 years ago

What's the answer of a + b + c

morpeh [17]

Answer:

The question or picture isn't on there

But if you actually talking about a + b+ c =(cb)a

6 0

3 years ago

Please help ! 20 pts please

Ksenya-84 [330]

The given ratios expresses the number of time a value is larger or smaller

than another value.

The correct responses are;

3. (B) 12 and 24

4. (D) 6, 9, 21

5. $\underline{(E) \ \displaystyle \frac{11}{2}}$

6. $\underline{(E) \ \displaystyle \frac{5}{14}}$

7. (B) $\overline{EF}$ = 6, $\overline{AC}$ = 9·√5

8. (C) The values are equal

9. (A) The value in column A is greater

Reasons:

3. Given that the perimeter of the rectangle = 72

The ratio of the lengths of the sides = 1:2

Let a and b represent the sides, we have;

2·a + 2·b = 72

$\displaystyle \frac{a}{b} = \mathbf{\frac{1}{2}}$

Which gives;

2·a = b

2·a + 2·(2·a) = 72

6·a = 72

a = 72 ÷ 6 = 12

b = 2·a = 2 × 12 = 24

The lengths of the sides are; (B) 12 and 24

4. Extended ratio = 2:3:7

The perimeter = 36

The lengths of the sides are;

$\displaystyle \frac{2}{2 + 3 + 7} \times 36 = \mathbf{6}$

$\displaystyle \frac{3}{2 + 3 + 7} \times 36 = \mathbf{9}$

$\displaystyle \frac{7}{2 + 3 + 7} \times 36 = \mathbf{21}$

The lengths are; (D) 6, 9, 21

5. The given equation is presented as follows;

$\displaystyle \frac{5}{x + 7} = \mathbf{\frac{3}{x + 2}}$

5 × (x + 2) = 3 × (x + 7)

5·x + 10 = 3·x + 21

5·x - 3·x = 21 - 10

2·x = 11

$\displaystyle x = \mathbf{ \frac{11}{2}}$

The correct option is; $\displaystyle \underline{(E) \ \frac{11}{2}}$

6. The width to length ratio is $\displaystyle \mathbf{\frac{2.5}{7.0}}$

The simplified ratio is therefore;

$\displaystyle \frac{2.5}{7.0} = \frac{2 \times 2.5}{2 \times 7.0} = \mathbf{\frac{5}{14}}$

The correct option is (E) $\displaystyle \underline{(E) \ \frac{5}{14}}$

7. The given ratio of the lengths is 3:1

Therefore;

$\overline{BC}$ : $\overline{EF}$ = 3:1

Which gives;

$\displaystyle \mathbf{\frac{\overline{BC}}{\overline{EF}}} = \frac{3}{1}$

$\overline{BC}$ = 18

Therefore;

$\displaystyle \frac{18}{\overline{EF}} = \frac{3}{1}$

18 × 1 = 3 × $\overline{EF}$

$\displaystyle \overline{EF} = \frac{18 \times 1}{3} = 6$

$\overline{EF}$ = 6

By Pythagorean theorem, we have;

$\overline{DF}$ ² = $\mathbf{\overline{DE}}$ ² + $\mathbf{\overline{EF}}$ ²

Which gives;

$\overline{DF}$ ² = 3² + 6² = 45

$\overline{DF}$ = √(45) = 3·√5

Using the given ratio, we have;

$\overline{AC}$ = 3 × $\mathbf{\overline{DF}}$

Which gives;

$\overline{AC}$ = 3 × 3·√5 = 9·√5

$\overline{AC}$ = 9·√5

The correct option is; (B) $\overline{EF}$ = 6, $\overline{AC}$ = 9·√5

8. EF = 1, AB = 2

CD = 2, CE = 4

Therefore;

$\displaystyle \mathbf{\frac{EF}{AB}} =\frac{1}{2}$

$\displaystyle \mathbf{\frac{CD}{CE}} =\frac{2}{4} = \frac{1}{2}$

Which gives;

$\displaystyle \frac{EF}{AB} =\displaystyle \mathbf{\frac{CD}{CE}}$

(C) The values are equal

9. AC = 6, BE = 8

DF = 3, BD = 6

Column A

$\displaystyle \frac{AC}{BE} =\displaystyle \mathbf{\frac{6}{8}} = \frac{3}{4}$

Column B

$\displaystyle \frac{DF}{BD} =\displaystyle \mathbf{\frac{3}{6}} = \frac{1}{2}$

$\displaystyle \frac{3}{4} > \mathbf{\frac{1}{2}}$

Therefore;

Column A is greater than column B

(A) The value in column A is greater

Learn more about ratios here:

brainly.com/question/2774839

7 0

3 years ago