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fiasKO [112]
3 years ago
6

What is

+ \sqrt{-20} }{24}" alt="\frac{-8 + \sqrt{-20} }{24}" align="absmiddle" class="latex-formula">?
Mathematics
1 answer:
sdas [7]3 years ago
8 0

Answer:

\displaystyle \frac{-4 + i\sqrt{5}}{12}

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right<u> </u>

<u>Algebra I</u>

  • Factoring

<u>Algebra II</u>

  • Imaginary Numbers: √-1 = <em>i</em>

Step-by-step explanation:

<u>Step 1: Define</u>

<u />\displaystyle \frac{-8 + \sqrt{-20}}{24}<u />

<u />

<u>Step 2: Simplify</u>

  1. [Fraction] [√Radical] Factor:                                                                           \displaystyle \frac{-8 + \sqrt{-1}\sqrt{20}}{24}
  2. [Fraction] [√Radical] Evaluate:                                                                       \displaystyle \frac{-8 + i\sqrt{20}}{24}
  3. [Fraction] [√Radical] Simplify:                                                                        \displaystyle \frac{-8 + 2i\sqrt{5}}{24}
  4. [Fraction] Factor numerator:                                                                          \displaystyle \frac{2(-4 + i\sqrt{5})}{24}
  5. [Fraction] Simplify:                                                                                          \displaystyle \frac{-4 + i\sqrt{5}}{12}
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Answer:

The woman invested $15,000 at 7% interest rate and $5,000 at  6% interest rate.

Step-by-step explanation:

We are given the following in the question:

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The woman invested has three times as much invested at 7% as she does at 6%.

Thus, we can write the equation:

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Answer:

1. (x - 3)² = 8

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3. (x + 6)² = $ \frac{101}{2} $

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In the following problems the terms in the RHS of the above equation may be missing. We balance the equation. Simplify it and re write it in terms of LHS.

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Taking the constant term to the other side, we get:

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⇒ (x - 3)² = 8 is the answer.

2. 3x² + 12x + 3 = 0

Note that the co-effecient of x² is not 1. We make it 1, by dividing the whole equation by 3. And then proceed like the previous problem.

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⇒ x² + 2(6)x + 36 = $ \frac{29}{2} $ + 36

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⇒ (x + 6)² = $ \frac{101}{2} $ is the answer.

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4 years ago
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