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svp [43]
2 years ago
12

Caroline was thinking of a number. Caroline adds 7 to it, then doubles it and gets an answer of 82.8. What was the original numb

er?
Mathematics
1 answer:
Soloha48 [4]2 years ago
5 0

Answer:

n = 34.4

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  

Equality Properties

  • Multiplication Property of Equality
  • Division Property of Equality
  • Addition Property of Equality
  • Subtraction Property of Equality<u> </u>

Step-by-step explanation:

<u>Step 1: Set Up</u>

Let's let our number be set by variable <em>n</em>.

We add 7 to it: n + 7

We then double that entire expression: 2(n + 7)

That expression is equal to 82.8: 2(n + 7) = 82.8

<u>Step 2: Solve for </u><em><u>n</u></em>

  1. [Division Property of Equality] Divide 2 on both sides:                               n + 7 = 41.4
  2. [Subtraction Property of Equality] Subtract 7 on both sides:                      n = 34.4

∴ Caroline's original number is 34.4.

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DIA [1.3K]

Answer:

a. \  \dfrac{625 \cdot m}{27 \cdot n^{11}}

b. \  \dfrac{x^{3 \cdot m - 2}}{y^{ 3 + n}}

Step-by-step explanation:

The question relates with rules of indices

(a) The give expression is presented as follows;

\dfrac{m^3 \times \left (n^{-2} \right )^4 \times (5 \cdot m)^4}{\left (3 \cdot m^2 \cdot n \right )^3}

By expanding the expression, we get;

\dfrac{m^3 \times n^{-8} \times 5^4 \times m^4}{\left 3^3 \times m^6 \times n^3}

Collecting like terms gives;

\dfrac{m^{(3 + 4 - 6)}  \times 5^4}{ 3^3 \times n^{3 + 8}} = \dfrac{625 \cdot m}{27 \cdot n^{11}}

\dfrac{m^3 \times \left (n^{-2} \right )^4 \times (5 \cdot m)^4}{\left (3 \cdot m^2 \cdot n \right )^3}= \dfrac{625 \cdot m}{27 \cdot n^{11}}

(b) The given expression is presented as follows;

x^{3 \cdot m + 2} \times \left (y^{n - 1} \right )^3 \div (x \cdot y^n)^4

Therefore, we get;

x^{3 \cdot m + 2} \times \left (y^{n - 1} \right )^3 \times  x^{-4} \times y^{-4 \cdot n}

Collecting like terms gives;

x^{3 \cdot m + 2 - 4} \times \left (y^{3 \cdot n - 3 -4 \cdot n}} \right ) = x^{3 \cdot m - 2} \times \left (y^{ - 3 -n}} \right ) = x^{3 \cdot m - 2} \div \left (y^{ 3 + n}} \right )

x^{3 \cdot m - 2} \div \left (y^{ 3 + n}} \right ) = \dfrac{x^{3 \cdot m - 2}}{y^{ 3 + n}}

x^{3 \cdot m + 2} \times \left (y^{n - 1} \right )^3 \times  x^{-4} \times y^{-4 \cdot n} =\dfrac{x^{3 \cdot m - 2}}{y^{ 3 + n}}

4 0
3 years ago
There are 12 people in a class. 10 are randomly chosen. How many possible combinations are there?
Mazyrski [523]

long way

12 x 11 x 10 x 9 x 8 x 7 x6 x5 x4 x3x2/ 10x9x8x7x6x5x4x3x2x


but you can shorten that by crossing out identical numbers so you get 12 x 11

12 x 11 = 132 combinations

3 0
3 years ago
2(n+2)=10 solve for n
astra-53 [7]

Answer :

<em>\:  \:  \:  \:  \:  \: 2(n + 2) = 10 \\  =  > 2n + 4 = 10 \\  =  > 2n = 10 - 4 \\  =  > 2n = 6 \\  =  > n =  \frac{6}{2}  \\   = > n = 3</em>

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The floor at a roller skating rink is 72.25 feet long and 51.5 feet wide. How much longer is the rink than it is wide?
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Answer:

The rink is 20.75 ft longer

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Simply subtract the width from the length.  

72.25-51.5= 20.75 ft


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seraphim [82]
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