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Rufina [12.5K]
3 years ago
7

What is 3.7 repeating, as a mixed number

Mathematics
2 answers:
Molodets [167]3 years ago
5 0

Answer:

3\frac{7}{9}

Step-by-step explanation:

We can rewrite 3.7 repeating as 3.7777777.....

Let x = 3.7777777....... -------(1)      [multiply 10 to both side]

10x = 37.777777...... ----------(2)     [subtract equation (1) from equation(2)]

10x - x = 37.777777 - 3.7777777

9x = 34

x = \frac{34}{9}

  = 3\frac{7}{9}

The mixed number of 3.7 repeating is 3\frac{7}{9}

Marianna [84]3 years ago
4 0
I believe it is 3 7/11
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What is the value of the remainder if 10x^4 – 6x^3 + 5x^2 – x + 1 is divided by x – 3?
ludmilkaskok [199]

Answer: 691

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

There are 3 different ways to find the remainder.  I am not sure which method you are supposed to use, so I will solve using all 3 methods.

Long Division:

       <u>  10x³ + 24x² + 77x + 230 </u>

x - 3 ) 10x⁴ -  6x³  + 5x²   - x  +  1

      - <u>(10x⁴ - 30x³) </u>   ↓       ↓      ↓

                   24x³ + 5x²     ↓      ↓

               - <u>(24x³ - 72x²) </u>   ↓      ↓

                              77x²  - x       ↓

                         -  <u>(77x² - 231x) </u>  ↓

                                        230x + 1

                                     - <u>(230x - 690)</u>

                                                    691 ← remainder

Synthetic Division:

x - 3 = 0   ⇒  x = 3

3  |  10     -6        5       -1        1

   |<u>   ↓      30     72    231    690</u>

      10      24     77    230   691 ← remainder

Remainder Theorem:

f(x) = 10x⁴ - 6x³ + 5x²  - x  +  1

f(3) = 10(3)⁴ - 6(3)³ + 5(3)² - (3)  +  1

     =  810   - 162    + 45    -  3  +  1

     = 691

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What is the equation of a line with slope -2 and passes through the point (0, 3)?
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The equation that you are looking for is y = -2x + 3
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