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2 years ago

If 2 is a factor of a number, is that number a prime number? ___________ explain

Mathematics

1 answer:

Nataliya [291]2 years ago

4 0

Yes it is. It is the only even number that is prime that is multiplied by 1.

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Which expression is equivalent to *picture attached*

DiKsa [7]

Answer:

The correct option is;

$4 \left (\dfrac{50 (50+1) (2\times 50+1)}{6} \right ) +3 \left (\dfrac{50(51) }{2} \right )$

Step-by-step explanation:

The given expression is presented as follows;

$\sum\limits _{n = 1}^{50}n\times \left (4\cdot n + 3 \right )$

Which can be expanded into the following form;

$\sum\limits _{n = 1}^{50} \left (4\cdot n^2 + 3 \cdot n\right ) = 4 \times \sum\limits _{n = 1}^{50} \left n^2 + 3 \times\sum\limits _{n = 1}^{50} n$

From which we have;

$\sum\limits _{k = 1}^{n} \left k^2 = \dfrac{n \times (n+1) \times(2n+1)}{6}$

$\sum\limits _{k = 1}^{n} \left k = \dfrac{n \times (n+1) }{2}$

Therefore, substituting the value of n = 50 we have;

$\sum\limits _{n = 1}^{50} \left k^2 = \dfrac{50 \times (50+1) \times(2\cdot 50+1)}{6}$

$\sum\limits _{k = 1}^{50} \left k = \dfrac{50 \times (50+1) }{2}$

Which gives;

$4 \times \sum\limits _{n = 1}^{50} \left n^2 = 4 \times \dfrac{n \times (n+1) \times(2n+1)}{6} = 4 \times \dfrac{50 \times (50+1) \times(2 \times 50+1)}{6}$

$3 \times\sum\limits _{n = 1}^{50} n = 3 \times \dfrac{n \times (n+1) }{2} = 3 \times \dfrac{50 \times (51) }{2}$

$\sum\limits _{n = 1}^{50}n\times \left (4\cdot n + 3 \right ) = 4 \times \dfrac{50 \times (50+1) \times(2\times 50+1)}{6} +3 \times \dfrac{50 \times (51) }{2}$

Therefore, we have;

$4 \left (\dfrac{50 (50+1) (2\times 50+1)}{6} \right ) +3 \left (\dfrac{50(51) }{2} \right )$ .

4 0

2 years ago

What is the power of 256

Juli2301 [7.4K]

In mathematics. 256 is a composite number, with the factorization 256 = 28, which makes it a power of two. 256 is 4 raised to the 4th power, so in tetration notation 256 is 24.

4 0

3 years ago

A black line is longer than a gray line. The gray line is longer than a white line. Is the black line shorter or longer than the

enot [183]

The gray line is longer than the white line.
The black line is longer than the gray line.

White    -------------------------

Gray     ------------------------------------------

Black    --------------------------------------------------------

Answer: The black line is longer than the white line.

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2 years ago

HELP FAST select the correct answer

Aleks04 [339]

Answer:

Step-by-step explanation:

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2 years ago

If a square root parent function is vertically stretched by a factor of 6, what is

natita [175]

Parent function = √x

On stretching vertically by factor of 6

New function G(x) = 6√x

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1 year ago