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dmitriy555 [2]
3 years ago
15

TELL ME WHERE THESE GO PLEASE?

Mathematics
1 answer:
ValentinkaMS [17]3 years ago
3 0

<u>Answers</u>

-x + 5y = 4  ⇔ slope 1/5, y-intercept 4/5

5y - x = 15  ⇔   slope: 1/5, y-intercept: 3

2y - 3x = 7  ⇔ slope: 3/2, y-intercept: 7/2

2y = 5x + 7  ⇔ slope: 5/2, y-intercept: 7/2

<u>Explanation</u>

-x + 5y = 4

5y = x + 4

y = (1/5)x + 4/5                   slope 1/5, y-intercept 4/5


5y - x = 15

5y = x + 15

y = (1/5)x + 3                       slope: 1/5, y-intercept: 3


2y - 3x = 7

2y = 3x + 7

y = (3/2)x + 7/2                 slope: 3/2, y-intercept: 7/2


2y = 5x + 7

y = (5/2)x + 7/2              slope: 5/2, y-intercept: 7/2

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Prove that for any natural n the number 3^(n+4)−3^n is divisible by 16.
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Answer:

Proved (See Explanation)

Step-by-step explanation:

Show that 3ⁿ⁺⁴ - 3ⁿ is divisible by 16.

This is done as follows

\frac{3^{n+4} - 3^n}{16}

From laws of indices;

aᵐ⁺ⁿ = aᵐ * aⁿ.

So, 3ⁿ⁺⁴ can be written as 3ⁿ * 3⁴.

\frac{3^{n+4} - 3^n}{16} becomes

\frac{3^n * 3^4 - 3^n}{16}

Factorize

\frac{3^n(3^4 - 1)}{16}

\frac{3^n(81 - 1)}{16}

\frac{3^n(80)}{16}

3ⁿ * 5

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<em>The expression can not be further simplified.</em>

<em>However, we can conclude that when 3ⁿ⁺⁴ - 3ⁿ is divisible by 16, because 5(3ⁿ) is a natural whole number as long as n is a natural whole number.</em>

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6x²+4x+8

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