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Margarita [4]
3 years ago
15

The perimeter of a rectangular garden is 38 feet. If the length is 5 feet longer than the width, find the width of the

Mathematics
1 answer:
son4ous [18]3 years ago
4 0

Answer:

Step-by-step explanation:

L and W are the length and width of the garden, respectively.

perimeter = 2L+2W = 38 ft

L+W = 19

the length is 5 ft longer than the width

L = W+5

substitution

(W+5)+W = 19

2W+5  = 19

W = 7

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Prove that for any natural n the number 3^(n+4)−3^n is divisible by 16.
gtnhenbr [62]

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

5(3ⁿ)

<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>

3 0
3 years ago
Please write step by step of how you got the answer. Thankyou
stealth61 [152]

Answer:

The solution in the attached figure

Step-by-step explanation:

step 1

Place the numbers  -4, 4, 0, and -3 in the left side

Adds the numbers

-4+4+0-3=-3 ----> is correct

step 2

Place the numbers  3, -1, and -2 in the right side

Adds the numbers

-3+3-1-2=-3 ----> is correct

step 3

Place the numbers  1 and 2 in the base side

Adds the numbers

-4+1+2-2=-3 ----> is correct

The solution in the attached figure

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3 years ago
Determine the perimeter of ABCD.
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I hope this helps.
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