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Likurg_2 [28]
2 years ago
12

A rectangular pool is 20 feet wide and 50 feet long. A deck used for sunning surrounds the pool. The deck is the same width all

the way around the pool. The total area of the deck is 456 square feet. How wide is the deck around the pool?
Mathematics
1 answer:
rodikova [14]2 years ago
4 0

Answer:

  3 feet

Step-by-step explanation:

Let x represent the width of the deck. The deck adds to the pool dimensions on both sides, so the area of the site including pool and deck will be ...

  A = (20 +2x)(50 +2x) = 1000 +140x +4x^2

The area of the pool alone is

  A = (20)(50) = 1000

So, the area of the deck is the difference:

  456 = (4x^2 +140x +1000) -(1000)

Dividing by 4 and subtracting 114, we have ...

  x^2 +35x -114 = 0

  (x -3)(x +38) = 0

Solutions to this are x = 3 and x = -38. The positive solution is the one of interest.

The deck is 3 feet wide.

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Both x and y equal 2.

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3 years ago
Can someone help me please
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Answer: It will be set: a), e), g)

Step-by-step explanation:

In order to form a triangle then the sum of its angles has to be equal to 180 degrees. In order to find out if it’s possible to form a triangle from a specific set of angles, then you have to add them up and see if they are equal to 180 degrees. If they are then it’s a triangle if they less than or greater than 180 then a triangle cannot he formed.

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-6/7,-3/7,0,3/7 .... create a formula that explains the arithmetic sequence
LenKa [72]

The formula that explain the arithmetic sequence is a_{n}=\frac{3}{7}n-\frac{9}{7}

Step-by-step explanation:

The formula of the nth term in an arithmetic sequence is

a_{n}=a+(n-1)d , where

  • a is the first term
  • d is the common difference between the consecutive terms

∵ \frac{-6}{7} , \frac{-3}{7} , 0 , \frac{3}{7} are some terms of an arithmetic sequence

∵ The difference between two consecutive terms = \frac{-3}{7} - \frac{-6}{7}

∴ The difference between two consecutive terms = \frac{-3}{7} + \frac{6}{7} = \frac{3}{7}

∴ The common difference = \frac{3}{7}

∴ d = \frac{3}{7}

∵ The first term is \frac{-6}{7}

∴ a = \frac{-6}{7}

- Substitute a and d in the formula above

∴ a_{n}=\frac{-6}{7}+(n-1)\frac{3}{7}

- Simplify the right hand side

∴ a_{n}=\frac{-6}{7}+\frac{3}{7}n-\frac{3}{7}

- Add like terms

∴ a_{n}=\frac{3}{7}n-\frac{9}{7}

The formula that explain the arithmetic sequence is a_{n}=\frac{3}{7}n-\frac{9}{7}

Learn more:

You can learn more about the sequences in brainly.com/question/7221312

#LearnwithBrainly

3 0
2 years ago
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