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jeka94
2 years ago
15

A rectangular swimming pool is surrounded by a deck as shown. The area (in square feet) of the pool is represented by x^2-10x+16

. a. Write a binomial that represents the width of the pool. b. Find the perimeter of the pool when the width of the deck is 17 feet.
Mathematics
1 answer:
maw [93]2 years ago
8 0

Answer:

Step-by-step explanation:

First we need to factorize the given area of the rectangle as shown;

Given

A(x) = x^2-10x+16

Factorize

A(x) = x²-8x-2x+16

A(x) = (x²-8x)-(2x+16)

A(x) = x(x-8)-2(x-8)

A(x) = (x-2)(x-8)

Since area of a rectangle = length ×width

Hence the binomial that represents the width of the pool is w(x) = x-2

b) If the width of the deck is 17feet

Width = x-2

17 = x-2

x = 17+2

x = 19feet

Get the length

Length = x-8

Length = 19-8

Length = 11

Get the perimeter

P = 2(L+W)

P = 2(17+11)

P =2(28)

P = 56feet

Perimeter of the deck is 56feet

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Answer:

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Step-by-step explanation:

As we can see, the arc is bounded by the chord MO

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Setler [38]

Answer: 11

Step-by-step explanation:

Set up an equation

Based on the question, we can determine that 4x = 22 + 2x where x in is the number

"Four times a number" -> <u>4x</u>

"was" -> <u>=</u>

"22 greater than" -> <u>22 +</u>

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Put the underlined parts together to get <u>4x = 22 + 2x</u>

Solve equation

Rearrange/collect like terms to solve for x by subtracting 2x from both sides

4x = 22 + 2x

2x = 22

Solve for x by dividing each side by 2

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x = 11

Final Answer

x = 11

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3 years ago
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