To make an enclosure for chickens, a rectangular area will be fenced next to a house. Only three sides will need to be fenced. There is 120 ft of fencing material. What quadratic function represents the area of the rectangular enclosure, where x is the distance from the house? What dimensions will maximize the area of the enclosure?

Answers

Answer 1

Answer:

Let the length parallel to the house be y

let each of the other two equal sides be x

2x + y = 120

y = 120 - 2x

Area = xy

= x(120 - 2x) or -2x^2 + 120x

b) you want the vertex.

x of the vertex is -120/(-4) = 30

when x = 30

y = 60

Maximum area = xy = 1800 ft^2

Answer 2

The quadratic function that represents the area of the rectangular enclosure is  -2x² + 120x and x = 30 and y = 60 will make the area maximize.

What is a rectangle?

A rectangle is a geometrical figure in which opposite sides are equal.

The angle between any two consecutive sides will be 90 degrees.

Area of rectangle = length × width.

Perimeter of rectangle = 2( length + width).

Let's suppose the length parallel to the house is y

And the remaining side is x then,

Perimeter = x + x + y

2x + y = 120

y = 120 - 2x

The area of the rectangle = xy

Area = x(120 - 2x)

⇒ -2x² + 120x

To find the maximum first derivate of the function area with respect to x compare with zero.

d/dx(-2x² + 120x) = 0 ⇒ -4x + 120 = 0

x = 30 so y = 120 - 2(30) = 60

Hence "The quadratic function that represents the area of the rectangular enclosure is  -2x² + 120x and x = 30 and y = 60 will make the area maximize".

For more about rectangles,

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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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Answer:Me!" (stylized in all caps) is a song recorded by American singer-songwriter Taylor Swift featuring American singer Brendon Urie of Panic! at the Disco. It was released on April 26, 2019, through Republic Records, as Swift's first single after signing with the label. The song was revealed and released at the end of a thirteen-day countdown, as the lead single from her seventh studio album, Lover (2019). It was written by Swift, Joel Little and Urie, and produced by Swift and Little. The song was recorded at Electric Lady Studios, New York City and Golden Age West in Auckland, New Zealand in 2018. "Me!" is a cheery, campy bubblegum pop and synth-pop duet, driven by a marching band drumline. It is about embracing one's individuality, with lyrics on self-affirmation and self-love.

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Step-by-step explanation:

Answer:

D. Group A, because four children in the group have the least forearm length of 10 inches.

Step-by-step explanation:

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Answers

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Step-by-step explanation:

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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Answers

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Step-by-step explanation:

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Step-by-step explanation:

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Step-by-step explanation:

Answer:

178.5

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Answers

Answer:

6

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Step-by-step explanation:

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Answer

1) x=5

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Answer:

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Step-by-step explanation:

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Answers

Answer:

What is 2x+1 is equal to

??!

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Answers

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Answers

Answer:

2

Step-by-step explanation:

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Answers

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Step-by-step explanation:

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