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3 years ago

Find the area of the pentagon pictured below.

Mathematics

1 answer:

podryga [215]3 years ago

8 0

Answer:

84.3

Step-by-step explanation:

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You are designing a rectangular garden. the garden will be enclosed by fencing on three sides and by a house on the fourth side.

RUDIKE [14]

Suppose the dimensions of the rectangle is x by y and let the side enclosed by a house be one of the sides measuring x, then the sides that is to be enclosed are two sides measuring y and one side measuring x.

Thus, the length of fencing needed is given by

P = x + 2y

The area of the rectangle is given by xy,

i.e.

$xy = 288 \\ \\ \\ \\ \Rightarrow y= \frac{288}{x}$

Substituting for y into the equation for the length of fencing needed, we have

$P=x+2\left( \frac{288}{x} \right)=x+ \frac{576}{x}$

For the amount of fencing to be minimum, then

$\frac{dP}{dx} =0 \\ \\ \Rightarrow1- \frac{576}{x^2} =0 \\ \\ \Rightarrow \frac{576}{x^2} =1 \\ \\ \Rightarrow x^2=576 \\ \\ \Rightarrow x=\sqrt{576}=24$

Now, recall that

$y= \frac{288}{x} = \frac{288}{24} =12$

Thus, the length of fencing needed is given by

P = x + 2y = 24 + 2(12) = 24 + 24 = 48.

Therefore, 48 feets of fencing is needed to enclose the garden.

8 0

3 years ago

Arbara sells iced tea for $1.49 per bottle and water for $1.25 per bottle. She wrote an equation to find the number of drinks sh

pashok25 [27]

If ice tea is lets say y (ice tea = y) and water is x (water = x) then the answer is
1.25x + 1.49y = 100
the error is that she forgot the second variable(y).

8 0

2 years ago

Will give brainliest to correct! “Write the equation of the line.”

viktelen [127]

Answer: y=1/3x-2

Step-by-step explanation:

y=Mx+b

1/3 is rise over run

-2 is the y intercept

8 0

3 years ago

In triangle XYZ, an exterior angle to angle X had measure 100° and an exterior angle to angle Z has measure 120°. Which side of

DaniilM [7]

Answer:

Side YZ is the longest

Step-by-step explanation:

The longest side is across from the largest angle.

Angle X must be 80° because its exterior angle is 100° and they're supplementary. Angle Z is 60° for the same reason. Inside a triangle is always 180°, and since the measures of angle Z and X add up to 140°, so there's 40° left, meaning angle X is the largest.

Angle X is across from size YZ, so that's the longest

5 0

2 years ago

Helps me pls what is 283x2492÷8(89)=2838(82x) what is x

Andrei [34K]

Answer:

Hey it’s 283

Step-by-step explanation:

3 0

3 years ago