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ryzh [129]
3 years ago
5

A town is planning a playground. It wants to fence in a rectangular space using an existing wall. What is the greatest area it c

an fence in using 100 feet of donated fencing?
Mathematics
1 answer:
777dan777 [17]3 years ago
3 0

Answer:

1250 ft^{2}

Step-by-step explanation:

We are given that the playground is fenced on three sides of the playground and the four side has an existing wall.

Let the length of the rectangle be 'X' feet and width be 'Y' feet.

As the fencing is done using 100 feet of fence. We get the relation between the sides and the fence as, X + 2Y = 100.

As, X + 2Y = 100 → X = 100 - 2Y

Now, the area of the rectangle = XY = X × ( 100 - 2Y ).

i.e Area of the rectangle = -2Y^{2} +100Y.

The general form of a quadratic equation is y=ax^{2}+bx+c.

The maximum value of a quadratic equation is given by x=\frac{-b}{2a}.

Therefore, the greatest value of -2Y^{2} +100Y is at Y = \frac{-100}{2 \times -2} = \frac{-100}{-4} = 25.

Thus, Y = 25 and X = 100 - 2Y → X = 100 - 2 × 25 → X = 50.

Hence, the area of the rectangle is XY = 50 × 25 = 1250 ft^{2}.

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Answer:

\mathrm{B.} All real numbers except x = 2, x = 5

Step-by-step explanation:

If the denominator is equal to 0 then the function would be undefined.

Set the denominator equal to 0.

x² - 7x + 10 = 0

Factor the left side of the equation.

(x - 5)(x - 2) = 0

Set the factors equal to 0.

x - 5 = 0

x = 5

x - 2 = 0

x = 2

The domain is all real numbers except x = 2 and x = 5.

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3 years ago
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2 years ago
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-8k+8m+5

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Inscribed circles on the arc; improvement answer is required in full.
e-lub [12.9K]

Answer:

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8 0
3 years ago
Nivyana and Ana are selling their apparel to earn money for a cruise. Knitted scarves are $50 each in Mittens are $25 per pair.
Katarina [22]

Answer:

The number of knitted scarves is 10

The number of knitted mitten is 20

Step-by-step explanation:

Given as :

The cost of each knitted scarves = $50

The cost of pairs of mittens = $25

Total number of scarves and mitten bought = 30

The total money invested to pay for items = $1000

Let The number of knitted scarves = k

Let The number of mitten = m

<u>Now, According to question</u>

The total money invested to pay for items = cost of each knitted scarves × number of knitted scarves + cost of pairs of mittens × number of mitten

i.e $1000 = $50 × k + $25 × m

Or, 40 = 2 k + m

i.e 2 k + m = 40           ........A

And

Total number of scarves and mitten bought =  number of knitted scarves +  number of mitten

i.e k + m = 30            ...........B

Now, solving eq A and eq B

So, (2 k + m ) - ( k + m ) = 40 - 30

Or, (2 k - k) + ( m - m) = 10

Or, k + 0 = 10

∴  k = 10

So,  The number of knitted scarves = k = 10

Put the value of k into eq B

∵ k + m = 30

So, m = 30 - k

or, m = 30 - 10

∴  m = 20

The number of knitted mitten = m = 20

Hence,  The number of knitted scarves is 10 and The number of knitted mitten is 20  . Answer

7 0
3 years ago
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