The length of a new rectangular playing field is 7 yards longer than triple the width. If the perimeter of the rectangular playing field is 438 ​yards, what are its​ dimensions?

Answers

Answer 1

Explanation:

L = 7+ 3W

the perimeter = 438

2(L+W) = 438

by using substitution :

2(7+3W+W) = 438

2(4W+7) = 438

4W+7 = 438/2

4W+7 = 219

4W = 219-7

4W = 212

W = 212/4 = 53

L = 7 + 3(53)

L = 7 + 159 = 166

so, the dimensions : the length = 166 yards

and the width = 53 yards

Answer 2

L = 7+ 3W

the perimeter = 438

2(L+W) = 438

by using substitution :

2(7+3W+W) = 438

2(4W+7) = 438

4W+7 = 438/2

4W+7 = 219

4W = 219-7

4W = 212

W = 212/4 = 53

L = 7 + 3(53)

L = 7 + 159 = 166

so, the dimensions : the length = 166 yards

and the width = 53 yards

What is the area of rectangular field?

Width = w

triple the width = 3*w = 3w

Length = 7 yards longer than triple the width = 3w + 7

Perimeter = 438 yards

2*(length +width) = 438

2*(3w+ 7 + w) = 438       {Combine like terms}

2 * (4w + 7)     = 438

2*4w +2*7 = 438       {Use distributive property}

8w + 14 = 438          {Subtract 14 from both side}

8w = 438 - 14

8w = 424          {Divide both sides by 8}

w = 424/8

w = 53 yards

Length = 3*53 +7 = 159 + 7 = 166 yards

Width = 53 yards

Length = 166 yards

The length and width of another rectangular field with same perimeter but a larger area is 80 m by 70 m.The perimeter of the existing field is

2(l + b)

= 2(90 + 60) = 2(150) = 300 yards

So we want another field having the same perimeter but a larger area.

Therefore, L = 7+ 3W

the perimeter = 438

2(L+W) = 438

by using substitution :

2(7+3W+W) = 438

2(4W+7) = 438

4W+7 = 438/2

4W+7 = 219

4W = 219-7

4W = 212

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Answer:

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Explanation:

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.........

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The sum of 3 consecutive integers is 18 more than 2 times the largest number. Find the three numbers. (Please help)

Answers

Answer:

19

20

21

Explanation:

Givens

Let the first integer = x - 1

Let the second    = x

Let the third = x + 1

Equation

x - 1 + x + x + 1 = 3x

Solution

3x = 2(x + 1) + 18                Remove the brackets

3x = 2x + 2 + 18                 Combine the terms on the right

3x = 2x + 20                      Subtract 2 x from both sides

x = 20

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Check

Sum = 60

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There, we found it.

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CALCULUS AB

Given g(x), name the piecewise function and graph:
g(x)+1
g(x-1)
-g(x)
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-g(x-1)
|g(x)|

Answers

A piecewise function is one that has different operations, depending on the values of the input

The piecewise function is;

[tex]g(x) = \begin{cases} -\left | x + 2 \right |&\mathbf{ \text{ if } -5 \leq x < 0 }\\ 2 \cdot x - 2 &\mathbf{ \text{ if } 0 < x \leq 2}\\ 2 &\mathbf{ \text{ if } 2 \leq x \leq 5}\end{cases}[/tex]

Reason:

The general form of the absolute value function is presented as follows;

[tex]f(x) = \mathbf{a \left | x - h \right | + k}[/tex]

The function given in the graph are;

Domain; -5 ≤ x < 0

Function;  [tex]g(x) = -\left | x + 2 \right |[/tex]

Domain; 0 < x ≤ 2

Points on the graph are;

(0, -2), and (2, 2)

Slope = (2 - (-2))/(2 - 0) = 2

g(x) - (-2) = 2·(x - 0)

∴ Function; g(x)  = 2·x - 2

Domain; 2 ≤ x ≤ 5

Function; g(x) = 2

Therefore, we have the following piecewise function;

[tex]g(x) = \mathbf{ \begin{cases} -\left | x + 2 \right |& \text{ if } -5 \leq x < 0 \\ 2 \cdot x - 2 & \text{ if } 0 < x \leq 2\\ 2 & \text{ if } 2 \leq x \leq 5\end{cases}}[/tex]

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See attached for the graphs of the various transformations of g(x).

• g(x) + 1 is a vertical shift upward by one unit

• g(x - 1) is a horizontal shift to the right by one unit

• -g(x) is a reflection across the x-axis

• 2g(x) is a scaling by a factor of 2

• -g(x - 1) is the composition of g(x - 1) and -g(x), hence a reflection and a horizontal shift

• |g(x)| leaves the positive parts of g(x) alone, and negates the negative parts (in other words, the parts of the graph of g(x) below the x-axis are reflected, the rest stays the same)

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Answers

Answer:

society was patriarchy where there was a presence of male dominance.

Explanation:

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Which theory states that citizens taking part in political processes is essential to
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B. Civil societies like the church organization are sponsored by local governments,
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O The AARP advocates for the interests of the common good, whereas the church
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The charitable church organization acts in the interest of the common good, whereas
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Answer:

The AARP advocates for the interests of the common good, whereas the church

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Explanation:

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Answers

D = many immigrants live in New York City

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New York City's significant human characteristic is its rich cultural diversity shaped by the vast number of immigrants who call it home.

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that what i got. hope that help

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Answer:

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PLS ANSWER :(

Answers

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Answers

Answer:

Um

Explanation:

False it's better free cause they all the same it's just a assignment kids gone learn one way or the other so you don't need to pay for better assignments when you can get better assignments free.

I hope this was helpful ∵

Answer:

true.

Explanation:

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Answers

Answer:

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Answer:

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