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Black_prince [1.1K]
3 years ago
12

The length of a new rectangular playing field is 6 yards longer than double the width. If the perimeter of the rectangular playi

ng field is 294 yards what are the dimensions?
Mathematics
1 answer:
Andru [333]3 years ago
4 0

Answer:

width = 47

Length = 100

Step-by-step explanation:

The perimeter of the rectangle has the formula

P = 2(L + W)

P = 2L + 2W

Length = 6 yards longer than double it's width.

Mathematically,

length = 6 + 2W

We put this into the formula for perimeter

P = 2(6+2W)+2W

294 = 12+4W+2W

294 = 12+6W

Collect like terms

294-12 = 6W

282 = 6w

Divide through by 6

W = 282/6

W = 47

This is the width

Remember length = 6 + 2(W)

So

Length = 6+2(47)

= 6+94

= 100

Width = 47

L = 100

These are the dimensions

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A radio is on sale for $76.50 at a 15% discount. What was the original selling price?
Colt1911 [192]

Answer:

87.975

Step-by-step explanation:

76.5 x 15% = 11.475

76.5 + 11.475 = 87.975

4 0
2 years ago
Is each expression equivalent to 2x^2 - 50?
puteri [66]
We would first determine how to solve this, and then from there, we would then see whether the following answer would be the correct answers.

2x^2 -  50 \\ \\ Pull \ out \ like \ factors : \\ 

   2x^2 - 50  =   2 * (x^2 - 25) \\ \\    Factoring: \\    x^2 - 25 \\ \\ (your \  answer)...\\ \\   2 * (x + 5) * (x - 5)

Now, we can determine whether the say "yes" or "no" to the following answers.

<span>a 2(x-5)(x+5) = YES
b -2(x+5)(x+5) = NO
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3 0
3 years ago
100 points!!!
Bogdan [553]

Answer:

(1, 5)

Step-by-step explanation:

The solution to the system of equations is the point of intersection of the two lines.  From inspection of the graph, the point of intersection is at (1, 5).

<u>Proof</u>

The solution to a system of equations is the point at which the two lines meet.  

⇒ g(x) = f(x)

⇒ 3x + 2 = |x - 4| + 2

⇒ 3x = |x - 4|

⇒ 3x = x - 4   and   3x = -(x - 4)

⇒ 3x = x - 4

⇒ 2x = -4

⇒ x = -2

Inputting x = -2 into the 2 equations:

⇒ g(-2) = 3 · -2 + 2 = -4

⇒ f(-2) = |-2 - 4| + 2 = 8

Therefore, as the y-values are different, x = -2 is NOT a solution

⇒ 3x = -(x - 4)

⇒ 3x = 4 - x

⇒ 4x = 4

⇒ x = 1

Inputting x = 1 into the 2 equations:

⇒ g(1) = 3 · 1 + 2 = 5

⇒ f(1) = |1 - 4| + 2 = 5

Therefore, as the y-values are the same, x = 1  IS a solution

and the solution is (1, 5)

8 0
2 years ago
What value of b will cause the system to have an infinite
m_a_m_a [10]

Answer:

b=6

Step-by-step explanation:

<u><em>The correct question is</em></u>

What value of b will cause the system to have an infinite number of solutions?

y = 6x – b

–3x + 1/2y = –3

we have

y=6x-b ----->equation A

-3x+\frac{1}{2}y=-3 -----> equation B

we know that

If the system has infinite number of solutions then, the equation A must be equal to the equation B

so

isolate variable y in the equation B

-3x+\frac{1}{2}y=-3

Multiply by 2 both sides

-6x+y=-6

y=6x-6 -------> new equation B

To find out the value of b, equate equation A and equation B

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4 0
2 years ago
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OLEGan [10]
The question is saying that the line KJ is approximately equal to the line JN and that the line JN is perpendicular to the line NL. The line labeled LKN is shorter than LNK due to the fact that the line segments in LNK are longer because JN is perpendicular to NL:) 
3 0
3 years ago
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