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Tema [17]
3 years ago
7

Write three different equations that have x=5 as a solution

Mathematics
2 answers:
Oliga [24]3 years ago
8 0
The easiest ways to do this is to add, subtract, multiply, or devide 5 from a number, do that operation to x, and set that number as the equivelent.

For example
3*5=15
so
3x=15
svlad2 [7]3 years ago
7 0

Answer: The three different equations will be

x+3=8\\\\2x-8=2\\\\4x-4=16

Step-by-step explanation:

We have to write three equation that have x = 5 as a solution:

1) First equation will be

x+3=8\\\\x=8-3\\\\x=5

2) Second equation will be

2x-8=2\\\\2x=8+2\\\\2x=10\\\\x=\frac{10}{2}\\\\x=5

3) Third equation will be

4x-4=16\\\\4x=16+4\\\\4x=20\\\\x=\frac{20}{4}\\\\x=5

Hence, the three different equations will be

x+3=8\\\\2x-8=2\\\\4x-4=16



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17 minutes

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MAXImum [283]
The answer is Letter C - 1/2,775

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P = 2 / 75 * 1 / 74
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8 0
3 years ago
A norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular. Find the dimensions of a norman
Yanka [14]

Answer:

W\approx 8.72 and L\approx 15.57.

Step-by-step explanation:

Please find the attachment.

We have been given that a norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular. The total perimeter is 38 feet.

The perimeter of the window will be equal to three sides of rectangle plus half the perimeter of circle. We can represent our given information in an equation as:

2L+W+\frac{1}{2}(2\pi r)=38

We can see that diameter of semicircle is W. We know that diameter is twice the radius, so we will get:

2L+W+\frac{1}{2}(2r\pi)=38

2L+W+\frac{\pi}{2}W=38

Let us find area of window equation as:

\text{Area}=W\cdot L+\frac{1}{2}(\pi r^2)

\text{Area}=W\cdot L+\frac{1}{2}(\pi (\frac{W}{2})^2)

\text{Area}=W\cdot L+\frac{\pi}{2}(\frac{W}{2})^2)

\text{Area}=W\cdot L+\frac{\pi}{2}(\frac{W^2}{4})

\text{Area}=W\cdot L+\frac{\pi}{8}W^2

Now, we will solve for L is terms W from perimeter equation as:

L=38-(W+\frac{\pi }{2}W)

Substitute this value in area equation:

A=W\cdot (38-W-\frac{\pi }{2}W)+\frac{\pi}{8}W^2

Since we need the area of window to maximize, so we need to optimize area equation.

A=W\cdot (38-W-\frac{\pi }{2}W)+\frac{\pi}{8}W^2  

A=38W-W^2-\frac{\pi }{2}W^2+\frac{\pi}{8}W^2  

Let us find derivative of area equation as:

A'=38-2W-\frac{2\pi }{2}W+\frac{2\pi}{8}W  

A'=38-2W-\pi W+\frac{\pi}{4}W    

A'=38-2W-\frac{4\pi W}{4}+\frac{\pi}{4}W

A'=38-2W-\frac{3\pi W}{4}

To find maxima, we will equate first derivative equal to 0 as:

38-2W-\frac{3\pi W}{4}=0

-2W-\frac{3\pi W}{4}=-38

\frac{-8W-3\pi W}{4}=-38

\frac{-8W-3\pi W}{4}*4=-38*4

-8W-3\pi W=-152

8W+3\pi W=152

W(8+3\pi)=152

W=\frac{152}{8+3\pi}

W=8.723210

W\approx 8.72

Upon substituting W=8.723210 in equation L=38-(W+\frac{\pi }{2}W), we will get:

L=38-(8.723210+\frac{\pi }{2}8.723210)

L=38-(8.723210+\frac{8.723210\pi }{2})

L=38-(8.723210+\frac{27.40477245}{2})

L=38-(8.723210+13.70238622)

L=38-(22.42559622)

L=15.57440378

L\approx 15.57

Therefore, the dimensions of the window that will maximize the area would be W\approx 8.72 and L\approx 15.57.

8 0
3 years ago
Sofia is comparing celluer plans. Company A charges a flat fee of 59.99 a month and .43 additional minutes. Company B charges 69
Vsevolod [243]

Answer: it will take 125 additional minutes for both costs to be equal.

Step-by-step explanation:

Let a represent the number of additional minutes that it will it take for the two to be the same.

Company A charges a flat fee of 59.99 a month and .43 additional minutes. This means that the total cost of a additional units would be

0.43x + 59.99

Company B charges 69.99 a month and .35 for additional minutes. This means that the total cost of a additional units would be

0.35x + 69.99

For the cost of the two plans to be the same, it means that

0.43x + 59.99 = 0.35x + 69.99

0.43x - 0.35x = 69.99 - 59.99

0.08x = 10

x = 125

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3 years ago
For some JKL the side lengths are such that LJ< JK< KL what must be true about angles J, K, L
katovenus [111]

Answer:

it does not matter didjebejsusudhdhe

4 0
2 years ago
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