Yumiko has a rectangular-shaped patio. She wants to double the area of the patio by increasing the length and the width by the same amount.
The length is 14 and the width is 10.

a. Write a function, in factored form, to calculate the number of feet Yumiko would need to add to the length and width.

b. What are the dimensions of the patio, rounded to the nearest hundredth feet?

I am not very good with completing the square and would like to understand it better. Any help would be very appreciated!

Answers

Answer 1

Answer:

For a rectangle of length L and width W, the area is:

A = L*W

In this case, we start with:

L = 14ft

W = 10ft

Then the initial area is:

A = 14ft*10ft = 140ft^2

a) Now she wants to increase the same amount in each measure, then the new measures will be:

L = 14ft + x

W = 10ft + x

Now we want this new area to be twice the one that we got before, then the equation will be:

(14ft + x)*(10ft + x) = 2*140ft^2 = 280ft^2.

b) Let's solve the equation:

(14ft + x)*(10ft + x) = 280ft^2

First lets distribute the multiplication:

140ft + x*10ft + 14ft*x + x^2 = 280ft

Now let's group terms with the same power of x.

x^2 + (10ft + 14ft)*x + 140ft - 280ft = 0.

x^2 + 24ft*x  - 140ft = 0.

Now we need to solve this quadratic equation, here we must use the Bhaskara equation for quadratic equations, and we will get two solutions for x.

[tex]x = \frac{-24ft +- \sqrt{(24ft)^2 - 4*140ft*1} }{2*1} = \frac{-24ft +- 33.7ft}{2}[/tex]

Then the two solutions are:

x = (-24ft - 33.7ft)/2 = -28.9 ft

This solution is negative, so it does not make sense and we can discard it.

x = (-24ft + 33.7ft)/2 = 4.85ft

This is positive, so we can use this.

Now we can find the new length and width:

L =  14ft + 4.85ft = 18.85ft

W = 10ft + 4.85ft = 14.85ft


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Answer:

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Answer:

5.1

Step-by-step explanation:

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Answer:

5 inches.

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Sorry if this is incorrect, but I do believe it is correct, have a good day!

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[tex]12[/tex]

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Step-by-step explanation:

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Please help I will mark you

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Hey :)

20b−16


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Hope this helps :)

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[tex]f(x)=e^\frac{1}{x}=\left(e^\frac{1}{x}\right)'\cdot\left(\dfrac{1}{x}\right)'=e^\frac{1}{x}\cdot\left(-\dfrac{1}{x^2}\right)=-\dfrac{e^\frac{1}{x}}{x^2}[/tex]

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Answers

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Step-by-step explanation:

Equations have an equals sign, while expressions do not.

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Answers

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The required length of the legs of triangle is 11√2. Option D is correct.

From figure
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What are triangles?

The triangle is geometric shape which includes 3 sides and sum of interior angle equal to 180°.

Let the length of the legs be x

sin45 = perpendicular/Hypotenuse
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x = 11√2

Thus, the required length of the legs of triangle is 11√2.

Get more information about triangles here:
https://brainly.com/question/2773823

#SPJ2

PLS HELP ASAP!!!!!!!!!!!!!!!!!!!!!11

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I have done it before and I did the work.

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I believe it’s b I hope this helps

Answer:

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Step-by-step explanation:

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Answers

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Step-by-step explanation:

Hi there !

1/2 × 2/5 = 1×2/2×5 = 2⁽²/10 = 1/5

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Good luck !

Answer:

1/5

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Step-by-step explanation:

These are the answers because:

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2) In this case it would be:

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