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Lera25 [3.4K]
2 years ago
5

the length of the swimming pool is 8 m longer than its width and the area is 105 m squared write in quadratic equation ​

Mathematics
1 answer:
weqwewe [10]2 years ago
5 0

Answer:

Step-by-step explanation:

The length of the swimming pool is 8m longer than it's width.

If we say L = length, W = width

From the information above, we can say

L= 8 + w

We are also told the area is 105 m squared.

<em>Note: </em>

<em>Area of a Rectangle = Length x Width </em>

105 =  (8 + w ) x w

105 = 8w + w^2\\

Subtract 105 from both sides:

w^2 + 8w - 105 = 0

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Answer:

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-2/3,0.6,3/4,-7/4,0,3 from least to greatest
Alja [10]

Answer:

-7/4 < -2/3 < 0 < 0.6 < 3/4 < 3

Step-by-step explanation:

7 0
3 years ago
<img src="https://tex.z-dn.net/?f=%5Ctext%7BSolve%20the%20system%20of%20equations%3A%7D%5C%5C%5C%5C%5Cleft%20%5C%7B%20%7B%7By%3D
Anika [276]

Hi there!  

»»————- ★ ————-««

I believe your answer is:  

(0.286, 5.587)

»»————- ★ ————-««  

Here’s why:  

⸻⸻⸻⸻

  • I have graphed the two equations in a program. When graphed, the lines intersect at point (0.286, 5.587).
  • See the graph attached.

⸻⸻⸻⸻

»»————- ★ ————-««  

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4 0
3 years ago
1. Write the form of the partial fraction decomposition of the rational expression. Do not solve for the constants.
german

Answer:

Step-by-step explanation:

1.

To write the form of the partial fraction decomposition of the rational expression:

We have:

\mathbf{\dfrac{8x-4}{x(x^2+1)^2}= \dfrac{A}{x}+\dfrac{Bx+C}{x^2+1}+\dfrac{Dx+E}{(x^2+1)^2}}

2.

Using partial fraction decomposition to find the definite integral of:

\dfrac{2x^3-16x^2-39x+20}{x^2-8x-20}dx

By using the long division method; we have:

x^2-8x-20 | \dfrac{2x}{2x^3-16x^2-39x+20 }

                  - 2x^3 -16x^2-40x

                 <u>                                         </u>

                                            x+ 20

So;

\dfrac{2x^3-16x^2-39x+20}{x^2-8x-20}= 2x+\dfrac{x+20}{x^2-8x-20}

By using partial fraction decomposition:

\dfrac{x+20}{(x-10)(x+2)}= \dfrac{A}{x-10}+\dfrac{B}{x+2}

                         = \dfrac{A(x+2)+B(x-10)}{(x-10)(x+2)}

x + 20 = A(x + 2) + B(x - 10)

x + 20 = (A + B)x + (2A - 10B)

Now;  we have to relate like terms on both sides; we have:

A + B = 1   ;   2A - 10 B = 20

By solvong the expressions above; we have:

A = \dfrac{5}{2}     B =  \dfrac{3}{2}

Now;

\dfrac{x+20}{(x-10)(x+2)} = \dfrac{5}{2(x-10)} + \dfrac{3}{2(x+2)}

Thus;

\dfrac{2x^3-16x^2-39x+20}{x^2-8x-20}= 2x + \dfrac{5}{2(x-10)}+ \dfrac{3}{2(x+2)}

Now; the integral is:

\int \dfrac{2x^3-16x^2-39x+20}{x^2-8x-20} \ dx =  \int \begin {bmatrix} 2x + \dfrac{5}{2(x-10)}+ \dfrac{3}{2(x+2)} \end {bmatrix} \ dx

\mathbf{\int \dfrac{2x^3-16x^2-39x+20}{x^2-8x-20} \ dx =  x^2 + \dfrac{5}{2}In | x-10|\dfrac{3}{2} In |x+2|+C}

3. Due to the fact that the maximum words this text box can contain are 5000 words, we decided to write the solution for question 3 and upload it in an image format.

Please check to the attached image below for the solution to question number 3.

4 0
2 years ago
Which of the following is the correct slope-intercept form of the equation -4x + 2y = 14? y = 4x + 14 y = -4x + 14 y = 2x + 7 y
DerKrebs [107]

Answer:

Step-by-step explanation:

The slope intercept form equation of a straight line is expressed as

y = mx + c

Where

m represents slope

c represents y intercept.

Comparing the given equations with the slope intercept form equation,

2) y = 4x + 14 is in the slope intercept form. Its slope is 4 and the intercept is 14.

3) y = -4x + 14 is in the slope intercept form. Its slope is - 4 and the intercept is 14.

4) y = 2x + 7 is in the slope intercept form. Its slope is 2 and the intercept is 7.

5) y = -2x + 7 is in the slope intercept form. Its slope is - 2 and the intercept is 7.

6 0
3 years ago
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