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Tema [17]
3 years ago
13

How do you do this problem?

Mathematics
1 answer:
umka2103 [35]3 years ago
6 0

Answer:

Step-by-step explanation:

You are going to work entirely on the right, until you can compare what is on the right with what you are given on the left.

a/1 + b/(x + 2) + c/(x - 8)

The first step is to determine the common denominator which is

(x + 2)(x - 8)

Now put each fraction over the common denominator.

<u>a(x + 2)(x - 8) + b(x - 8) + c(x + 2)</u>

             (x + 2)(x - 8)

The denominators on the left and right are the same, so you need only work with the numerators.

Remove the brackets.

a(x^2 - 6x - 16) + bx - 8b + cx + 2c

ax^2 - 6ax - 16a + bx - 8b + cx + 2c

In that whole expression, there is only 1 term that has an x^2 in it and that is the very first term.

a = 2 when you compare it to the left. You do this so you can get a value for  a.

Now put a = 2 in the first three terms on the expression above

2x^2 - 6*2x - 16(2) + bx - 8b + cx + 2c

2x^2 - 12x - 32 + bx - 8b + cx + 2c

The next thing is to get all the terms containing x together.

-12x + bx + cx = - 14x That's the term on the left (-14x). Divide by x

-12 + b + c = - 14          Add 12 to both sides

b + c = -14 + 12

b + c = - 2                    (x)

======================

Now you equate the terms with no x's in them.

-32 - 8b + 2c = - 76      Add 32 to both sides.

-8b + 2c = - 76 + 32

-8b + 2c = - 44             Divide by 2

-4b + c = - 22               (y)

Subtract (y) - (x)

-4b + c = - 22

 <u> b + c = - 2</u>

- 5b = - 20                   Divide by - 5

-5b/-5 = - 20/-5

b = 4

==============

b + c = - 2                     Find c substitute b = 4

4 + c = - 2                     Subtract 4 from both sides

c = - 2 - 4

c = - 6      

===============  

Answer

a = 2

b = 4

c = -6

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Find out the what is the perimeter of the rectangle .

To prove

Now as shown in the figure.

Name the coordinates as.

A(−3, 4) ,B (7, 2) , C(6, −3) , and D(−4, −1) .

In rectangle opposite sides are equal.

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AB = DC

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Disatnce\ formula = \sqrt{(x_{2} - x_{1})^{2} +(y_{2} - y_{1})^{2}}

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AB = \sqrt{(7- (-3))^{2} +(2- 4)^{2}}

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Now the points

A (−3, 4) , D (−4, −1)

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Here

Length = 2\sqrt{26}\ units

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Perimeter\ of\ rectangle = 2(3\sqrt{26})

Perimeter\ of\ rectangle = 6\sqrt{26}

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Perimeter\ of\ rectangle = 6\times 5.1

Perimeter of a rectangle = 30.6 units.

Therefore the perimeter of a rectangle is 30.6 units.

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