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melamori03 [73]
3 years ago
8

What is the answer for number 8 and pls give step by step

Mathematics
1 answer:
Pie3 years ago
8 0

Answer:

Trapezoid 1 (left side):

Base 1 = 2

Base 2 = 5

Trapezoid 2 (right side):

Base 1 = 6

Base 2 = 8

Step-by-step explanation:

<u>1st trapezoid:</u>

b_1 = x

b_2 = x + 3

h = 4

Hence, area (from formula) would be:

A=\frac{h}{2}(b_1+b_2)\\A=\frac{4}{2}(x+x+3)\\A=2(2x+3)\\A=4x+6

<u>2nd trapezoid:</u>

b_1 = 3x

b_2 = 4x

h = 2

Putting into formula, we get:

A=\frac{h}{2}(b_1+b_2)\\A=\frac{2}{2}(3x+4x)\\A=1(7x)\\A=7x

Let's equate both equations for area and find x first:

4x+6=7x\\6=7x-4x\\6=3x\\x=\frac{6}{3}\\x=2

We can plug in 2 into x and find length of each base of each trapezoid.

Trapezoid 1 (left side):

Base 1 = x = 2

Base 2 = x + 3 = 2 + 3 = 5

Trapezoid 2 (right side):

Base 1 = 3x = 3(2) = 6

Base 2 = 4x = 4(2) = 8

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3 years ago
Partial fraction decomposition<br> 20x+9/25x^2+20x+4
ozzi

Step-by-step explanation:

We have

\frac{20x + 9}{25 {x}^{2} + 20x + 4 }

Let's factor the denomiator first,

the denomaitor is a perfect square so we get

\frac{20x + 9}{(5x + 2) {}^{2} }

Now, we must think of two fractions that

\frac{a}{(5x + 2) {}^{2} }  +  \frac{b}{5x + 2}

We use a perfect square term for one fraction, then a linear one for the next, because if we set both of the denomiator to the same factor, we would get a inconsistent system.

So right now, we have

\frac{a}{(5x + 2) { }^{2} }  +  \frac{b}{5x + 2}  =  \frac{20x +9 }{25 {x}^{2} + 20x + 4 }

a + (5x  + 2)b = 20x + 9

5b (x)= 20

a + 2b = 9

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so that means that a is

a + (2)(4) = 9

a + 8 = 9

a = 1

So our equation is

\frac{1}{(5x + 2) {}^{2} }  +  \frac{4}{5x + 2}

6 0
2 years ago
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