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nataly862011 [7]
3 years ago
11

Need help fast! need the value of x and please show the work!

Mathematics
1 answer:
lions [1.4K]3 years ago
6 0

By the external angle of a triangle theorem

m < ABD = m < BDC + m < BCD

That is  5x + 2 = x^2 - 1 + 4x - 3

x^2  + 4x - 5x - 1 - 3 - 2 = 0

x^2 - x - 6 = 0

(x - 3)(x + 2) = 0

x = 3,  -2

x cannot be -2 because that would make the external angle, 5x-2 negative.

Answer x = 3

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Solve for x.<br> logo(x-2) + log(x + 3) = 2
amid [387]

Answer:

x=-1-5√17/2

Step-by-step explanation:

logo((x-2)(x+2))=2

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2 years ago
6.<br> The area of the book cover is 14 in.? and the length is 2} in. What is the width?
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the width is 7 inches

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A = l * w

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3 years ago
Integrate 1 - x / x(x2 + 1) d x by partial fractions.
solniwko [45]

Answer:

log x-\frac{log(x^{2}+1) }{2}-tan^{-1} x

Step-by-step explanation:

step 1:-   by using partial fractions

[tex]\frac{1-x}{x(x^{2}+1) } =\frac{A(x^{2}+1)+(Bx+C)(x }{x(x^{2}+1) }......(1)

<u>step 2:-</u>

solving on both sides

1-x=A(x^{2} +1)+(Bx+C)x......(2)

substitute x =0 value in equation (2)

1=A(1)+0

<u>A=1</u>

comparing x^2 co-efficient on both sides (in equation 2)

0 = A+B

0 = 1+B

B=-1

comparing x co-efficient on both sides (in equation 2)

<u>-</u>1  =  C

<u>step 3:-</u>

substitute A,B,C values in equation (1)

now  

\\\int\limits^ {} \, \frac{1-x}{x(x^{2}+1) } d x =\int\limits^ {} \frac{1}{x} d x +\int\limits^ {} \frac{-x}{x^{2}+1 }  d x -\int\limits \frac{1}{x^{2}+1 }  d x

by using integration formulas

i)  by using \int\limits \frac{1}{x}   d x =log x+c........(a)\\\int\limits \frac{f^{1}(x) }{f(x)} d x= log(f(x)+c\\.....(b)

\int\limits tan^{-1}x  dx =\frac{1}{1+x^{2} } +C.....(c)

<u>step 4:-</u>

by using above integration formulas (a,b,and c)

we get answer is

log x-\frac{log(x^{2}+1) }{2}-tan^{-1} x

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