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bazaltina [42]
2 years ago
6

Write the equation of the line through (5, -4); m = 1

Mathematics
2 answers:
andreev551 [17]2 years ago
7 0
Use photo math it helps with pretty much all equations
Snowcat [4.5K]2 years ago
4 0
(0+4) = 1(5-0)
point slope form
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Can someone please help me on this problem I’m struggling
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Integral of x"2+4/x"2+4x+3
dolphi86 [110]

I'm guessing you mean

\displaystyle \int\frac{x^2+4}{x^2+4x+3}\,\mathrm dx

First, compute the quotient:

\displaystyle \frac{x^2+4}{x^2+4x+3} = 1 + \frac{4x-1}{x^2+4x+3}

Split up the remainder term into partial fractions. Notice that

<em>x</em> ² + 4<em>x</em> + 3 = (<em>x</em> + 3) (<em>x</em> + 1)

Then

\displaystyle \frac{4x-1}{x^2+4x+3} = \frac a{x+3} + \frac b{x+1} \\\\ \implies 4x - 1 = a(x+1) + b(x+3) = (a+b)x + a+3b \\\\ \implies a+b=4 \text{ and }a+3b = -1 \\\\ \implies a=\frac{13}2\text{ and }b=-\frac52

So the integral becomes

\displaystyle \int \left(1 + \frac{13}{2(x+3)} - \frac{5}{2(x+1)}\right) \,\mathrm dx = \boxed{x + \frac{13}2\ln|x+3| - \frac52 \ln|x+1| + C}

We can simplify the result somewhat:

\displaystyle x + \frac{13}2\ln|x+3| - \frac52 \ln|x+1| + C \\\\ = x + \frac12 \left(13\ln|x+3| - 5\ln|x+1|\right) + C \\\\ = x + \frac12 \left(\ln\left|(x+3)^{13}\right| - \ln\left|(x+1)^5\right|\right) + C \\\\ = x + \frac12 \ln\left|\frac{(x+3)^{13}}{(x+1)^5}\right| + C \\\\ = \boxed{x + \ln\sqrt{\left|\frac{(x+3)^{13}}{(x+1)^5}\right|} + C}

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2 years ago
Figure B is the image of Figure A when reflected across line ℓ. Are Figure A and Figure B congruent
soldi70 [24.7K]

Answer:

If they are reflection. I think they are congruent

Step-by-step explanation:

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3 years ago
What measures of variation indicate spread about the mean?
KIM [24]
<span>standard deviation and variance</span>
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3 years ago
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