Answer:
it’s B
Step-by-step explanation:
Answer:
y=5x-78
Step-by-step explanation:
y=5x+b
first plug in -3 for y and 15 for x
-3=5(15)+b
-3=75+b
subtract 75 on both sides
-78=b
y=5x-78
<span>Congruent triangles are
triangles with the same sides and the same measure of angles. You are given
triangle DEF which is similar to triangle FGH. From the figure, side FH is
larger than side DF. So the statement of them being congruent cancels out. Triangle
DEF is smaller in size than triangle FGH. So they are not congruent. The slope
is defined as the rise over run. Side DF has the same slope as side FH. Sides DE
and FE are proportional to sides FG and HG. Only C and D is correct.
</span>
I'm going to guess that you meant to include parentheses somewhere, so that the ODE is supposed to be
![y'=\dfrac{y^2x}{y^3+x^3}+\dfrac yx](https://tex.z-dn.net/?f=y%27%3D%5Cdfrac%7By%5E2x%7D%7By%5E3%2Bx%5E3%7D%2B%5Cdfrac%20yx)
Then substitute
so that
. Then
![xv'+v=\dfrac{x^3v^2}{x^3v^3+x^3}+v](https://tex.z-dn.net/?f=xv%27%2Bv%3D%5Cdfrac%7Bx%5E3v%5E2%7D%7Bx%5E3v%5E3%2Bx%5E3%7D%2Bv)
![xv'=\dfrac{v^2}{v^3+1}](https://tex.z-dn.net/?f=xv%27%3D%5Cdfrac%7Bv%5E2%7D%7Bv%5E3%2B1%7D)
which is separable as
![\dfrac{v^3+1}{v^2}\,\mathrm dv=\dfrac{\mathrm dx}x](https://tex.z-dn.net/?f=%5Cdfrac%7Bv%5E3%2B1%7D%7Bv%5E2%7D%5C%2C%5Cmathrm%20dv%3D%5Cdfrac%7B%5Cmathrm%20dx%7Dx)
Integrate both sides: on the left,
![\displaystyle\int\frac{v^3+1}{v^2}\,\mathrm dv=\int\left(v+\frac1{v^2}\right)\,\mathrm dv=\dfrac12v^2-\dfrac1v](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint%5Cfrac%7Bv%5E3%2B1%7D%7Bv%5E2%7D%5C%2C%5Cmathrm%20dv%3D%5Cint%5Cleft%28v%2B%5Cfrac1%7Bv%5E2%7D%5Cright%29%5C%2C%5Cmathrm%20dv%3D%5Cdfrac12v%5E2-%5Cdfrac1v)
The other side is trivial. We end up with
![\dfrac12v^2-\dfrac1v=\ln|x|+C](https://tex.z-dn.net/?f=%5Cdfrac12v%5E2-%5Cdfrac1v%3D%5Cln%7Cx%7C%2BC)
Solve in terms of
:
![\boxed{\dfrac{y^2}{2x^2}-\dfrac xy=\ln|x|+C}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Cdfrac%7By%5E2%7D%7B2x%5E2%7D-%5Cdfrac%20xy%3D%5Cln%7Cx%7C%2BC%7D)
Answer:
However, the likelihood of getting one head and one tail (in any order) is 2 in 4 (. 5). Note: the probability of a coin flip does not depend on what has happened in previous flips; this is very important !!
Step-by-step explanation: