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lorasvet [3.4K]
3 years ago
11

How do you rewrite this problem in slope-intercept form

Mathematics
1 answer:
Sergio039 [100]3 years ago
5 0

Solution

-6x - 3y = 9              Add 6x to both sides

-6x + 6x - 3y = 9 + 6x

-3y = 9 + 6x             Or more conventionally

-3y = 6x + 9             Divide by - 3

y = 6x/-3 + 9/-3

y = - 2x - 3  

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Which region did the Visigoths most likely settle?
Naddika [18.5K]

Answer:

It was Romania, so Spain.

6 0
3 years ago
Read 2 more answers
1. Express <img src="https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bx%282x%2B3%29%20%7D" id="TexFormula1" title="\frac{1}{x(2x+3) }" a
katovenus [111]

1. Let a and b be coefficients such that

\dfrac1{x(2x+3)} = \dfrac ax + \dfrac b{2x+3}

Combining the fractions on the right gives

\dfrac1{x(2x+3)} = \dfrac{a(2x+3) + bx}{x(2x+3)}

\implies 1 = (2a+b)x + 3a

\implies \begin{cases}3a=1 \\ 2a+b=0\end{cases} \implies a=\dfrac13, b = -\dfrac23

so that

\dfrac1{x(2x+3)} = \boxed{\dfrac13 \left(\dfrac1x - \dfrac2{2x+3}\right)}

2. a. The given ODE is separable as

x(2x+3) \dfrac{dy}dx} = y \implies \dfrac{dy}y = \dfrac{dx}{x(2x+3)}

Using the result of part (1), integrating both sides gives

\ln|y| = \dfrac13 \left(\ln|x| - \ln|2x+3|\right) + C

Given that y = 1 when x = 1, we find

\ln|1| = \dfrac13 \left(\ln|1| - \ln|5|\right) + C \implies C = \dfrac13\ln(5)

so the particular solution to the ODE is

\ln|y| = \dfrac13 \left(\ln|x| - \ln|2x+3|\right) + \dfrac13\ln(5)

We can solve this explicitly for y :

\ln|y| = \dfrac13 \left(\ln|x| - \ln|2x+3| + \ln(5)\right)

\ln|y| = \dfrac13 \ln\left|\dfrac{5x}{2x+3}\right|

\ln|y| = \ln\left|\sqrt[3]{\dfrac{5x}{2x+3}}\right|

\boxed{y = \sqrt[3]{\dfrac{5x}{2x+3}}}

2. b. When x = 9, we get

y = \sqrt[3]{\dfrac{45}{21}} = \sqrt[3]{\dfrac{15}7} \approx \boxed{1.29}

8 0
2 years ago
Ace does various odd jobs over the summer on one of his jobs he was paid $81 for a job he completed in nine hours. if he average
Vikentia [17]
He is making $9 an hour bc 81/9=9
9x26=$234
9x35=$315
after working 26 full hours he will have made a total of $234
total earnings:$315

I hope that is what you were looking for!
8 0
3 years ago
Help me please please help with is!
frozen [14]
The answer for the question is 21
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I need help with this
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