<span>(x^(2)-3x-54)/(x^(2)-18x+81)*(x^(2)+12x+36)/(x+16)
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![\frac{x^2-3x-54}{x^2-18x+81} * \frac{x^2+12x+36}{x+16} =\\ \\ = \frac{(x-9)(x+6)}{(x-9)^2} * \frac{(x+6)^2}{x+16} = \\ \\ = \frac{x+6}{x-9} * \frac{(x+6)^2}{x+16} = \\ \\ = \frac{(x+6)^3}{(x-9)(x+16)}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bx%5E2-3x-54%7D%7Bx%5E2-18x%2B81%7D%20%2A%20%5Cfrac%7Bx%5E2%2B12x%2B36%7D%7Bx%2B16%7D%20%3D%5C%5C%20%20%5C%5C%20%3D%20%5Cfrac%7B%28x-9%29%28x%2B6%29%7D%7B%28x-9%29%5E2%7D%20%2A%20%5Cfrac%7B%28x%2B6%29%5E2%7D%7Bx%2B16%7D%20%3D%20%5C%5C%20%20%5C%5C%20%3D%20%5Cfrac%7Bx%2B6%7D%7Bx-9%7D%20%2A%20%5Cfrac%7B%28x%2B6%29%5E2%7D%7Bx%2B16%7D%20%3D%20%5C%5C%20%20%5C%5C%20%3D%20%5Cfrac%7B%28x%2B6%29%5E3%7D%7B%28x-9%29%28x%2B16%29%7D)
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Answer:
<em>~ Jill needs a minimum score of 90% to recieve an average of at least 92% on all her math quizzes ~</em>
Step-by-step explanation:
1. The table shows that her past weeks math quiz scores are: 92, 96, 94, 88
2. If she were to get a mean, or average, of at least 92, we could set up an equation to determine the minimum score she will recieve on her next quiz:
92 + 96 + 94 + 88 + x/ 5 = 92 ⇒ <em>(where x is the minimum score she should recieve on her next quiz to get an average of at least 92%)</em>
3. Now let us solve this equation for x through simple algebra ⇒
92 + 96 + 94 + 88 + x/ 5 = 92 ⇒
370 + x/5 = 92 ⇒
x/5 + 74 = 92 ⇒
x/5 = 18
x = 90
4. <em>Jill needs a minimum score of 90% to recieve an average of at least 92% on all her math quizzes</em>
Answer:
child same I don't know either
Step-by-step explanation:
ask the lord he shall help lol
Answer/Step-by-step explanation:
1. ![\frac{(-2)^{-5}}{(-2)^{-10}}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%28-2%29%5E%7B-5%7D%7D%7B%28-2%29%5E%7B-10%7D%7D%20)
Apply the Quotient rule: i.e. ![\frac{x^n}{x^m} = x^{n - m}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bx%5En%7D%7Bx%5Em%7D%20%3D%20x%5E%7Bn%20-%20m%7D%20)
![= (-2)^{-5 - (-10)} = (-2)^5} = -32](https://tex.z-dn.net/?f=%20%3D%20%28-2%29%5E%7B-5%20-%20%28-10%29%7D%20%3D%20%28-2%29%5E5%7D%20%3D%20-32%20)
2. ![2^{-1} * 2^{-4}](https://tex.z-dn.net/?f=%202%5E%7B-1%7D%20%2A%202%5E%7B-4%7D%20)
Apply the product rule: i.e.
.
![= 2^{-1 + (-4)} = 2^{-1 - 4}](https://tex.z-dn.net/?f=%20%3D%202%5E%7B-1%20%2B%20%28-4%29%7D%20%3D%202%5E%7B-1%20-%204%7D%20)
![= 2^{-5}](https://tex.z-dn.net/?f=%20%3D%202%5E%7B-5%7D%20)
Apply the negative exponent rule: i.e. ![x^{-n} = \frac{1}{x^n}](https://tex.z-dn.net/?f=%20x%5E%7B-n%7D%20%3D%20%5Cfrac%7B1%7D%7Bx%5En%7D%20)
![= 2^{-5} = \frac{1}{2^5}](https://tex.z-dn.net/?f=%20%3D%202%5E%7B-5%7D%20%3D%20%5Cfrac%7B1%7D%7B2%5E5%7D%20)
![= \frac{1}{32}](https://tex.z-dn.net/?f=%20%3D%20%5Cfrac%7B1%7D%7B32%7D%20)
3. ![(-\frac{1}{2})^3 * (-\frac{1}{2})^2](https://tex.z-dn.net/?f=%20%28-%5Cfrac%7B1%7D%7B2%7D%29%5E3%20%2A%20%28-%5Cfrac%7B1%7D%7B2%7D%29%5E2%20)
Apply product rule
![= (-\frac{1}{2})^{3 + 2}](https://tex.z-dn.net/?f=%20%3D%20%28-%5Cfrac%7B1%7D%7B2%7D%29%5E%7B3%20%2B%202%7D%20)
![= (-\frac{1}{2})^{5}](https://tex.z-dn.net/?f=%20%3D%20%28-%5Cfrac%7B1%7D%7B2%7D%29%5E%7B5%7D%20)
![= -\frac{1^5}{2^5}](https://tex.z-dn.net/?f=%20%3D%20-%5Cfrac%7B1%5E5%7D%7B2%5E5%7D%20)
![= -\frac{1}{32}](https://tex.z-dn.net/?f=%20%3D%20-%5Cfrac%7B1%7D%7B32%7D%20)
4. ![\frac{2}{2^{-4}}](https://tex.z-dn.net/?f=%20%5Cfrac%7B2%7D%7B2%5E%7B-4%7D%7D%20)
Apply the rules of 1 and quotient rule
![= 2^{1 - (-4)}](https://tex.z-dn.net/?f=%20%3D%202%5E%7B1%20-%20%28-4%29%7D%20)
![= 2^{1 + 4}](https://tex.z-dn.net/?f=%20%3D%202%5E%7B1%20%2B%204%7D%20)
![= 2^{5} = 32](https://tex.z-dn.net/?f=%20%3D%202%5E%7B5%7D%20%3D%2032%20)
Take
![\begin{cases}u=x-y\\v=x+y\end{cases}](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7Du%3Dx-y%5C%5Cv%3Dx%2By%5Cend%7Bcases%7D)
so that
![\begin{cases}\mathbf x(u,v)=\dfrac{u+v}2\\\\\mathbf y(u,v)=\dfrac{-u+v}2\end{cases}](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7D%5Cmathbf%20x%28u%2Cv%29%3D%5Cdfrac%7Bu%2Bv%7D2%5C%5C%5C%5C%5Cmathbf%20y%28u%2Cv%29%3D%5Cdfrac%7B-u%2Bv%7D2%5Cend%7Bcases%7D)
and the Jacobian determinant is
![|\det J|=\left|\begin{vmatrix}\mathbf x_u&\mathbf x_v\\\mathbf y_u&\mathbf y_v\end{vmatrix}\right|=\dfrac12](https://tex.z-dn.net/?f=%7C%5Cdet%20J%7C%3D%5Cleft%7C%5Cbegin%7Bvmatrix%7D%5Cmathbf%20x_u%26%5Cmathbf%20x_v%5C%5C%5Cmathbf%20y_u%26%5Cmathbf%20y_v%5Cend%7Bvmatrix%7D%5Cright%7C%3D%5Cdfrac12)
So the integral is (NOTE: I'm guessing on what the integrand is supposed to be)
![\displaystyle\iint_R7xye^{x^2-y^2}\,\mathrm dA=\frac78\int_{u=0}^{u=10}\int_{v=0}^{v=4}e^{uv}(v^2-u^2)\,\mathrm dv\,\mathrm du](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Ciint_R7xye%5E%7Bx%5E2-y%5E2%7D%5C%2C%5Cmathrm%20dA%3D%5Cfrac78%5Cint_%7Bu%3D0%7D%5E%7Bu%3D10%7D%5Cint_%7Bv%3D0%7D%5E%7Bv%3D4%7De%5E%7Buv%7D%28v%5E2-u%5E2%29%5C%2C%5Cmathrm%20dv%5C%2C%5Cmathrm%20du)