Answer:
29 years
Step-by-step explanation:
In 29 years the grandson will be 40 and the grandfather will be 80. 80 is twice as much as 40.
Answer:
<u>(x+9)^2</u> +<u> (y+6)^2</u>
9 4 =1
Step-by-step explanation:
I believe this is correct, if not feel free to let me know and I will fix it. I'm sorry in advance if it is incorrect.
You put all x on left side and numercial on the right side
13x-12x = 4+4
x = 8
Answer:
The solution of the system of equations is, (1,-1,2)
Step-by-step explanation:
Given system equation;
x + 5y - 3z = -10
-5x + 6y – 5z = -21
-x + 8y - 8z = -25
Matrix form is written as;
![\left[\begin{array}{ccc}1&5&-3\\-5&6&-5\\-1&8&-8\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right] = \left[\begin{array}{ccc}-10\\-21\\-25\end{array}\right] \\\\\\det. = 1\left[\begin{array}{cc}\\6&-5\\8&-8\end{array}\right] -5\left[\begin{array}{cc}\\-5&-5\\-1&-8\end{array}\right] -3\left[\begin{array}{cc}\\-5&6\\-1&8\end{array}\right] \\\\\\det. = 1(-8) -5(35)-3(-34)= -8 - 175+ 102 = -81](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%265%26-3%5C%5C-5%266%26-5%5C%5C-1%268%26-8%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-10%5C%5C-21%5C%5C-25%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5C%5C%5Cdet.%20%3D%201%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%5C%5C6%26-5%5C%5C8%26-8%5Cend%7Barray%7D%5Cright%5D%20-5%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%5C%5C-5%26-5%5C%5C-1%26-8%5Cend%7Barray%7D%5Cright%5D%20-3%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%5C%5C-5%266%5C%5C-1%268%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5C%5C%5Cdet.%20%3D%201%28-8%29%20-5%2835%29-3%28-34%29%3D%20-8%20-%20175%2B%20102%20%3D%20-81)
Cofactor;
![First \ row \left[\begin{array}{cc}+\\ 6&-5\\\ 8&-8\end{array}\right \left\begin{array}{cc}-\\ -5&-5\\-1&-8\end{array}\right \left\begin{array}{cc}+\\-5&6\\-1&8\end{array}\right] = [-8 \ \ -35 \ \ -34]\\\\\\\ Second \ row \left[\begin{array}{cc}-\\ 5&-3\\\ 8&-8\end{array}\right \left\begin{array}{cc}+\\ 1&-3\\-1&-8\end{array}\right \left\begin{array}{cc}-\\1&5\\-1&8\end{array}\right] = [16\ \ -11 \ \ -13]\\\\\\](https://tex.z-dn.net/?f=First%20%5C%20row%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%2B%5C%5C%206%26-5%5C%5C%5C%208%26-8%5Cend%7Barray%7D%5Cright%20%20%5Cleft%5Cbegin%7Barray%7D%7Bcc%7D-%5C%5C%20-5%26-5%5C%5C-1%26-8%5Cend%7Barray%7D%5Cright%20%5Cleft%5Cbegin%7Barray%7D%7Bcc%7D%2B%5C%5C-5%266%5C%5C-1%268%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5B-8%20%20%5C%20%5C%20-35%20%5C%20%5C%20-34%5D%5C%5C%5C%5C%5C%5C%5C%20Second%20%5C%20row%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-%5C%5C%205%26-3%5C%5C%5C%208%26-8%5Cend%7Barray%7D%5Cright%20%20%5Cleft%5Cbegin%7Barray%7D%7Bcc%7D%2B%5C%5C%201%26-3%5C%5C-1%26-8%5Cend%7Barray%7D%5Cright%20%5Cleft%5Cbegin%7Barray%7D%7Bcc%7D-%5C%5C1%265%5C%5C-1%268%5Cend%7Barray%7D%5Cright%5D%20%20%3D%20%5B16%5C%20%5C%20-11%20%5C%20%5C%20-13%5D%5C%5C%5C%5C%5C%5C)
![Third \ row \left[\begin{array}{cc}+\\ 5&-3\\\ 6&-5\end{array}\right \left\begin{array}{cc}-\\ 1&-3\\-5&-5\end{array}\right \left\begin{array}{cc}+\\1&5\\-5&6\end{array}\right]= [-7 \ \ 20\ \ 31]](https://tex.z-dn.net/?f=Third%20%5C%20row%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%2B%5C%5C%205%26-3%5C%5C%5C%206%26-5%5Cend%7Barray%7D%5Cright%20%20%5Cleft%5Cbegin%7Barray%7D%7Bcc%7D-%5C%5C%201%26-3%5C%5C-5%26-5%5Cend%7Barray%7D%5Cright%20%5Cleft%5Cbegin%7Barray%7D%7Bcc%7D%2B%5C%5C1%265%5C%5C-5%266%5Cend%7Barray%7D%5Cright%5D%3D%20%5B-7%20%5C%20%20%5C%2020%5C%20%5C%2031%5D)
![\left[\begin{array}{ccc}-8&-35&-34\\16&-11&-13\\-7&20&31\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-8%26-35%26-34%5C%5C16%26-11%26-13%5C%5C-7%2620%2631%5Cend%7Barray%7D%5Cright%5D)
![inverse \ matrix =-\frac{1}{81} \left[\begin{array}{ccc}-8&16&-7\\-35&-11&20\\-34&-13&31\end{array}\right] \\\\\\](https://tex.z-dn.net/?f=inverse%20%5C%20matrix%20%3D-%5Cfrac%7B1%7D%7B81%7D%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-8%2616%26-7%5C%5C-35%26-11%2620%5C%5C-34%26-13%2631%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5C%5C%5C)
Solution of the matrix:
![\left[\begin{array}{c}x\\y\\z\end{array}\right] = -\frac{1}{81} \left[\begin{array}{ccc}-8&16&-7\\-35&-11&20\\-34&-13&31\end{array}\right] X \left[\begin{array}{c}-10\\-21\\-25\end{array}\right] = \left[\begin{array}{c}\frac{-8*-10 }{-81 } +\frac{16*-21 }{-81 } + \frac{-7*-25 }{-81 }\\\\\frac{-35*-10 }{-81 } +\frac{-11*-21 }{-81 }+ \frac{20*-25 }{-81 }\\\\\frac{-34*-10 }{-81 }+ \frac{-13*-21 }{-81 }+ \frac{31*-25 }{-81 }\end{array}\right] \\\\\](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D%20%3D%20-%5Cfrac%7B1%7D%7B81%7D%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-8%2616%26-7%5C%5C-35%26-11%2620%5C%5C-34%26-13%2631%5Cend%7Barray%7D%5Cright%5D%20%20X%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D-10%5C%5C-21%5C%5C-25%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D%5Cfrac%7B-8%2A-10%20%7D%7B-81%20%7D%20%2B%5Cfrac%7B16%2A-21%20%7D%7B-81%20%7D%20%2B%20%5Cfrac%7B-7%2A-25%20%7D%7B-81%20%7D%5C%5C%5C%5C%5Cfrac%7B-35%2A-10%20%7D%7B-81%20%7D%20%2B%5Cfrac%7B-11%2A-21%20%7D%7B-81%20%7D%2B%20%5Cfrac%7B20%2A-25%20%7D%7B-81%20%7D%5C%5C%5C%5C%5Cfrac%7B-34%2A-10%20%7D%7B-81%20%7D%2B%20%5Cfrac%7B-13%2A-21%20%7D%7B-81%20%7D%2B%20%5Cfrac%7B31%2A-25%20%7D%7B-81%20%7D%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5C%5C)
![\left[\begin{array}{c}x\\y\\z\end{array}\right] = \left[\begin{array}{c}\frac{-81}{-81} \\\\\frac{81}{-81} \\\\\frac{-162}{-81} \end{array}\right] = \left[\begin{array}{c}1\\-1\\2\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D%5Cfrac%7B-81%7D%7B-81%7D%20%5C%5C%5C%5C%5Cfrac%7B81%7D%7B-81%7D%20%5C%5C%5C%5C%5Cfrac%7B-162%7D%7B-81%7D%20%5Cend%7Barray%7D%5Cright%5D%20%3D%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D1%5C%5C-1%5C%5C2%5Cend%7Barray%7D%5Cright%5D)
Therefore, the correct option is (1,-1,2)
Answer:
4 students are working on fractions
Step-by-step explanation:
