Answer:
5
Step-by-step explanation:
<u>Definition of term:</u>
A term is a single mathematical expression. It may be a single number (positive or negative), a single variable ( a letter ), several variables multiplied but never added or subtracted.
6w- 3x+9y- 8z+ 12
\/
6w - 3x +9y - 8z + 12
Hope this helps, have a nice day! :D
Answer:
n, they will drive from Fort Worth to San Antonio, a distance of 229 miles, to visit his grandparents. On the way back, Mike reverses his trip and travels from San Antonio to Dallas through Forth Worth. Write one equation to show the distance traveled from Dallas to San Antonio, and a second equation to show the distance traveled from San Antonio to Dallas. What do you notice about the distance traveled each w
Step-by-step explanation:
n, they will drive from Fort Worth to San Antonio, a distance of 229 miles, to visit his grandparents. On the way back, Mike reverses his trip and travels from San Antonio to Dallas through Forth Worth. Write one equation to show the distance traveled from Dallas to San Antonio, and a second equation to show the distance traveled from San Antonio to Dallas. What do you notice about the distance traveled each w
Answer:
![\left(3m+5n\right)\left(9m^2-15mn+25n^2\right)](https://tex.z-dn.net/?f=%5Cleft%283m%2B5n%5Cright%29%5Cleft%289m%5E2-15mn%2B25n%5E2%5Cright%29)
Step-by-step explanation:
![27m^3+125n^3=\left(3m\right)^3+\left(5n\right)^3](https://tex.z-dn.net/?f=27m%5E3%2B125n%5E3%3D%5Cleft%283m%5Cright%29%5E3%2B%5Cleft%285n%5Cright%29%5E3)
Apply sum of cubes formula: ![x^3+y^3=\left(x+y\right)\left(x^2-xy+y^2\right)](https://tex.z-dn.net/?f=x%5E3%2By%5E3%3D%5Cleft%28x%2By%5Cright%29%5Cleft%28x%5E2-xy%2By%5E2%5Cright%29)
![\left(3m\right)^3+\left(5n\right)^3=\left(3m+5n\right)\left(3^2m^2-3m\times 5n+5^2n^2\right)](https://tex.z-dn.net/?f=%5Cleft%283m%5Cright%29%5E3%2B%5Cleft%285n%5Cright%29%5E3%3D%5Cleft%283m%2B5n%5Cright%29%5Cleft%283%5E2m%5E2-3m%5Ctimes%205n%2B5%5E2n%5E2%5Cright%29)
![\left(3m+5n\right)\left(9m^2-15mn+25n^2\right)](https://tex.z-dn.net/?f=%5Cleft%283m%2B5n%5Cright%29%5Cleft%289m%5E2-15mn%2B25n%5E2%5Cright%29)
<h2>
The required solution is x = 6 and y = 11 </h2>
Step-by-step explanation:
Given system of equations are
x+5y = 11 and x-y =5
![X=\left[\begin{array}{c}x\\y\end{array}\right]](https://tex.z-dn.net/?f=X%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%5C%5Cy%5Cend%7Barray%7D%5Cright%5D)
and ![B= \left[\begin{array}{c}11\\5\end{array}\right]](https://tex.z-dn.net/?f=B%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D11%5C%5C5%5Cend%7Barray%7D%5Cright%5D)
∴AX=B
![adj A = \left[\begin{array}{cc}{-1}&{-5}\\{-1}&1\end{array}\right]](https://tex.z-dn.net/?f=adj%20A%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%7B-1%7D%26%7B-5%7D%5C%5C%7B-1%7D%261%5Cend%7Barray%7D%5Cright%5D)
![A= \left|\begin{array}{cc}1&5\\1&-1\end{array}\right|=-6](https://tex.z-dn.net/?f=A%3D%20%5Cleft%7C%5Cbegin%7Barray%7D%7Bcc%7D1%265%5C%5C1%26-1%5Cend%7Barray%7D%5Cright%7C%3D-6)
∴![A^{-1} =\frac{adj A}{|A|}](https://tex.z-dn.net/?f=A%5E%7B-1%7D%20%3D%5Cfrac%7Badj%20A%7D%7B%7CA%7C%7D)
So,![A^{-1} =\frac{ \left[\begin{array}{cc}{-1}&{-5}\\{-1}&1\end{array}\right]}{-6}](https://tex.z-dn.net/?f=A%5E%7B-1%7D%20%3D%5Cfrac%7B%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%7B-1%7D%26%7B-5%7D%5C%5C%7B-1%7D%261%5Cend%7Barray%7D%5Cright%5D%7D%7B-6%7D)
![A^{-1} ={ \left[\begin{array}{c \c} {{\frac{1}{6} }}&{\frac{5}{6}}\ \\ {{\frac{1}{6} }}&{\frac{-1}{6}} \end{array}\right]}](https://tex.z-dn.net/?f=A%5E%7B-1%7D%20%3D%7B%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%20%5Cc%7D%20%20%7B%7B%5Cfrac%7B1%7D%7B6%7D%20%7D%7D%26%7B%5Cfrac%7B5%7D%7B6%7D%7D%5C%20%5C%5C%20%20%7B%7B%5Cfrac%7B1%7D%7B6%7D%20%7D%7D%26%7B%5Cfrac%7B-1%7D%7B6%7D%7D%20%5Cend%7Barray%7D%5Cright%5D%7D)
![X =A^{-1}\times B](https://tex.z-dn.net/?f=X%20%3DA%5E%7B-1%7D%5Ctimes%20B)
⇒![\left[\begin{array}{c}x\\y\end{array}\right] ={ \left[\begin{array}{c \c} {{\frac{1}{6} }}&{\frac{5}{6}}\ \\ {{\frac{1}{6} }}&{\frac{-1}{6}} \end{array}\right]} \times \left[\begin{array}{c}11\\5\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%5C%5Cy%5Cend%7Barray%7D%5Cright%5D%20%3D%7B%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%20%5Cc%7D%20%20%7B%7B%5Cfrac%7B1%7D%7B6%7D%20%7D%7D%26%7B%5Cfrac%7B5%7D%7B6%7D%7D%5C%20%5C%5C%20%20%7B%7B%5Cfrac%7B1%7D%7B6%7D%20%7D%7D%26%7B%5Cfrac%7B-1%7D%7B6%7D%7D%20%5Cend%7Barray%7D%5Cright%5D%7D%20%5Ctimes%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D11%5C%5C5%5Cend%7Barray%7D%5Cright%5D)
⇒![\left[\begin{array}{c}x\\y\end{array}\right] ={ \left[\begin{array}{c} {6}\\ {11} \end{array}\right]}](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%5C%5Cy%5Cend%7Barray%7D%5Cright%5D%20%3D%7B%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D%20%20%7B6%7D%5C%5C%20%20%7B11%7D%20%5Cend%7Barray%7D%5Cright%5D%7D)
∴ x= 6 and y = 11
The required solution is x = 6 and y = 11