Answer:
30
Step-by-step explanation:
To find the determinant of a parallelogram given points (a, b), (c, d), and (e, f), we can use
![\left[\begin{array}{ccc}a&b&1\\c&d&1\\e&f&1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Da%26b%261%5C%5Cc%26d%261%5C%5Ce%26f%261%5Cend%7Barray%7D%5Cright%5D)
and calculate the determinant of that. Three points on the parallelogram are (-1,1), (-1, -5), and (4, 5). Plugging these into the matrix, we get
![\left[\begin{array}{ccc}-1&1&1\\-1&-5&1\\4&5&1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-1%261%261%5C%5C-1%26-5%261%5C%5C4%265%261%5Cend%7Barray%7D%5Cright%5D)
. The determinant is equal to
![-1 *det \left[\begin{array}{ccc}-5&1\\5&1\end{array}\right] \\- 1 * det \left[\begin{array}{ccc}-1&1\\4&1\end{array}\right] \\\\+ 1 * det \left[\begin{array}{ccc}-1&-5\\4&5\end{array}\right] \\= -1 * (-5*1 - (1*5))- 1 * (-1 * 1 - (4*1)) + 1 * (-1 * 5 - (-5*4)) \\= -1 *(-5-5) -1 * (-1 - 4) + 1 * (-5 - (-20))\\= -1 * (-10) -1 * (-5) +1 * (15)\\= 10 + 5 + 15\\=30](https://tex.z-dn.net/?f=-1%20%2Adet%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-5%261%5C%5C5%261%5Cend%7Barray%7D%5Cright%5D%20%5C%5C-%201%20%2A%20det%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-1%261%5C%5C4%261%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5C%2B%201%20%2A%20det%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-1%26-5%5C%5C4%265%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%3D%20-1%20%2A%20%28-5%2A1%20-%20%281%2A5%29%29-%201%20%2A%20%28-1%20%2A%201%20-%20%284%2A1%29%29%20%2B%201%20%2A%20%28-1%20%2A%205%20-%20%28-5%2A4%29%29%20%5C%5C%3D%20-1%20%2A%28-5-5%29%20-1%20%2A%20%28-1%20-%204%29%20%2B%201%20%2A%20%28-5%20-%20%28-20%29%29%5C%5C%3D%20-1%20%2A%20%28-10%29%20-1%20%2A%20%28-5%29%20%2B1%20%2A%20%2815%29%5C%5C%3D%2010%20%2B%205%20%2B%2015%5C%5C%3D30)
Answer:
vruvuvuutgnb4uuy
Step-by-step explanation:
tu4gnutun4g45tgun
The balance point, or average value of those numbers, would be 4.75 or 4 and 3/4
Answer: 4
Step-by-step explanation: To have an equation with no solution you have to get something like 0=1 meaning you have to remove all the variables. In this equation you would distribute to get xy+2y+2x=2x+12+4x where y is the missing number. then combining like terms you get xy+2x+2y=6x+12. Subtracting 2x from both sides you get xy+2y=4x+12. Now to get the variables gone y has to be 4 so that the variables to cancel out. By plugging in 4 you can see this works; 4x+8=4x+12 and by subtracting 4x from both sides you get 8=12 which is not true meaning there is no solution.
