Answer:
(x +5)^2 = -2
Step-by-step explanation:
We can subtract the constant to get ...
x^2 +10x = -27
Then add the square of half the x-coefficient:
x^2 +10x +5^2 = -27 +5^2
(x +5)^2 = -2 . . . . . . write as a square
Answer:
A² - 6A + 11 I = ![\left[\begin{array}{ccc}0&0\\0&0\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%260%5C%5C0%260%5Cend%7Barray%7D%5Cright%5D)
Step-by-step explanation:
Given the matrix
![A=\left[\begin{array}{ccc}2&3\\-1&4\end{array}\right]](https://tex.z-dn.net/?f=A%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%263%5C%5C-1%264%5Cend%7Barray%7D%5Cright%5D)
Calculate A² - 6A + 11 I
![A^2 = A*A= \left[\begin{array}{ccc}2&3\\-1&4\end{array}\right] *\left[\begin{array}{ccc}2&3\\-1&4\end{array}\right] = \left[\begin{array}{ccc}2*2-3*1&2*3+3*4\\-1*2-4*1&-1*3+4*4\end{array}\right] =\left[\begin{array}{ccc}1&18\\-6&13\end{array}\right]](https://tex.z-dn.net/?f=A%5E2%20%3D%20A%2AA%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%263%5C%5C-1%264%5Cend%7Barray%7D%5Cright%5D%20%2A%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%263%5C%5C-1%264%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%2A2-3%2A1%262%2A3%2B3%2A4%5C%5C-1%2A2-4%2A1%26-1%2A3%2B4%2A4%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%2618%5C%5C-6%2613%5Cend%7Barray%7D%5Cright%5D)
![6A=6*\left[\begin{array}{ccc}2&3\\-1&4\end{array}\right] =\left[\begin{array}{ccc}12&18\\-6&24\end{array}\right]](https://tex.z-dn.net/?f=6A%3D6%2A%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%263%5C%5C-1%264%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D12%2618%5C%5C-6%2624%5Cend%7Barray%7D%5Cright%5D)
![11 I = 11 * \left[\begin{array}{ccc}1&0\\0&1\end{array}\right] =\left[\begin{array}{ccc}11&0\\0&11\end{array}\right]](https://tex.z-dn.net/?f=11%20I%20%3D%2011%20%2A%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%5C%5C0%261%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D11%260%5C%5C0%2611%5Cend%7Barray%7D%5Cright%5D)
∴ A² - 6A + 11 I = ![\left[\begin{array}{ccc}1&18\\-6&13\end{array}\right] -\left[\begin{array}{ccc}12&18\\-6&24\end{array}\right] +\left[\begin{array}{ccc}11&0\\0&11\end{array}\right] =\left[\begin{array}{ccc}0&0\\0&0\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%2618%5C%5C-6%2613%5Cend%7Barray%7D%5Cright%5D%20-%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D12%2618%5C%5C-6%2624%5Cend%7Barray%7D%5Cright%5D%20%2B%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D11%260%5C%5C0%2611%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%260%5C%5C0%260%5Cend%7Barray%7D%5Cright%5D)
Answer: 3/8
There are only three numbers in there that 2 and 3 can go into evenly.
The probability that you will randomly select one of those numbers is 3/8.
-Brainly Answerer
So approximately 14.5% of the scores are higher than 600. This means in a sample of 7500, one could expect to see
scores above 600.
