Answer: A
Step-by-step explanation: Alright so- it says that Justin is both in half of his friends photos (which would be 15 photos) and half of his family's photos (6 photos). The total amount of photos period is 50 photos and 15 is greater than 6. Therefore I would say A.
Answer:
Pretty Simple!
Now that you know about ratios and all that, this is pretty tame compared to the last problem.
Now, the problem is talking 2D(2 Dimensions)
The ratio is not going to work because it has only one parameter.
Thus, we need to square it!

Thus, we have your correct ratio.
Now, we only need to do the same thing for the triangle problem. Meaning that, we need to compare the ratios, with x as the thing we are looking for.

See? X is practically handed to us.
Hope this helps!
The different combinations is 9, since we can't rearrange the two novels.
I did 3*3 which equals 9.
Answer: The required characteristic polynomial of the given matrix A is 
Step-by-step explanation: We are given to find the characteristic polynomial of the following 3 × 3 matrix A with unknown variable x :
![A=\left[\begin{array}{ccc}0&0&1\\4&-3&4\\-2&0&-3\end{array}\right].](https://tex.z-dn.net/?f=A%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%260%261%5C%5C4%26-3%264%5C%5C-2%260%26-3%5Cend%7Barray%7D%5Cright%5D.)
We know that
for any square matrix M, the characteristic polynomial is given by
where I is an identity matrix of same order as M.
Therefore, the characteristic polynomial of matrix A is
![|A-xI|=0\\\\\\\Rightarrow \left|\left[\begin{array}{ccc}0&0&1\\4&-3&4\\-2&0&-3\end{array}\right]-x\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right]\right|=0\\\\\\\Rightarrow \left|\left[\begin{array}{ccc}-x&0&1\\4&-3-x&4\\-2&0&-3-x\end{array}\right] \right|=0\\\\\\\Rightarrow -x(3+x)^2+1(0-6-2x)=0\\\\\Rightarrow (x+3)(-3x-x^2-2)=0\\\\\Rightarrow (x+3)(x^2+3x+2)=0\\\\\Rightarrow x^3+6x+11x+6=0.](https://tex.z-dn.net/?f=%7CA-xI%7C%3D0%5C%5C%5C%5C%5C%5C%5CRightarrow%20%5Cleft%7C%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%260%261%5C%5C4%26-3%264%5C%5C-2%260%26-3%5Cend%7Barray%7D%5Cright%5D-x%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%260%5C%5C0%261%260%5C%5C0%260%261%5Cend%7Barray%7D%5Cright%5D%5Cright%7C%3D0%5C%5C%5C%5C%5C%5C%5CRightarrow%20%5Cleft%7C%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-x%260%261%5C%5C4%26-3-x%264%5C%5C-2%260%26-3-x%5Cend%7Barray%7D%5Cright%5D%20%5Cright%7C%3D0%5C%5C%5C%5C%5C%5C%5CRightarrow%20-x%283%2Bx%29%5E2%2B1%280-6-2x%29%3D0%5C%5C%5C%5C%5CRightarrow%20%20%28x%2B3%29%28-3x-x%5E2-2%29%3D0%5C%5C%5C%5C%5CRightarrow%20%28x%2B3%29%28x%5E2%2B3x%2B2%29%3D0%5C%5C%5C%5C%5CRightarrow%20x%5E3%2B6x%2B11x%2B6%3D0.)
Thus, the required characteristic polynomial of the given matrix A is 