Answer:
(-1)(11)(3)(5)
Step-by-step explanation:
First off: -165 separates into the factors (-1) and (165). Next, we divide 165 by 15, obtaining 15(11).
So far, we have (-1)(11)(15).
15 is still factorable. We get:
(-1)(11)(3)(5), which is the desired prime factorization of -165.
Answer:
360 yards in 2 hours
Step-by-step explanation:
6 yards in 2 minutes = 3 yards in 1 minute
2 hours = 120 minutes
3*120
360 yards
You find the eigenvalues of a matrix A by following these steps:
- Compute the matrix
, where I is the identity matrix (1s on the diagonal, 0s elsewhere) - Compute the determinant of A'
- Set the determinant of A' equal to zero and solve for lambda.
So, in this case, we have
![A = \left[\begin{array}{cc}1&-2\\-2&0\end{array}\right] \implies A'=\left[\begin{array}{cc}1&-2\\-2&0\end{array}\right]-\left[\begin{array}{cc}\lambda&0\\0&\lambda\end{array}\right]=\left[\begin{array}{cc}1-\lambda&-2\\-2&-\lambda\end{array}\right]](https://tex.z-dn.net/?f=A%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%26-2%5C%5C-2%260%5Cend%7Barray%7D%5Cright%5D%20%5Cimplies%20A%27%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%26-2%5C%5C-2%260%5Cend%7Barray%7D%5Cright%5D-%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%5Clambda%260%5C%5C0%26%5Clambda%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1-%5Clambda%26-2%5C%5C-2%26-%5Clambda%5Cend%7Barray%7D%5Cright%5D)
The determinant of this matrix is

Finally, we have

So, the two eigenvalues are

Answer:
5) 35 / 100 = X / 74 X = 2590 / 100 = 25.9
or .35 * 74 = 25.9
6) 78 / 95 = X * 100
X = 7800 / 95 = 82.1 %
or X = 78/95 * 100 = 82.1 %
7) 60/100 * X = 28
X = 2800 / 60 = 46.7
Or .6 * X = 28
X = .28 / .6 = 46.7