1) You must add 4 to each side to complete the square.
2) You must add 16 to each side to complete the square.
3) You must add 27 to each side to complete the square.
Explanation:
1) x²-4x=0
To find the number that we add to both sides, we look at b, the cofficient of x. It is -4. We divide it by 2 and square it; -4/2 = -2; (-2)² = 4. This is the value that we add to both sides.
2) x²-8x=6
-8/2 = -4; (-4)²=16
We add 16 to each side to complete the square.
3) 3x²+18x=24
First we can factor a 3 out of the left side:
3(x²+6x) = 24
Our b value is now 6. 6/2 = 3; 3²=9. The 9 would, however, go in the parentheses, so it would be multiplied by 3, which makes 27; this means we would add 27 to both sides.
Answer:
Step-by-step explanation:
<u>Eigenvalues of a Matrix</u>
Given a matrix A, the eigenvalues of A, called 
are scalars who comply with the relation:
Where I is the identity matrix
![I=\left[\begin{array}{cc}1&0\\0&1\end{array}\right]](https://tex.z-dn.net/?f=I%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%260%5C%5C0%261%5Cend%7Barray%7D%5Cright%5D)
The matrix is given as
![A=\left[\begin{array}{cc}3&5\\8&0\end{array}\right]](https://tex.z-dn.net/?f=A%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3%265%5C%5C8%260%5Cend%7Barray%7D%5Cright%5D)
Set up the equation to solve
![det\left(\left[\begin{array}{cc}3&5\\8&0\end{array}\right]-\left[\begin{array}{cc}\lambda&0\\0&\lambda \end{array}\right]\right)=0](https://tex.z-dn.net/?f=det%5Cleft%28%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3%265%5C%5C8%260%5Cend%7Barray%7D%5Cright%5D-%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%5Clambda%260%5C%5C0%26%5Clambda%20%5Cend%7Barray%7D%5Cright%5D%5Cright%29%3D0)
Expanding the determinant
![det\left(\left[\begin{array}{cc}3-\lambda&5\\8&-\lambda\end{array}\right]\right)=0](https://tex.z-dn.net/?f=det%5Cleft%28%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3-%5Clambda%265%5C%5C8%26-%5Clambda%5Cend%7Barray%7D%5Cright%5D%5Cright%29%3D0)
Operating Rearranging
Factoring
Solving, we have the eigenvalues
Answer:
The large container holds 6 cups of water
Step-by-step explanation:
If two small containers and one large container equal 10 cups and one large minus one small equals 4 cups then that means that each small container has to equal 2 cups of water.
Answer:
look it up
Step-by-step explanation:
go on your phone
click google
type in your question
don't be trash player
14) You would put 14 over unknown is poportional to 40 over 100. Then multiply 14 by 100 then divide it by 40 to receive 35.
