9514 1404 393
Answer:
(a, b) = (-2, -1)
Step-by-step explanation:
The transpose of the given matrix is ...
![A^T=\left[\begin{array}{ccc}1&2&a\\2&1&2\\2&-2&b\end{array}\right]](https://tex.z-dn.net/?f=A%5ET%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%262%26a%5C%5C2%261%262%5C%5C2%26-2%26b%5Cend%7Barray%7D%5Cright%5D)
Then the [3,1] term of the product is ...
![(A\cdot A^T)_{31}=\left[\begin{array}{ccc}a&2&b\end{array}\right]\cdot\left[\begin{array}{ccc}1&2&2\end{array}\right]=a+2b+4](https://tex.z-dn.net/?f=%28A%5Ccdot%20A%5ET%29_%7B31%7D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Da%262%26b%5Cend%7Barray%7D%5Cright%5D%5Ccdot%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%262%262%5Cend%7Barray%7D%5Cright%5D%3Da%2B2b%2B4)
and the [3,2] term is ...
![(A\cdot A^T)_{32}=\left[\begin{array}{ccc}a&2&b\end{array}\right]\cdot\left[\begin{array}{ccc}2&1&-2\end{array}\right]=2a-2b+2](https://tex.z-dn.net/?f=%28A%5Ccdot%20A%5ET%29_%7B32%7D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Da%262%26b%5Cend%7Barray%7D%5Cright%5D%5Ccdot%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%261%26-2%5Cend%7Barray%7D%5Cright%5D%3D2a-2b%2B2)
Both of these terms in the product matrix are 0. We can solve the system of equations by adding these two terms:
(a +2b +4) +(2a -2b +2) = (0) +(0)
3a +6 = 0
a = -2
Substituting for 'a' in term [3,1] gives ...
-2 +2b +4 = 0
b = -1
The ordered pair (a, b) is (-2, -1).
Answer:
<u>∠J = 31.06°</u>
Step-by-step explanation:
Taking the inverse sin function :
- sin ∠J = 1.6/3.1
- J = sin⁻¹ (0.516)
- <u>∠J = 31.06°</u>
So when you change the mixed numbers into improper fractions, they become 85/4 and 74/4. Your new problem is 85/4-74/4. Basically 85-74. That equals 9. So the improper fraction answer is 9/4. We now make that back into a mixed number, creating 2 1/4, or A.
2n = 3n - 5 (get all of n on one side by subtracting)
-1n = -5 (when you get here you have to divide by -1 to make n positive)
n = 5
Answer: 21%
Step-by-step explanation:
Percent by definition is based on "out of 100." If 21 out of 100 has high cholesterol, then the percentage is 21%
