Answer: β ≠ ±1
Step-by-step explanation: For a system of equations to have an unique solution, its determinant must be different from 0: det |A| ≠ 0. So,
det ![\left[\begin{array}{ccc}1&\beta&1-\beta\\2&2&0\\2-2\beta&4&0\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26%5Cbeta%261-%5Cbeta%5C%5C2%262%260%5C%5C2-2%5Cbeta%264%260%5Cend%7Barray%7D%5Cright%5D)
≠ 0
Determinant of a 3x3 matrix is calculated by:
det ![\left[\begin{array}{ccc}1&\beta&1-\beta\\2&2&0\\2-2\beta&4&0\end{array}\right]\left[\begin{array}{ccc}1&\beta\\2&2\\2-2\beta&4\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26%5Cbeta%261-%5Cbeta%5C%5C2%262%260%5C%5C2-2%5Cbeta%264%260%5Cend%7Barray%7D%5Cright%5D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26%5Cbeta%5C%5C2%262%5C%5C2-2%5Cbeta%264%5Cend%7Barray%7D%5Cright%5D)
![8(1-\beta)-[2(2-2\beta)(1-\beta)]](https://tex.z-dn.net/?f=8%281-%5Cbeta%29-%5B2%282-2%5Cbeta%29%281-%5Cbeta%29%5D)
β ≠ ±1
For the system to have only one solution, β ≠ 1 or β ≠ -1.
Answer:
m = 2
Step-by-step explanation:
To find the slope, simply use this equation:
m = y2 - y1 / x2 - x1
Now we need to insert some points:
m = 10 - 0 / 11 - 6
m = 10/5
m = 2
Therefore, the slope of the line is 2.
Answer:
41,055
Step-by-step explanation:
If there are 805 students in each of 51 schools, the total number of students is ...
(805 students/school) × (51 schools) = 41,055 students
_____
We have to assume that all of the students in the county go to county schools. Apparently, we are to ignore the students that are dropouts or homeschooled, or that go to schools not in the county.
1)
C ≈ 3.14 • 9
C ≈ 28.26
The circumference is 28.3 cm to the nearest tenth of a centimeter
2)
C ≈ 3.14 (2 • 13)
C ≈ 3.14 • 26
C ≈ 81.64
The circumference is 81.6 in to the nearest tenth of a inch
3)
C = 3.14 (13)
C = 40.82
C = 40.8
4)
C = 3.14 (2 • 5)
C = 3.14 (10)
C = 31.4
5)
C = 3.14 (2 • 1.5)
C = 3.14(3)
C = 9.42
C = 9.4
Answer:
a
Step-by-step explanation:
slope= rise/run
y-intercept= where the slope intersects with the y-axis
have a great day! :)
