Find value of determinant.
The determinant is a term that is inside a square root and part of the quadratic formula used for solving quadratic equations.
Let determinant be 'd'.
If d >0, Then there are 2 real solutions
If d = 0, Then there is only 1 real solutions
If d < 0, Then there are 0 real solutions but 2 imaginary solutions
d = b^2 - 4ac
For this problem, the coefficients are:
a = 1, b = -3, c = 8
d = (-3)^2 - 4(1)(8)
d = 9 -32 = -23
d is less than 0, therefore there are 0 real solutions and 2 imaginary solutions.
This is true because you cannot take square root of a negative number.
There would need to be 25 adult chaperones.
The ratio would be 3 adults to every 15 kids. 3:15
To find how many adults are needed for 125 kids you would simply divide.
125/5=25
Hope this helps! :)
You dont have anything that we can answer to.
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.
