Answer:
Domain -∞ < x < +∞
Range f(x) ≤ - 4
Step-by-step explanation:
The given quadratic function is f(x) = - 4 (x + 1)² - 4
Now, we have to find the domain and range of the quadratic function.
Now, it is clear from the given function that f(x) will have real value for all real value of x.
Therefore, the domain of the function is -∞ < x < +∞ (Answer)
Now, (x + 1)² is always ≥ 0
i.e. (x + 1)² ≥ 0
⇒ - 4 (x + 1)² ≤ 0 {Since the inequality sign changes for multiplying both sides of the equation by a negative term}
⇒ - 4 (x + 1)² - 4 ≤ - 4
⇒ f(x) ≤ - 4
Therefore, this is the required range of the function f(x). (Answer)
Answer:
Option A is correct.
Step-by-step explanation:
The following matrix represent the augmented matrix
In augmented matrix the left side represent the co-efficient of the variables and right side represent the value of variables.
Since the matrix has been solved and reduced so, the solution of variables x, y and z is written on right side of augmented matrix
The given matrix is:
![\left[\begin{array}{cccc}1&0&5&-2\\0&0&3&0\\0&0&0&-1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%260%265%26-2%5C%5C0%260%263%260%5C%5C0%260%260%26-1%5Cend%7Barray%7D%5Cright%5D)
Since the last row is all zero and we have a non zero entry for the solution, the matrix is inconsistent.
As the variables have zero values, there cannot be any solution
So, there is no solution.
So, Option A is correct.
Answer:
-20
Step-by-step explanation:
answer 6cm , 3cm , 6cm, this the answer
Answer:
x = 5
Step-by-step explanation:
Just use the Pythagorean Triangle:
13^2 - 12^2 = x^2
x^2 = 25
x = 5
