Answer:
The correct option is (A).
Step-by-step explanation:
If the reduced row echelon form of the coefficient matrix of a linear system of equations in four different variables has a pivot, i.e. 1, in each column, then the reduced row echelon form of the coefficient matrix is say A is an identity matrix, here I₄, since there are 4 variables.
![\left[\begin{array}{cccc}1&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&0&1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%260%260%260%5C%5C0%261%260%260%5C%5C0%260%261%260%5C%5C0%260%260%261%5Cend%7Barray%7D%5Cright%5D)
Then the corresponding augmented matrix [ A|B] , where the matrix is the representation of the linear system is AX = B, must be:
![\left[\begin{array}{ccccc}1&0&0&0&a\\0&1&0&0&b\\0&0&1&0&c\\0&0&0&1&d\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccccc%7D1%260%260%260%26a%5C%5C0%261%260%260%26b%5C%5C0%260%261%260%26c%5C%5C0%260%260%261%26d%5Cend%7Barray%7D%5Cright%5D)
Now the given linear system is consistent as the right most column of the augmented matrix is a linear combination of the columns of A as the reduced row echelon form of A has a pivot in each column.
Thus, the correct option is (A).
Answer:
C.
Step-by-step explanation:
Transformations within the quadratic is given by the form:
![y=a(x-h)^2+k](https://tex.z-dn.net/?f=y%3Da%28x-h%29%5E2%2Bk)
Where a is the vertical stretch, h is the horizontal translations, and k is the vertical translations.
We have:
![y=x^2+14](https://tex.z-dn.net/?f=y%3Dx%5E2%2B14)
If we translate this 5 units to the right, we are letting h=5. This yields:
![y=(x-5)^2+14](https://tex.z-dn.net/?f=y%3D%28x-5%29%5E2%2B14)
If we shift the function down 6 units, we are subtracting 6 from the function. This will yield:
![y=(x-5)^2+14-6](https://tex.z-dn.net/?f=y%3D%28x-5%29%5E2%2B14-6)
Subtract:
![y=(x-5)^2+8](https://tex.z-dn.net/?f=y%3D%28x-5%29%5E2%2B8)
Therefore, our answer is C.
Answer:
A
Step-by-step explanation:
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Answer:
The answer is B.
5/6 approximately 0.83 = 83%
71%
0.6 = 60%
56%
Hope this helps! Have a good night!