So here are the rules of horizontal asymptotes:
- Degree of Numerator > Degree of Denominator: No horizontal asymptote
- Degree of Numerator = Degree of Denominator:
![y=\frac{\textsf{leading coefficient of numerator}}{\textsf{leading coefficient of denominator}}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B%5Ctextsf%7Bleading%20coefficient%20of%20numerator%7D%7D%7B%5Ctextsf%7Bleading%20coefficient%20of%20denominator%7D%7D)
- Degree of Numerator < Degree of Denominator: y = 0
Looking at the rational function, since the degree of the numerator is 2 and the degree of the denominator is 1 (and 2 > 1), this means that <u>this function has no horizontal asymptote.</u>
I believe that there are four different outcomes.
In this question, we are given a matrix, and we have to perform the given operation.
The matrix is:
![\left[\begin{array}{ccc}6&-1&|5\\1&-5&|0\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D6%26-1%26%7C5%5C%5C1%26-5%26%7C0%5Cend%7Barray%7D%5Cright%5D)
The following operation is given:
![R_1 \rightarrow -6R_2 + R_1](https://tex.z-dn.net/?f=R_1%20%5Crightarrow%20-6R_2%20%2B%20R_1)
In which
is the element at the first line and
is the element at the second line.
Updating the first line:
![R_{1,1} = -6*1 + 6 = 0](https://tex.z-dn.net/?f=R_%7B1%2C1%7D%20%3D%20-6%2A1%20%2B%206%20%3D%200)
![R_{1,2} = -6*-5 - 1 = 30 - 1 = 29](https://tex.z-dn.net/?f=R_%7B1%2C2%7D%20%3D%20-6%2A-5%20-%201%20%3D%2030%20-%201%20%3D%2029)
![R_{1,3} = -6*0 + 5 = 5](https://tex.z-dn.net/?f=R_%7B1%2C3%7D%20%3D%20-6%2A0%20%2B%205%20%3D%205)
Thus, the filled matrix will be given by:
![\left[\begin{array}{ccc}0&29&|5\\1&-5&|0\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%2629%26%7C5%5C%5C1%26-5%26%7C0%5Cend%7Barray%7D%5Cright%5D)
For another example where row operations are applied on a matrix, you can check brainly.com/question/18546657
Answer: 75
Step-by-step explanation:
To find the value of 6c-15, we first want to finc the value of c. Once we find c, we can plug it in and solve.
-5c+6=-69 [subtract both sides by 6]
-5c=-75 [divide both sides by -5]
c=15
Now that we have the value of c, we can plug it in and solve.
6(15)-15 [multiply]
90-15 [subtract]
75
The value is 75.
The answer is 2x +y 3 and i hope i helped :) :)