6; because they are an equal distance apart
Answer: 9
Step-by-step explanation:
If you put all the numbers in order from least to greatest 9 is in the middle.
The answer is the last option because the graph goes no greater than 75 and it also goes no greater than zero but it does hit zero and 75
Answer:
x=4, y=4, λ=-16
Step-by-step explanation:
We have this 3x3 system of linear equations:
λ
λ

So, let's rewrite the system in its augmented matrix form
![\left[\begin{array}{cccc}4&0&1&0\\0&4&1&0\\1&1&0&8\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D4%260%261%260%5C%5C0%264%261%260%5C%5C1%261%260%268%5Cend%7Barray%7D%5Cright%5D)
Let´s apply row reduction process to its associated augmented matrix:
Swap R1 and R3
![\left[\begin{array}{cccc}1&1&0&8\\0&4&1&0\\4&0&1&0\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%261%260%268%5C%5C0%264%261%260%5C%5C4%260%261%260%5Cend%7Barray%7D%5Cright%5D)
R3-4R1
![\left[\begin{array}{cccc}1&1&0&8\\0&4&1&0\\0&-4&1&-32\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%261%260%268%5C%5C0%264%261%260%5C%5C0%26-4%261%26-32%5Cend%7Barray%7D%5Cright%5D)
R3+R2
![\left[\begin{array}{cccc}1&1&0&8\\0&4&1&0\\0&0&2&-32\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%261%260%268%5C%5C0%264%261%260%5C%5C0%260%262%26-32%5Cend%7Barray%7D%5Cright%5D)
Now we have a simplified system:
x+y+0=0
0+4y+λ=0
0+0+2λ=-32
Solving for λ, x, and y
λ=-16
x=4
y=4