Answer:
Graph on the top right.
Step-by-step explanation:
A function is a relation where one domain value is assigned to exactly one range value.
In a table, there would be no values repeating in the x-column.
The graph on the top right does not repeat any x values. Therefore, it is a function.
Why the other options are not functions:
- The top left graph has 4 for all it's domain values.
- The bottom left graph has '-2' repeating for the domain.
- The graph on the bottom right repeats '0' as the domain.
Hope this helps.
3x - 2 ≥ x - 6
<u>- x - x </u>
2x - 2 ≥ -6
<u> + 2 + 2</u>
<u>2x</u> ≥ <u>-4</u>
2 2
x ≥ -2
Answer:
x = 48
Step-by-step explanation:
3x + 9 = 153
subtract 9 from both sides -9 -9
3x = 144
divide both sides by 3 3x/3 = 144/3
2x + (x + 9) = 153
2(48) + (48 + 9) = 153
96 + 57 = 153
153 = 153
Answer:
x = -5; y = 4, z = 1
Step-by-step explanation:
Given the row echelon form as:
![\left[\begin{array}{cccc}1&0&\ \ 4|&-1\\0&1&-1|&3\\0&0&\ \ 1|&1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%260%26%5C%20%5C%204%7C%26-1%5C%5C0%261%26-1%7C%263%5C%5C0%260%26%5C%20%5C%201%7C%261%5Cend%7Barray%7D%5Cright%5D)
This matrix can be represented as:
![\left[\begin{array}{ccc}1&0&4\\0&1&-1\\0&0&1\end{array}\right]\left[\begin{array}{c}x\\y\\z\end{array}\right] =\left[\begin{array}{c}-1\\3\\1\end{array}\right] \\\\Performing\ matrix\ multiplication\ gives:\\\\\left[\begin{array}{c}x+4z\\y-z\\z\end{array}\right] =\left[\begin{array}{c}-1\\3\\1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%264%5C%5C0%261%26-1%5C%5C0%260%261%5Cend%7Barray%7D%5Cright%5D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D-1%5C%5C3%5C%5C1%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5CPerforming%5C%20matrix%5C%20multiplication%5C%20gives%3A%5C%5C%5C%5C%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%2B4z%5C%5Cy-z%5C%5Cz%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D-1%5C%5C3%5C%5C1%5Cend%7Barray%7D%5Cright%5D)
Therefore:
z = 1
y - z = 3;
y = 3 + z = 3 + 1 = 4.
Hence, y = 4
x + 4z = - 1;
x = -1 - 4z = -1 - 4(1) = -5
x = -5
