Answer:
89
Step-by-step explanation:
Plug 9 into the equation;
A number was written on the board. One student increased the number by 23, but another student decreased the number by 1. The fi
1 answer:
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Answer:
To see the steps to the diagonal form see the step-by-step explanation. The solution to the system is ,
,
and
Step-by-step explanation:
Gauss elimination method consists in reducing the matrix to a upper triangular one by using three different types of row operations (this is why the method is also called row reduction method). The three elementary row operations are:
- Swapping two rows
- Multiplying a row by a nonzero number
- Adding a multiple of one row to another row
To solve the system using the Gauss elimination method we need to write the augmented matrix of the system. For the given system, this matrix is:
For this matrix we need to perform the following row operations:
(multiply 1 row by 1 and subtract it from 2 row)
(multiply 1 row by 1 and add it to 3 row)
(multiply 1 row by 1 and subtract it from 4 row)
(interchange the 2 and 3 rows)
(divide the 2 row by 2)
(multiply 2 row by 1 and subtract it from 1 row)
(multiply 2 row by 1 and subtract it from 4 row)
(multiply the 3 row by -1)
(multiply 3 row by 1 and subtract it from 2 row)
(multiply 3 row by 3 and add it to 4 row)
(divide the 4 row by 4.5)
After this step, the system has an upper triangular form
The triangular matrix looks like:
If you later perform the following operations you can find the solution to the system.
(multiply 4 row by 0.5 and add it to 1 row)
(multiply 4 row by 0.5 and add it to 2 row)
(multiply 4 row by 2 and subtract it from 3 row)
After this operations, the matrix should look like:
Thus, the solution is:
,
,
and
To best emphasize the number of defects. Manager should use graph 3 (refer the image shown):
If we talk about graph 1, it can also be used but usually we put the time line on the horizontal axis, for the convenience and the quantity to be measured on the y-axis. In the graph 1, the time is placed on the vertical axis (x-axis) so it would not be a good pick for the manager.
Same is the case with graph 2 again we have time on the vertical axis. So it is not a good idea to with graph 2.
Graph 3 could be the best to emphasize the number of defects because first of all time is placed on the horizontal axis and the quantity to be shown is on the vertical axis. Secondly, the range of the vertical axis is less so it is easy to observe the data set on the graph quite distinctively. Therefore, graph 3 is the best pick.
Graph 4 is placed correctly in terms of vertical and horizontal axes but the range of vertical axis is quite high due to which the dispersion or the display of the data is quite compressed and it gets hard to visualize.
