Answer:
Part A: x + 2y ≤ 12.
Part B: y = -1/2x + 6.
Part C: (0, 0).
Step-by-step explanation:
Part A: The total hours of homework have to be 12 hours, and it has to be either 12 hours or less. So, we have ≤ 12.
They take 1 math course with x hours of homework, so in total, that is 1 * x = x hours of math homework.
They take 2 science courses with y hours of homework, so in total, that is 2 * y = 2y hours of science homework.
The inequality would then be x + 2y ≤ 12.
Part B: x + 2y = 12
2y = -x + 12
y = -1/2x + 6
You can use the Math is Fun: Function Grapher and Calculator to find the graph of the line, shown below.
Part C: Since the inequality uses a ≤ symbol, we know that the shading will be underneath the line. An appropriate point below the line includes (0, 0). We will test out whether it works as a point included in the inequality.
x + 2y ≤ 12
0 + 2 * 0 ≤ 12
0 + 0 ≤ 12
0 ≤ 12
Since this is a true statement, (0, 0) holds true for the inequality.
Hope this helps!
Answer:
We have the equation
Then, the augmented matrix of the system is
We exchange rows 1 and 4 and rows 2 and 3 and obtain the matrix:
This matrix is in echelon form. Then, now we apply backward substitution:
1.
2.
3.
4.
Then the system has unique solution that is and this imply that the vectors
are linear independent.
Answer:
<h2>B. The slope is 5 and (2, 4) is on the line.</h2>Step-by-step explanation:
The point-slope form of an equation of a line:
<em>m</em><em> - slope</em>
<em>(x₁, y₁)</em><em> - point</em>
<em />
We have the equation:
Therefore
<em>m = 5</em>
<em>(x₁, y₁) = (2, 4)</em>
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