Someone please help!! I have to finish this and Im dum.b lol
1 answer:
Answer:
1) False
2) True
3) True
4) False
Step-by-step explanation:
For the first statement, we can look at a graph with the line of y = 3.69x plotted. If we check the points (7.38, 2) and (11.07,3), they do not intersect with the line. So, the first statement is false.
For the second statement, we can check the equation for the line to find the slope. The equation, y = 3.69x, is in slope-intercept form, or . In this form,
is the slope of the line.
is the y-intercept. In this line, there is no y-intercept specified, so we can take this to mean the y-intercept is 0. The slope, we can see, is 3.69. The slope, multiplied by x, shows us any point of the line. The second statement, then, is true.
The next statement can be verified by finding just how much 16 gallons will cost. Like we've seen before, the slope can be multiplied by x, the number of gallons, to see where that point will be plotted. So, we can multiply the slope by 16.
3.69 · 16 = 59.04
The (x) value, we already know, is 16. The (y) value, we've found, is 59.04. So 16 gallons will be plotted at (16, 59.04). The third statement is true.
The last statement says that if the price increases by $0.05, the slope will be 3.64. We can tell this is false by adding 0.05 to the original slope, 3.69.
3.69 + 0.05 = 3.74
3.74 ≠ 3.64, so the last statement is false.
I hope this was helpful to you ^^
Good luck
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Answer:
See the proof below.
Step-by-step explanation:
What we need to proof is this: "Assuming X a vector space over a scalar field C. Let X= {x1,x2,....,xn} a set of vectors in X, where . If the set X is linearly dependent if and only if at least one of the vectors in X can be written as a linear combination of the other vectors"
Proof
Since we have a if and only if w need to proof the statement on the two possible ways.
If X is linearly dependent, then a vector is a linear combination
We suppose the set is linearly dependent, so then by definition we have scalars
in C such that:
And not all the scalars are equal to 0.
Since at least one constant is non zero we can assume for example that , and we have this:
We can divide by c1 since we assume that and we have this:
And as we can see the vector can be written a a linear combination of the remaining vectors
. We select v1 but we can select any vector and we get the same result.
If a vector is a linear combination, then X is linearly dependent
We assume on this case that X is a linear combination of the remaining vectors, as on the last part we can assume that we select and we have this:
For scalars defined in C. So then we have this:
So then we can conclude that the set X is linearly dependent.
And that complet the proof for this case.