Please help me out please
2 answers:
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Answer:
Step-by-step explanation:
We are given;
- A point (6, -4)
- An equation of a line, 9x - 3y = 9
We are required to determine the equation a line passing through a point (6, -4) and perpendicular to the given line;
- To answer the question we need to get the gradient of the given line first.
- We write the equation 9x - 3y = 9 in the form of y = mx + c, where m is the slope;
- That is;
y = 3x -3
- Thus, the slope of the line is 3
But; m₁ × m₂ = -1 (For perpendicular lines)
Therefore;
m₂ = -1 ÷ 3
= -1/3
Therefore, the slope of the line in question is -1/3 and the line passes through (6, -4).
To get its equation, we get another point (x, y)
Then;
Thus;
In the form of slope-intercept, the equation will be;
Thus, the equation of the line is;
Answer:
(C) 3 kg is the maximum possible weight of the lightest box
Step-by-step explanation:
given data is:
- mean = 7 kg
- median = 9 kg
- total number of boxes = 3
so since we know that the median is 9 and the total boxes are 3. We already know the weight of one of the three boxes.
so we can think of the sum of the three weights in ascending order as: A+9+B.
here A and B are the unknown weights of the remaining two boxes.
- We can first use all of the given data in the mean formula
mean = (sum of all weights)/(number of boxes)
put all the known values in the formula
and rearrange the formula so one of A and B as the subject.
now you can use the given values in the Multiple choices from the question and find the maximum value. try each value to be equal to B, so you can find A.
but you need to be smart about it, and keep in mind that the only one of the value of A and B should be greater than the median i.e. 9, or else that will rearrange the way we have set up our boxes:: A + 9 + B (ascending order).
- start from (E), where B = 5
here, no value is greater than the median: 3+9+7 (not ascending)
- now check (D), where B = 4.
here no value is greater than the median: 4+9+8 (not ascending)
- now check (C), where B = 3
here, one of the boxes is equal to the median: 3+9+9 (ascending)
you see a pattern here, the value of A is increasing, thus B is decreasing.
- check (B), where B = 2
here, you can realize that B = 2 is not correct since this is not maximum possible weight of the lightest box: 2+9+10 (ascending, but the weight of the lightest box is not maximum possible)
Since, we want maximum possible weight for the lightest box, that is only possible when B = 3 (maximum possible)