How to do this problem
2 answers:
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Answer:
a. -⅓
b. 3
c. y = 3x - 10
Step-by-step explanation:
a. Gradient of line AB:
A(1, 3), B(7, 1)
Gradient (m) = -⅓
b. The of the line that is perpendicular to line AB would be the negative reciprocal of the gradient of line AB.
Thus, the negative reciprocal of -⅓ = 3
Gradient of the line perpendicular to line AB = 3
c. Equation of the line that passes through (4, 2) and is perpendicular to line AB:
We can write the equation using the point-slope form equation, y - b = m(x - a), where,
(a, b) represents a point on the line, and,
m = gradient/slope
We know that the gradient/slope (m) = 3
Also, a point, (a, b) = (4, 2).
Therefore, substitute a = 4, b = 2, and m = 3 into y - b = m(x - a)
Thus:
y - 2 = 3(x - 4)
y - 2 = 3x - 12
Add 2 to both sides
y = 3x - 12 + 2
y = 3x - 10
We want to find the mean of two elements in a set, given that we know the other elements of the set and the mean of the whole set.
The answer is: -490
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For a set with N elements {x₁, x₂, ..., xₙ} the mean is given by:
Here we know that:
- The mean of the set is 0.
- The set has 1000 elements.
- 998 of these elements are ones, the other two are A and B.
We want to find the mean of the values of A and B.
First, we can start by writing the equation for the mean:
We can rewrite this as:
And we have 998 ones, then:
Now we have B isolated.
With this, the mean of A and B can be written as:
So we can conclude that the mean of the other two numbers is -490.
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