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Alexxx [7]
3 years ago
12

b) The sum of 9 times a larger number and twice a smaller is 6. The difference of 3 times the larger and the smaller is 7. Compu

te the numbers. (10marks) Remarks: These questions involved several scenarios 1. Assign the variables -2marks 2. Assumptions of the context of the two numbers -2marks 3. Apply linear systems -2marks 4. Compute using the applicable method of system of linear system -2marks 5. Compute both numbers from above-2marks
Mathematics
1 answer:
Romashka [77]3 years ago
6 0

Answer:

1) let the larger number be x and the smaller is y

2) 9x + 2y = 6

3x - y = 7

3) 9x+2y=6 and 9x -3y = 21

5y = -15

y= -3

5)

3x=4

x=4/3

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Perhaps the easiest way to find the midpoint between two given points is to average their coordinates: add them up and divide by 2.

A) The midpoint C' of AB is
.. (A +B)/2 = ((0, 0) +(m, n))/2 = ((0 +m)/2, (0 +n)/2) = (m/2, n/2) = C'
The midpoint B' is
.. (A +C)/2 = ((0, 0) +(p, 0))/2 = (p/2, 0) = B'
The midpoint A' is
.. (B +C)/2 = ((m, n) +(p, 0))/2 = ((m+p)/2, n/2) = A'

B) The slope of the line between (x1, y1) and (x2, y2) is given by
.. slope = (y2 -y1)/(x2 -x1)
Using the values for A and A', we have
.. slope = (n/2 -0)/((m+p)/2 -0) = n/(m+p)

C) We know the line goes through A = (0, 0), so we can write the point-slope form of the equation for AA' as
.. y -0 = (n/(m+p))*(x -0)
.. y = n*x/(m+p)

D) To show the point lies on the line, we can substitute its coordinates for x and y and see if we get something that looks true.
.. (x, y) = ((m+p)/3, n/3)
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.. n/3 = n*((m+p)/3)/(m+p)
The expression on the right has factors of (m+p) that cancel*, so we end up with
.. n/3 = n/3 . . . . . . . true for any n

_____
* The only constraint is that (m+p) ≠ 0. Since m and p are both in the first quadrant, their sum must be non-zero and this constraint is satisfied.

The purpose of the exercise is to show that all three medians of a triangle intersect in a single point.
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5.33

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