Answer:
m=-29/3 and n=65/3
Step-by-step explanation:
The given system has equations:
3m+3n=36
8m+5n=31
Multiply the top equation by 5 and bottom equation by 3 to get:
15m+15n=180
24m+15n=93
Subtract the top equation from the bottom equation to get:
9m=-87
Divide both sides by 9
We substitute this value into the first equation to get:
The distances between the two points, in units, are given as follows:
7.
8.
9.
10.
The midpoints are given as follows:
11. (7,-4.5).
12. (2,4).
13. (7,0.5).
14. (5.5,-1.5).
<h3>What is the distance between two points?</h3>Suppose that we have two points, and
. The distance between them is given by:
For item 7, the points are (-3,-2) and (-4,-3), hence the distance is:
For item 8, the points are (-3,1) and (5,3), hence the distance is:
For item 9, the points are (-3,0) and (0,-3), hence the distance is:
For item 10, the points are (1,-2) and (4,4), hence the distance is:
The midpoint between two points is the halfway point between them, and is found using the mean of the coordinates.
Hence, for item 11, the midpoint is given by:
[0.5(9 + 5), 0.5(1-10)] = (7,-4.5).
For item 12, the midpoint is given by:
[0.5(-5 + 9), 0.5(7 + 1)] = (2,4).
For item 13, the midpoint is given by:
[0.5(9 + 5), 0.5(9 - 8)] = (7,0.5).
For item 14, the midpoint is given by:
[0.5(10 + 1), 0.5(4 - 7)] = (5.5,-1.5).
More can be learned about the distance between two points at brainly.com/question/18345417
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