<span>(3.5, 3) is the circumcenter of triangle ABC.
The circumcenter of a triangle is the intersection of the perpendicular bisectors of each side. All three of these perpendicular bisectors will intersect at the same point. So you have a nice self check to make sure your math is correct. Now let's calculate the equation for these bisectors.
Line segment AB:
Slope
(4-2)/(1-1) = 2/0 = infinity.
This line segment is perfectly vertical. So the bisector will be perfectly horizontal, and will pass through ((1+1)/2, (4+2)/2) = (2/2, 6/2) = (1,3).
So the equation for this perpendicular bisector is y = 3.
Line segment BC
(2-2)/(6-1) = 0/5 = 0
This line segment is perfectly horizontal. So the bisector will be perfectly vertical, and will pass through ((1+6)/2,(2+2)/2) = (7/2, 4/2) = (3.5, 2)
So the equation for this perpendicular bisector is x=3.5
So those two bisectors will intersect at point (3.5,3) which is the circumcenter of triangle ABC.
Now let's do a cross check to make sure that's correct.
Line segment AC
Slope = (4-2)/(1-6) = 2/-5 = -2/5
The perpendicular will have slope 5/2 = 2.5. So the equation is of the form
y = 2.5*x + b
And will pass through the point
((1+6)/2, (4+2)/2) = (7/2, 6/2) = (3.5, 3)
Plug in those coordinates and calculate b.
y = 2.5x + b
3 = 2.5*3.5 + b
3 = 8.75 + b
-5.75 = b
So the equation for the 3rd bisector is
y = 2.5x - 5.75
Now let's check if the intersection with this line against the other 2 works.
Determining intersection between bisector of AC and AB
y = 2.5x - 5.75
y = 3
3 = 2.5x - 5.75
8.75 = 2.5x
3.5 = x
And we get the correct value. Now to check AC and BC
y = 2.5x - 5.75
x = 3.5
y = 2.5*3.5 - 5.75
y = 8.75 - 5.75
y = 3
And we still get the correct intersection.</span>
-3/7 is greater than -2/5
how I found this do 3÷7 and this will give you a decimal of 0.4285. While doing 2÷7 equals 0.4
hope this helps
Answer:
it's 5000
Step-by-step explanation:
50*100=5000
hope it helps:p
She will have enough for the cat and dog food.the 6 cat food bags will be $108
To solve this problem, we should remember that the percentile rank of a single
value is the rank of that value in the series of data set when that data set is
arranged in ascending order.
Therefore arranging the data set, gives the sequence:
5581, 5700, 5700, 5896,
5972, 5993, 6075, 6274, 6283, 6381
<span>Since we are to find the
30th percentile (30 %) and there are a total of 10 values, therefore
the 30th percentile is:</span>
10 * 30% = 3
<span>This means we look for
the 3rd number in the ordered sequence.</span>
<span>
</span>
<span>Answer: 5700 is the 30th
percentile of the series</span>
