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)
Putting these into our equation, we have
.. 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.
Answer:
3. 60% probability the student is over the age of 21.4
4. 4.17% probability Biff was selected if you know the student selected was over the age of 21.
5. 0% probability Biff was selected if you know the student selected was 21 or younger
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcoes.
In this question:
40 students
24 over the age of 21.
16 are 21 or younger.
3. Find the probability the student is over the age of 21.
24 of the 40 students are over the age of 21.
24/40 = 0.6
60% probability the student is over the age of 21.4
4. Find the probability Biff was selected if you know the student selected was over the age of 21.
24 students over the age of 21, one of which is Biff.
1/24 = 0.0417
4.17% probability Biff was selected if you know the student selected was over the age of 21.
5. Find the probability Biff was selected if you know the student selected was 21 or younger
Biff is not 21 or younger, he is over 21, so there are no desired outcomes.
So, 0% probability Biff was selected if you know the student selected was 21 or younger
Answer:
-5 divide by 28
Step-by-step explanation:
so the question supposed be " 15-20 divided by 2(4) + 20
15-20 which is also 15 + (-20)= -5
2(4)=8, 8+20=28
so it can simplify into -5 / 28
(hope it helps :)
Answer:
−
10
x
^3
−
4
x
^2
+
4
x
+
3
Step-by-step explanation:
Answer: a = -15
Step-by-step explanation:
3a + b = 9
b=54
3a + 54 = 9
3a = 9-54
3a= -45
<h3>
</h3>
- x + = -
<h2>a= -15</h2>
