Answer:
Step-by-step explanation:
The unit rate of the 100m race is 2.12... m/s which you get by dividing the 100 meters by the 47 seconds. The unit rate for the 50m race is 2.08... m/s which you get by dividing the 50 meters by the 24 seconds. This means that the record for the 100m race is faster.
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:
0.02651
Step-by-step explanation:
P(all 5 are boys) =
= 0.02651 ( wow low)
Answer:
A= -2,4 B=2,4 C= 2,5
Step-by-step explanation:
I tried my best even though C doesn't have a solid answer but A and B are correct so go off that.
Answer:
(x+16)²+(y-30)²=1156
Step-by-step explanation:
We have given:
center at (-16,30). It means h = -16 and k=30
and it passes through the origin (0,0)
Thus the radius will be distance between (-16,30) and (0,0)
r=√(-16 - 0)²+(30-0)²
r=√256+900
r²=(√1156)²
r²=1156
Now apply standard equation of circle:
(x-h)²+(y-k)² = r²
(x+16)²+(y-30)²=1156
Thus the equation is (x+16)²+(y-30)²=1156 ....
