Answer:
(12,10)
Step-by-step explanation:
Let the midpoint of the side opposite this vertex have coordinates B(a,b)
We have the centroid at C(8,7) and the vertex of the triangle at A(0,1).
The centroid divides AB internally in the ratio 2:1
We use the formula:
where m:n=2:1 is the ratio of internal division.
We substitute the coordinates of A and B and the ratio to get:
This should simplify and give us the centroid.
This implies that:
We solve for a and b
Therefore the midpoint of the side opposite this vertex is (12,10)
Option b bcz it is repeating decimal
it is non terminating number 11.333333333....
If
and
are mutually independent, then
and
.
If
and
are independent, then
. Ditto for
and
.
The inclusion/exclusion principle says that
Since
and
are mutually exclusive, their intersection is the empty set. It then follows that
also is the empty set, so the last probability is also 0.
Plug in what we know:
4×+7y=-12 __ -4x-y=-12 ________ 0x+6y=-24 , so you eleminated by it self 6y/6=-24/6 , you get : y=-4 and then you plug in 4x+7(-4)=-12 , that's your answer 4x-28 =-12 , you divided in both side 4x=-12+28 , 4x=16 , and then x=16/4 =4 , so x=4
To find the measure of angle OPQ, we have two equations...
y+5x-17=180 because angles OPN and OPQ are supplementary...
AND
x+17+2x-4+y=180 because the total degrees of a triangle must add up to 180.
The equations...
5x+y=197
3x+y=167
solce the system of equations...
x=15
y=122
Since we wanted to solve for y, 122 is the answer.
The measure of angle OPQ is 122.
Sorry this took forever. The website is hard to use because I'm used to using the app:)
Best of wishes!
