Answer:
![C = (\frac{11}{3},\frac{11}{3},\frac{7}{3})](https://tex.z-dn.net/?f=C%20%3D%20%28%5Cfrac%7B11%7D%7B3%7D%2C%5Cfrac%7B11%7D%7B3%7D%2C%5Cfrac%7B7%7D%7B3%7D%29)
Step-by-step explanation:
Given
![(x_1,y_1,z_1) = (1,3,-2)](https://tex.z-dn.net/?f=%28x_1%2Cy_1%2Cz_1%29%20%3D%20%281%2C3%2C-2%29)
![(x_2,y_2,z_2) = (4,5,0)](https://tex.z-dn.net/?f=%28x_2%2Cy_2%2Cz_2%29%20%3D%20%284%2C5%2C0%29)
![(x_3,y_3,z_3) = (6,3,9)](https://tex.z-dn.net/?f=%28x_3%2Cy_3%2Cz_3%29%20%3D%20%286%2C3%2C9%29)
Required
Determine the coordinates of the centroid
Represent the coordinates with C.
C is calculated as follows:
![C = (\frac{1}{3}(x_1+x_2+x_3),\frac{1}{3}(y_1+y_2+y_3),\frac{1}{3}(z_1+z_2+z_3}))](https://tex.z-dn.net/?f=C%20%3D%20%28%5Cfrac%7B1%7D%7B3%7D%28x_1%2Bx_2%2Bx_3%29%2C%5Cfrac%7B1%7D%7B3%7D%28y_1%2By_2%2By_3%29%2C%5Cfrac%7B1%7D%7B3%7D%28z_1%2Bz_2%2Bz_3%7D%29%29)
Substitute values of x and y in the given equation
![C = (\frac{1}{3}(1+4+6),\frac{1}{3}(3+5+3),\frac{1}{3}(-2+0+9}))](https://tex.z-dn.net/?f=C%20%3D%20%28%5Cfrac%7B1%7D%7B3%7D%281%2B4%2B6%29%2C%5Cfrac%7B1%7D%7B3%7D%283%2B5%2B3%29%2C%5Cfrac%7B1%7D%7B3%7D%28-2%2B0%2B9%7D%29%29)
![C = (\frac{1}{3}(11),\frac{1}{3}(11),\frac{1}{3}(7}))](https://tex.z-dn.net/?f=C%20%3D%20%28%5Cfrac%7B1%7D%7B3%7D%2811%29%2C%5Cfrac%7B1%7D%7B3%7D%2811%29%2C%5Cfrac%7B1%7D%7B3%7D%287%7D%29%29)
![C = (\frac{11}{3},\frac{11}{3},\frac{7}{3})](https://tex.z-dn.net/?f=C%20%3D%20%28%5Cfrac%7B11%7D%7B3%7D%2C%5Cfrac%7B11%7D%7B3%7D%2C%5Cfrac%7B7%7D%7B3%7D%29)
<em>The above is the coordinate of the centroid</em>
Answer:
y+(21)=-4(x-7)
Step-by-step explanation:
the point slope equation , two point
m=y2-y1/x2-x1
m=23+21/-4-7=44/-11= -4
y+(21)=-4(x-7)
It is 30 degrees. Add 90 and 60 to get 180. Then subtract that from 180, since all triangles interior angles add to 180. You’ll get 30.
Answer:
There are a total of 4 + r + 6 marbles in the bag
The probability of a blue is
The probability of a red is
The probability of choosing a blue, replacing it and then a red is
×
= [tex]\frac{4r}{100+20r+ r^{2} /[tex]
Step-by-step explanation: