A basketball team has twelve players. The starting lineup of five players must be chosen.

a. In how many ways can the starting five be chosen if no positions are assigned to the players?
b. In how many ways can the starting five be chosen if each player is assigned one of the following positions: center, power forward, small forward, off guard, and point guard?
c. Suppose all twelve players differ in height. In how many ways can the starting five in part b.) be chosen so that the center is taller than the power forward who is taller than the small forward who is taller than the off guard who is taller than the point guard?

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)

step-by-step explanation:

given that there are two triangles j'k'l' and jkl>

the former is got by dilating the second one.

when drawn on a grid, (graph paper) coordinates of vertices of first triangle is

(6,12)j, (9,6)k and (12,9)l

side jk has length = distance between j and k

=

side j'k'=distance between j' and k'

=

ie j'k'l' has sides 1/3 of that of corresponding sides of jkl.

hence scale factor of 1/3 is used to get j'k'l'from jkl

5

step-by-step explanation:

this is a good question! i'll do some research and come back when i have the answer!