Describe the possible configurations and the possible number of points of intersection of (a) 2 lines in the plane (b) 3 lines in the plane (c) 2 lines in space (d) 3 planes in space.

 The answer is given below.

Step-by-step explanation: The description is as follows:

(a) 2 lines in the plane : Any two lines in a plane can either be parallel or intersect at only one point.

(b) 3 lines in the plane : Any three lines in a plane may intersect at a point, if so, they are called concurrent lines, or they may never intersect.

(c) 2 lines in space :  There are exactly three possibilities.

* The two lines are distinct and they have no points in common.

* The two lines are distinct and they have exactly one point in common.

* The two lines are really the same line and they have all of their points in common.

(d) ) 3 planes in space : Here also, we have three possibilities:

* The three planes are distinct and they have no points in common.

* The three planes share exactly one point.

* The three planes share infinitely many points, i.e., they could all share a line or they could all be the same plane.

c

step-by-step explanation:

it isn't d, because the interquartile range is from 27-57. and the interquartile range is basically half the data, it's pretty obvious.

it isn't b, because like i said earlier, the interquartile range is from 27-57. 57-27 is 30. the real range has to be longer

not a either. although it looks like it, 3/4 of the data is not greater than 27. but if c is wrong than this should be correct

the correct answer is c, because 13 is the point in which the plot starts

there are many solutions.

step-by-step explanation:

step 1: simplify both sides of the equation.

4x+6=4x^2+10x−4

step 2: subtract 4x^2+10x-4 from both sides.

4x+6−(4x^2+10x−4)=4x^2+10x−4−(4x^2+10x−4)

−4x^2−6x+10=0

step 3: factor left side of equation.

−2(2x+5)(x−1)=0

step 4: set factors equal to 0.

x=-5/2 or x=1