If you draw 35 lines on a piece of paper so that no two lines are parallel to each other and no three lines are concurrent, how many times will they intersect?

The lines will intersect 595 times.

Step-by-step explanation:

We can do it in 2 methods.

1st method:- Let us count the number of intersections by drawing lines one by one.

1st line - 0 points=0

2nd line- new 1 point=1

3rd line - old 1 point + new 2 points with two old lines = 1+2

4th line - old (1+2) points+ new 3 points= 1+2+3

5th line - old (1+2+3) points + new 4 points=1+2+3+4

Like that from 35th line-1+2+3+4......34 =

2nd method:-

We have to choose 2 lines from 35 lines.

We can do it in ways = 595 points

77

step-by-step explanation:

a.

step-by-step explanation:

step 1 distribute 2 to every term in the parentheses

step 2 add 10 on both sides of the equal sign