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

walter needs to make at least 5 more cookies but no more than 40. 5 ≥ x ≥ 40;

step-by-step explanation:

walter has to make a minimum of 20 cookies. he already has 15 cookies made, so he must make 5 more to meet the minimum.

the maximum amount of cookies he can make is 55. he already has 15, so he has to make no more than 40 more cookies to meet the maximum.