How many distinct triangles can be drawn by using three of the seven dots below? (Two triangles are considered different if they don’t share the same three vertices.)

35triangles

Step-by-step explanation:

Given

Total distinct points = 7

If we are to form triangles using the dots,

Total points in a triangle = 3

Using the combination rule;

number of triangles formed = 7C3

7C3 = 7!/(7-3)!3!

7C3 = 7!/4!3!

7C3 = 7*6*5*4!/4!3!

7C3 = 7*6*5/6

7C3 = 7*5

7C3 = 35

Hence the amount of triangles that can be formed is 35triangles

arithmetic sequence

step-by-step explanation:

given that a sequence has terms as

19, 15, 11,

this is represented on a graph

the pattern indicates that the sequence is an arithmetic sequence with i term

a=19 and common difference d =-4

any general term

thus the sequence is reduced by 4 for each successive term starting from 1 and nth term is

24-5n.

first negative term would start after 5th term

5th term =24-25< 0

from 5th term onwards the sequence would be negative.