How many integers $n$ satisfy the inequality 3n^2-4 < = 44

9 integers.

Step-by-step explanation:  

We have been given an inequality and we are asked to find the solution set for our given inequality.

Let us solve our given inequality by adding 4 to both sides of our equation.

Upon dividing both sides of our equation by 3, we will get,

Taking square root of both sides of our equation we will get,

The solution set for our inequality is integers between -4 to 4 including -4 and 4 as : -4,-3,-2,-1,0,1,2,3,4.

Therefore, 9 integers will satisfy our given inequality.

18

step-by-step explanation:

draw the shape and you will see that f and k are actually at adjacent vertices (points of the hexagon that are neighboring).   so find the distance between (1,2) and (4,2).   that is easy since (1,2) and (4,2) is just a vertical distance to count, which is 3.   it is a regular polygon which means all sides are congruent.   you have 6 sides (hexa) so multiply 6 by 3 to receive 18.