You are building identical displays for the school fair using 65 blue boxes and 91 yellow boxes. What is the greatest number of displays you can build using all the boxes?

13

Step-by-step explanation:

The problem requires us to find the greatest number of displays that can be built using all the boxes.  

This is an application of the Greatest Common Factor.

DEFINITION

The GCF of two or more numbers is the biggest number that divides exactly into the numbers.

To find the GCF, we follow the steps below:

Step 1

We break down both numbers into product of prime factors.

65=5 X 13

91 =7 X 13

Step 2

We choose the common factors with the smallest exponent

Therefore the greatest common factor is 13.

The greatest number of displays can be built using all the boxes is 13.

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.

step-by-step explanation:

de-gf

hj=3x+20

ji=15x-64