The sum of four consecutive integers is 390. Find the integers (Please show your work)

Step-by-step explanation:

The sum of three consecutive even integers is 390. What are the integers?

   In order to ensure the numbers are even I generally call the first

   integer 2n  because 2 multiplied by any number will always be even.

   Our consecutive even integers are:  2n, 2n+2, 2n+4

   2n + 2n+2 + 2n+4 = 390

   6n + 6 = 390

   6n = 384

   n = 64

  Our 1st integer is 2n = 2(64) = 128

  Our integers are 128, 130, 132

Check:  128+130+132 = 390 which is correct.

2) The sum of three consecutive odd integers is 99. What are the integers?

    Same logic applies:  An odd integer will always result from 2n+1

    So we will call our 3 consecutive odd integers   2n+1, 2n+3, 2n+5

   2n+1 + 2n+3 + 2n+5 = 99

   6n+9 = 99

   6n = 90

   n = 15

   Our first odd integer is 2n+1 = 2(15) + 1 = 31

   Our 3 consecutive odd integers are 31, 33, 35

Check:  31 +33+45 = 99  Yes

3)Which equation defines three consecutive odd integers that add up to 81?

A) n(n+1)(n+2)=81

B) n(n+2)(n+4)=81

C) n+(n+1)+(n+3)=81

D) n+(n+1)+(n+2)=81

E) n+(n+2)+(n+4)=81

We can immediately discard answers A, B because they are multiplying

instead of adding.

That leaves C, D, E

This question does not follow the logic I utilized in question 1 and 2. 

Assuming the first number is indeed odd and is called n

The next odd number is n+2 followed by n+4

Thus we must have:  n + (n+2) + (n+4) = 81

The answer is E

By the way:  The numbers are 25, 27, 29

The integers are 96, 97, 98, and 99

Step-by-step explanation:

first integer = x

second integer = x+1

third integer = x+2

fourth integer = x+3

(that what consecutive means, like 4, 5, 6, 7 are just adding 1 more each time

The sum (add them all up) is (=) 390 so

x+(x+1)+(x+2)+(x+3) = 390

4x+6=390

4x+6-6=390-6

4x=384

4x/4=384/4

x=96

x+1=97

x+2=98

x+3=99

The integers are 96, 97, 98, and 99

the population of other specie of birds will decline or other specie of birds will find some alternate source of food to survive.

explanation:

according to the competitive exclusion principle, which is also known as gause's law, two specie living in the same niche and feeding on the same resource cannot co-exist stably.

as we have well studied the theory of natural selection which states that only those organisms survive which have better tendency to compete for food and adapt to the environmental conditions.

coming towards the question, what wi ll happen when one species outcompetes the other for the small fish , the other specie will not get enough food and will start to die or decline in population. eventually either other specie needs to find another alternative food source for itself or migrate at some other location where there is less competition otherwise it will just not exist anymore at that niche.

hope it !

answer: 7

step-by-step explanation: