1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
natka813 [3]
3 years ago
6

Carnegie Learning, Inc

Mathematics
1 answer:
Vlad [161]3 years ago
4 0

Answer:

The expression of the pattern is n² + 2

Step-by-step explanation:

* Lets explain how to solve the problem

- Charlie starts with 3 guppy fish in his tank

- After one month he finds 6 guppy fish in his tank

- The following month, he finds 11 guppy fish in his tank

∵ The increasing in the next month is ⇒ 6 - 3 = 3

∵ The increasing in the following month is ⇒ 11 - 6 = 5

- The number is increasing by the consecutive odd numbers

∴ The nth rule is quadratic ⇒ an² + bn + c, where

   a + b + c = 1st term

   3a - b = the first difference

   2a = the constant difference between each two difference

∵ The first term is 3

∴ a + b + c = 3

∵ The first difference is 6 - 3 = 3

∴ 3a - b = 3

∵ 6 - 3 = 3 and 11 - 6 = 5

∵ 5 - 3 = 2

∴ The constant difference is 2

∴ 2a = 2 ⇒ divide both sides by 2

∴ a = 1

∵ 3a - b = 3

∴ 3(1) - b = 3

∴ 3 - b = 3 ⇒ subtract 3 from both sides

∴ b = 0

∵ a + b + c = 3

∴ 1 + 0 + c = 3

∴ 1 + c = 3 ⇒ subtract 1 from both sides

∴ c = 2

∵ The nth rule is ⇒ an² + bn + c , where n is the position of the number

∴ The nth rule = (1)n² + (0)n + 2

∴ The nth rule = n² + 2

∴ The expression of the pattern is n² + 2

You might be interested in
IN WHICH PLACE IS THE FIRST DIGIT IN THE QUOTIENT 1,497 by 5?
BabaBlast [244]
The first digit of the quotient would be in the hundreds place.
6 0
3 years ago
Read 2 more answers
Find the whole. 20% of is 18.
Stolb23 [73]
Since 20% can be rewritten as 1/5, then we can multiply 18 by 5 to get 90, which is your answer. Hope this helps!
8 0
2 years ago
Write three factors if algebraic term 5k
ExtremeBDS [4]
5, k, 5k................
5 0
3 years ago
Read 2 more answers
PLS SOLVE ASAP!!!
cupoosta [38]
180 + 30x = 60 + 50x
⇒ 20x = 120
⇒ x = 6 minutes

<span>it will take 6 minutes for Millie to catch up with Ben</span>

3 0
3 years ago
Boxes of granola are on sale at a price of 2 for $4.50. There are 12 ounces of
Sholpan [36]

Answer:

3 dollars

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Other questions:
  • the weight of abes dog can be found using the expression 2(x+3), where x is the number of weeks. the weight of karens dog can be
    10·1 answer
  • What is the sum of b and 4
    15·1 answer
  • Translate the sentence into an inequality.
    9·1 answer
  • Sally's cat is 3 years older than Helen's dog. The product of their ages is 54. How old is Helen's dog?
    10·1 answer
  • Solve these two easy equations:<br><br> 0.04x-3.82=0.68<br><br> 8.5-1.2x=6.7
    5·2 answers
  • Just want to know if I got them right.I got 100 for number one
    6·2 answers
  • Select the following inequality and graph its solution set: 8(1-4x) &gt;40
    5·1 answer
  • Help please will give brainiest
    13·1 answer
  • The equation above shows how temperature F, measured in degrees Fahrenheit, relates to a temperature C, measured in degrees Cels
    7·1 answer
  • WHEN LOIS MARTIN WAS BORN, HER FATHER DEPOSITED $2000 IN A SAVINGS
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!