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
Please help this is due tomorrow
Lostsunrise [7]

\sf \left(\dfrac{1}{7}\right)^3\ is\ basically\ like\ saying\ you're\ multiplying\ \dfrac{1}{7}\ by\ \dfrac{1}{7},\ three\ times.

\implies\ \sf \dfrac{1}{7}\ \times\ \dfrac{1}{7}\ \times\ \dfrac{1}{7}\\\\\\\implies\ \dfrac{1}{343}

Therefore, (1/7)³ = 1/343, implying that the answer is option (D).

Hope it helps. :)

7 0
2 years ago
Read 2 more answers
The triangles are similar.<br> What is the value of x?<br> Enter your answer in the box.<br> X=
Volgvan
X=21

If the triangle are similar then you can divide.
75 divided by 25 is 3
72 divided by 21 is 3
so that means if you take 7 times 3 you will get 21
3 0
2 years ago
Read 2 more answers
Slope of 2 and passes through the point (-4,3). Write the equation in slope intercept form
erastova [34]

Answer:

The equation is y = 2x + 11.

Step-by-step explanation:

It is given that the gradient of the equation is 2. Using slope-form formula, y = mx+b where m is gradient and b is y-intercept. In order to find b, you have to substitute x-coordinate and y-coordinate into the equation :

y = mx + b

m = 2

At(-4,3),

3 = 2(-4) + b

b = 3 - 2(-4)

= 11

8 0
3 years ago
If you have drums that hold 60 gallons and you need to ship out 5,300 liters of liquid, how many drums will you need? Remember:
Serga [27]
You will need 89 drums to ship out 5,300 liters if each drum holds 60 gallons.
4 0
3 years ago
Guys i NEED HELP!!!!!!!!! please i asked a bunch of times now and i want 2 go to bed PLS HELP MEEEEEEEEEEE if u give a fake answ
djyliett [7]

Answer:

6) D

8) E

9) A

1) D

10) B

7 0
3 years ago
Other questions:
  • what is the probability of either a boy or girl being born when the probability of a boy being born equals .50 or 1/2 as does th
    6·1 answer
  • 1. At a speed of 80km/h, it takes 10hrs to travel between Abuja and Lagos. How long will it takes to cover the same distance at
    12·2 answers
  • Write "fourteen seven tenths squared in all three forms
    15·1 answer
  • Write (6a) without exponents.<br>(6a)²​
    5·1 answer
  • What is the answer?(math)
    9·1 answer
  • I GIVE 62 POINTS!!!!!Please help me..I am struggling with this question and my assignment is overdue already..
    5·1 answer
  • What is the area of this...
    6·1 answer
  • What is the measure of angle x?<br><br> A 44°<br><br> B 53°<br><br> C 83°<br><br> D 180°
    7·1 answer
  • So say selling a backpack thats used-like new and the original price is $54.00 how much should I set the price at??
    14·2 answers
  • STOP SCROLLING AND HELP ME WITH THIS!! IT IS DUE TOMORROW
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!