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Ratling [72]
3 years ago
7

Is 0.666666 irracional?

Mathematics
1 answer:
Mariana [72]3 years ago
4 0
While it may seem irrational because the decimal does not terminate. It is actually rational because repeating .666 can be written as a fraction which is 2/3. And any number written as a fraction is rational number.

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Question 2 of 5
AlekseyPX

Given:

The different recursive formulae.

To find:

The explicit formulae for the given recursive formulae.

Solution:

The recursive formula of an arithmetic sequence is f(n)=f(n-1)+d, f(1)=a,n\geq 2 and the explicit formula is f(n)=a+(n-1)d, where a is the first term and d is the common difference.

The recursive formula of a geometric sequence is f(n)=rf(n-1), f(1)=a,n\geq 2 and the explicit formula is f(n)=ar^{n-1}, where a is the first term and r is the common ratio.

The first recursive formula is:

f(1)=5

f(n)=f(n-1)+5 for n\geq 2.

It is the recursive formula of an arithmetic sequence with first term 5 and common difference 5. So, the explicit formula for this recursive formula is:

f(n)=5+(n-1)(5)

f(n)=5+5(n-1)

Therefore, the correct option is A, i.e., f(n)=5+5(n-1).

The second recursive formula is:

f(1)=5

f(n)=3f(n-1) for n\geq 2.

It is the recursive formula of a geometric sequence with first term 5 and common ratio 3. So, the explicit formula for this recursive formula is:

f(n)=5(3)^{n-1}

Therefore, the correct option is F, i.e., f(n)=5(3)^{n-1}.

The third recursive formula is:

f(1)=5

f(n)=f(n-1)+3 for n\geq 2.

It is the recursive formula of an arithmetic sequence with first term 5 and common difference 3. So, the explicit formula for this recursive formula is:

f(n)=5+(n-1)(3)

f(n)=5+3(n-1)

Therefore, the correct option is D, i.e., f(n)=5+3(n-1).

6 0
3 years ago
Read 2 more answers
Factor the polynomial below. 9x^2-1 A. (-1)(9x-1) B. (3x-1)(3x-1) C. (3x-1)(3x+1) D. (x-1)(9x+1)
telo118 [61]

Answer:

(3x-1) (3x+1)

Step-by-step explanation:

9x^2-1

Rewriting as

(3x)^2 - 1^2

This is the difference of squares

a^2 - b^2 = (a-b)(a+b)

(3x-1) (3x+1)

6 0
3 years ago
Activity 1: Performance task continued
ANTONII [103]

Answer:

Um wat?

Step-by-step explanation:

6 0
3 years ago
Which one doesn’t represent a function?
Olenka [21]
It’s 3. Each input can only go to one output and 2 goes to 2 outputs
4 0
2 years ago
A game room has a floor that is 120 feet by 75 feet. A scale drawing of the floor on grid paper uses a scale of 1 unit:5 feet. W
castortr0y [4]
Length: 24 units

1:5
24:120

Width: 15 units

1:5
15:75
8 0
2 years ago
Read 2 more answers
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