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4 years ago

What's the answer for this 20/6×5+20-20

Mathematics

2 answers:

Veseljchak [2.6K]4 years ago

7 0

Exact Form: 50/3

Decimal Form: 16.6 repeating

Mixed Number Form: 16 2/3

larisa [96]4 years ago

4 0

16.66666666666667
ANSWER IS THE ABOVE NO

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Determine formula of the nth term 2, 6, 12 20 30,42

nalin [4]

Check the forward differences of the sequence.

If $\{a_n\} = \{2,6,12,20,30,42,\ldots\}$ , then let $\{b_n\}$ be the sequence of first-order differences of $\{a_n\}$ . That is, for n ≥ 1,

$b_n = a_{n+1} - a_n$

so that $\{b_n\} = \{4, 6, 8, 10, 12, \ldots\}$ .

Let $\{c_n\}$ be the sequence of differences of $\{b_n\}$ ,

$c_n = b_{n+1} - b_n$

and we see that this is a constant sequence, $\{c_n\} = \{2, 2, 2, 2, \ldots\}$ . In other words, $\{b_n\}$ is an arithmetic sequence with common difference between terms of 2. That is,

$2 = b_{n+1} - b_n \implies b_{n+1} = b_n + 2$

and we can solve for $b_n$ in terms of $b_1=4$ :

$b_{n+1} = b_n + 2$

$b_{n+1} = (b_{n-1}+2) + 2 = b_{n-1} + 2\times2$

$b_{n+1} = (b_{n-2}+2) + 2\times2 = b_{n-2} + 3\times2$

and so on down to

$b_{n+1} = b_1 + 2n \implies b_{n+1} = 2n + 4 \implies b_n = 2(n-1)+4 = 2(n + 1)$

We solve for $a_n$ in the same way.

$2(n+1) = a_{n+1} - a_n \implies a_{n+1} = a_n + 2(n + 1)$

Then

$a_{n+1} = (a_{n-1} + 2n) + 2(n+1) \\ ~~~~~~~= a_{n-1} + 2 ((n+1) + n)$

$a_{n+1} = (a_{n-2} + 2(n-1)) + 2((n+1)+n) \\ ~~~~~~~ = a_{n-2} + 2 ((n+1) + n + (n-1))$

$a_{n+1} = (a_{n-3} + 2(n-2)) + 2((n+1)+n+(n-1)) \\ ~~~~~~~= a_{n-3} + 2 ((n+1) + n + (n-1) + (n-2))$

and so on down to

$a_{n+1} = a_1 + 2 \displaystyle \sum_{k=2}^{n+1} k = 2 + 2 \times \frac{n(n+3)}2$

$\implies a_{n+1} = n^2 + 3n + 2 \implies \boxed{a_n = n^2 + n}$

6 0

2 years ago

In the line y - 3 = -2 (x+5), which of the following are true?

blsea [12.9K]

Answer:

Options a, d and e

Step-by-step explanation:

We check the validity of each of the options.

Kindly note that we can express the equation fully and we have;

y-3 = -2x-10

y = -2x -10 + 3

y = -2x -7

So let’s now evaluate the options.

(a) Insert the value of x at this point, if it gives the value of y, then it’s on the line

the value of x to insert is -5 here.

Thus ; y = -2(-5)-7 = 10-7 = 3

since y is 3, then it is on the line

(b) same as a

insert x = 5

y = -2x-7

y = -2(5) -7

y = -10-7 = -17

This is definitely not on the line as the value of y gotten does not correlate with what was given

c. To get this , compare with the standard form of

y = mx + c

where m is slope

Here our m is -2 , so this is definitely wrong

d) From above , we can see that this is correct

e) compare this with y = mx + c

c is our intercept and this is equal to -7 which makes this option also correct

6 0

3 years ago

Consider polynomials P and Q.

romanna [79]

B. P+Q
This the answer on edmentum

7 0

3 years ago

Someone help please!!! Urgent!!!!!

Romashka [77]

What is it? ...........

8 0

4 years ago

7x+39>=53. And. 16x+ 15>31 X>=2 x>1. X<=2. No solution

bazaltina [42]

Answer:

7x+39>=53 and 16x+ 15>31 x>=2 (no solutions exist)

Step-by-step explanation:

4 0

3 years ago