All categories

3 years ago

ASAP PLEASE :( ........................................

Mathematics

1 answer:

MatroZZZ [7]3 years ago

5 0

Answer:

Step-by-step explanation:

slope= y/x

so 42/82= 21/41

You might be interested in

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

Please help on 5 and 6

fgiga [73]

Noah is right because 75% of 10 is 7.5 and 10% of 30 also equals 7.5

5 0

3 years ago

Alberts cabbage patch has 12 rows of cabbage. in each row, there are 15 heads of cabbage. how many cabbage does Albert have in a

Sedbober [7]

180 cabbages is how many he has

7 0

3 years ago

Read 2 more answers

So can someone help pleaseeee

Marat540 [252]

X=4. Hope this is the one you wanted me to answer.

6 0

4 years ago

Read 2 more answers

One student simplified x5 + x5 to x10 . A second student simplified x5 + x5 to 2x5 . Which student is correct? Explain.

dybincka [34]

An expression is defined as a set of numbers, variables, and mathematical operations. The second student is correct.

<h3>What is an Expression?</h3>

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

Given One student simplified x⁵ + x⁵ to x¹⁰. The second student simplified x⁵+x⁵ to 2x⁵. Since the simplification of (x⁵+x⁵) is equal to 2x⁵. Therefore, the second student is correct.

Learn more about Expression:

brainly.com/question/13947055

#SPJ1

5 0

2 years ago