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3 years ago

8

Eduardo counted the square tiles on the floor of his rectangular room the area of each tile is one square foot the floor has 6!r

ows of tiles and 7 tiles in each row what is the area of the floor of Eduardo's room?

1 answer:

Deffense [45]3 years ago

5 0

Answer:

6 X 7= 42

Step-by-step explanation:

to find the area of anything its length times width times height (LXWXH)

since they arent giving a width here its only LXH=?

so 6X7=42

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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

The scatterplot shown includes the (blue) least-squares regression line, whose equation is y = .975 + .005x, where y is calories

ziro4ka [17]

The scatterplot shown includes the (blue) least-squares regression line, whose equation is y = .975 + .005x, where y is calories (in thousands) and x is years after 1960. Choose the correct statement.

Answer: In the given regression equation, the calories are in thousands. Therefore, the slope 0.005 (0.005 x 1000 =5 calories) means the consumption is increasing at a rate of 5 calories per year.

Hence the option a. Consumption is increasing at a rate of 5 calories per year. is correct

4 0

3 years ago

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levacccp [35]

Easy hijdbggffafaysuwus

6 0

2 years ago

On May 1, you sign a $1000 note with simple interest of 8.5% and a maturity date of December 19. You make partial

Lelu [443]

Answer:

The amount to be repaid is $379.26.

Step-by-step explanation:

Period of note from May 1 to December 19 = 233 days

Amount of note or principal = $1,000

Simple interest rate = 8.5%

Maturity date = December 19

Repayments:

June 2 = $475

Nov. 4 = $200

Total paid $675

Simple interest = $54.26 ($1,000 * 8.5% * 233/365)

Total amount to be repaid = $1,054.26

Total amount repaid = 675.00

Balance to be paid on maturity $379.26

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3 years ago

Please awnser this one 2

almond37 [142]

The answer to the problem is c

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2 years ago

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