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3 years ago

Find the perimeter of each rectangle.

Mathematics

1 answer:

alexdok [17]3 years ago

4 0

Answer: A) 66 In

Step-by-step explanation:

2 sides are 23 Inches

2 Sides are 10 Inches

So you add 23 + 23 + 10 + 10 = 66 to get the perimeter

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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

What is the standard form of 80,000 + 5,000 + 700 +8?

DochEvi [55]

80,000 + 5,000 + 700 +8 = 85,708....standard form

hope it helps

3 0

4 years ago

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Please answer the question in the photo. 10 points available.

mestny [16]

No wonder you have posted this. It is not easy. Scale is a straight line measurement. You need to use a side of a square.

Left: 1 side of a square = 1 meter.

Center: 3 tops of a square = 1 meter.
Therefore 1 side of a square = 1/3 of a meter.

Right: 1 side of a square = 0.5 meters.

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3 years ago

Find the length x. х 14 cm 70°

adoni [48]

Answer:

14.90cm [a]

Step-by-step explanation:

To find x, we will apply " sine rule"

that is, $sin$ A/a= $sin$ B/b

here a= x A=90° B=70°anb b =14cm

so we input the values we have

1/x =0.94/14

cross multiply,

0.94x = 14

x = 14/0.94

=14.90cm

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3 years ago

Who wanna be my tutor add my Instagram : laylarainn help a girl out ‍♀️

Andrew [12]

For the second one, what is the number before the x?

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3 years ago

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