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3 years ago

21. Which property is used to simplify the expression 5(3x + 18) to 152 + 90?

Mathematics

1 answer:

chubhunter [2.5K]3 years ago

3 0

You distribute your 5 to 3x and 18 heirij irn is

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Find the general term of {a_n}

Assoli18 [71]

From the given recurrence, it follows that

$a_{n+1} = 2a_n + 1 \\\\ a_{n+1} = 2(2a_{n-1} + 1) = 2^2a_{n-1} + 1 + 2 \\\\ a_{n+1} = 2^2(2a_{n-2}+1) + 1 + 2 = 2^3a_{n-2} + 1 + 2 + 2^2 \\\\ a_{n+1} = 2^3(2a_{n-3} + 1) + 1 + 2 + 2^2 = 2^4a_{n-3} + 1 + 2 + 2^2 + 2^3$

and so on down to the first term,

$a_{n+1} = 2^na_1 + \displaystyle \sum_{k=0}^{n-1}2^k$

(Notice how the exponent on the 2 and the subscript of a in the first term add up to n + 1.)

Denote the remaining sum by S ; then

$S = 1 + 2 + 2^2 + \cdots + 2^{n-1}$

Multiply both sides by 2 :

$2S = 2 + 2^2 + 2^3 + \cdots + 2^n$

Subtract 2S from S to get

$S - 2S = 1 - 2^n \implies S = 2^n - 1$

So, we end up with

$a_{n+1} = 4\cdot2^n + S \\\\ a_{n+1} = 2^2\cdot2^n + 2^n-1 \\\\ a_{n+1} = 2^{n+2} + 2^n - 1 \\\\\implies \boxed{a_n = 2^{n+1} + 2^{n-1} - 1}$

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3 years ago

PLEASE HELP!!!!!! WILL MARK BRAINLIEST!! What is the probability that two "face" cards are drawn from a standard deck of 52 card

vivado [14]

Answer:

approximately 4.978%

Step-by-step explanation:

The probability of both happening is 3/13*11/51, or 33/663, or 11/221 (approximately 4.978%). Two cards are drawn one after the other with replacement from a pack of 52 cards.

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Add or subtract as indicated and write the result in standard form. 5i - (-5 - i)

AlexFokin [52]

Simplify by combing the real and imaginary parts of each expression.

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Ms. Manko has 4 grams of sprinkles

lukranit [14]

4 divided by 12 is 1/3.
So, she would sprinkle 1/3 of a gram on each cupcake.

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3 years ago

12 divided by 479, make sure to show your work. x+7=2x Please Solve

Dmitriy789 [7]

12/479
0.025

x+7=2x

Take x right

2x-x=7
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2 years ago