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Soloha48 [4]
3 years ago
7

The sum of nine and three times a number is 57 find the number and write an equation

Mathematics
1 answer:
Temka [501]3 years ago
7 0
Let "n" be a number

9 + 3n = 57
3n = 57 - 9
3n = 48
n = 48/3
n = 16
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There are 3 even numbers to choose from, and we can pick up to 3 additional odd numbers.

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The total count is then the sum of all possible selections with at least 1 even number and between 0 and 3 odd numbers.

\displaystyle \sum_{e=1}^3 \binom 3e \sum_{o=0}^3 \binom 3o = 2^3 \sum_{e=1}^3 \binom3e = 8 \left(\sum_{e=0}^3 \binom3e - \binom30\right) = 8(2^3 - 1) = \boxed{56}

where we use the binomial identity

\displaystyle \sum_{k=0}^n \binom nk = \sum_{k=0}^n \binom nk 1^{n-k} 1^k = (1+1)^n = 2^n

3 0
1 year ago
39 ft/min= ____ yd/s explain your reasoning
dimulka [17.4K]

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castortr0y [4]
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 The explanation is shown below:

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 3.  Then, you know the quadratic formula to solve quadratic equations, which is:

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Answer:

d. 60

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Question 3
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Answer:

Step-by-step explanation:

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