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sergij07 [2.7K]
3 years ago
8

Which statements about the graph of the function f(x) = –x2 – 4x + 2 are true? Check all that apply.

Mathematics
1 answer:
qwelly [4]3 years ago
4 0
<span>FALSE - The domain is all real numbers
TRUE - downward parabola, max-point vertex (-2, 6) So the range is </span><span>{y|y ≤ 6}.</span><span>
TRUE - increases to vertex over the interval (–∞ , –2).
FALSE - The function only decreases from vertex over the interval (−2, ∞).
TRUE - The function has a positive y-intercept. -(0)^2 - 4(0) + 2 = 2 </span>

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How many 3 digit numbers are possible when a) the leading digit cannot be zero and the number must be a multiple of 4?
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Step-by-step explanation:

I assume the digits can be repeated.

so, e.g. 555 is a valid number for this problem, right ?

that means we start with permutations with repetition :

n^r

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r = the number of items being picked per result.

we have 10 digits (0,1,2,3,4,5,6,7,8,9), and we pick 3 of them.

that gives us (with very little surprise, I hope)

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as we handled all digits the same way and with the same priority, there is the same amount of numbers for every digit in the leading position.

that means 1/10 of the total amount of numbers has a leading 0, or a leading 1, or a leading 2, ...

so, we need to subtract 1/10 × 1000 from 1000 :

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and we have one more condition : the number must be a multiple of 4.

how many are there ?

well, that's the funny thing about numbers : from all numbers 1/2 of them are multiples of 2 (or divisible by 2), 1/3 of them are multiples of 3 (or divisible by 3), and ... you guessed it, 1/4 of them are multiples of 4 (or divisible by 4). and so on.

and so, 1/4 of our 900 numbers are multiples of 4 :

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6 0
2 years ago
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3 years ago
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Veseljchak [2.6K]
30-8.25= 21.75


21.75/3.75= 5.8, you can't buy .8 of a soda so he could buy 5 sodas.
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3 years ago
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