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pogonyaev
3 years ago
9

Write the number of permutations in factorial form. Then simplify, how many different ways can you and six of your friends sit i

n your assigned seats in math class
A)6!; 120
B)6!;720
c)7!;2,520
D) 7!;5,040
Mathematics
2 answers:
kari74 [83]3 years ago
6 0
You and 6 of your friends. Total of 7 people.

The answer is D.) 7! ; 5,040
Rainbow [258]3 years ago
6 0

Answer: D) 7!;5,040

Step-by-step explanation:

Given: The number of friends = 7

Permutations says that the number of different ways of arranging r objects out  of n objects is given by ;-

^nP_r=\dfrac{n!}{(n-r)!}

By permutations the number of different ways they can sit is given by :-

^7P_7=\dfrac{7!}{(7-7)!}=\dfrac{7!}{0!}\\\\=7\times6\times5\times4times3\times2\times1\\\\=5,040

Therefore, the different ways can you and six of your friends sit in your assigned seats in math class = 5,040.

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Which is a factor of the polynomial f(x) = 6x4 – 21x3 – 4x2 + 24x – 35?
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<span>I note that this problem starts out with "Which is a factor of ... "  This implies that you were given several answer choices.  If that's the case, it's unfortunate that you haven't shared them.

I thought I'd try finding roots of this function using synthetic division.  See below:

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Please use " ^ " to denote exponentiation.  Thanks.

Possible zeros of this poly are factors of 35:  plus or minus 1, plus or minus 5, plus or minus 7.  Use synthetic division; determine whether or not there is a non-zero remainder in each case.  If none of these work, form rational divisors from 35 and 6 and try them:  5/6, 7/6, 1/6, etc.

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By graphing this function, I found that the graph crosses the x-axis at 7/2.  There is another root.

Using synth. div. to check whether or not 7/2 is a root:

         ___________________________
7/2   /   6    -21    -4    24    -35
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        ----------- ------------------------------
           6        0     -4    10       0

Because the remainder is zero, 7/2 (or 3.5) is a root of the polynomial.  Thus, (x-3.5), or (x-7/2), is a factor.

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