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Veseljchak [2.6K]
4 years ago
15

Seo-Yun hosted a party. She had 50 party favors to give away, and she gave 3 party favors to each of her guests

Mathematics
1 answer:
fgiga [73]4 years ago
7 0

Answer:

Arithmetic sequence

Step-by-step explanation:

-We notice that the difference between the number of favors already given out between any two consecutive number of party guests has an additive increment.

-This increment is called the Common Difference and has a value of 3.

-The number of tickets available is 50.

Hence, the number of tickets already given out can be calculated using the formula:

a_n=-dn+S_n\\\\n= n^{th} \ guest\\d=common \ difference\\S_n=Total \ tickets \ available\\\\\therefore a_n=-3n+50

Hence, this is an Arithmetic Sequence.

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A car has an initial value of $20,000. The value then "depreciates" or decreases by 10% of its initial value each year. Which eq
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Answer:

D) v = -2,000y + 20,000.

Step-by-step explanation:

The question gives a linear relationship between two quantities.  This means that the relationship between the initial value of the car and the amount it depreciates each year is proportional, or constant.  Since the value of the car decreases by 10% of its initial value each year, then each year the value will decrease by 10% of 20,000 or 0.10 x 20000 = $2,000.  Since we know the value is decreasing each year, this amount would be subtracted from the initial value of $20,000.  So, D) v = -2,000y + 20,000 would be the only equation that represents this scenario.  

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3 years ago
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3 years ago
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These roots of the polynomial equation x^4-4x^3-2x^2+12x+9=0 are 3,-1,-1. Explain why the fourth root must be a real number. Fin
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Roots with imaginary parts always occur in conjugate pairs. Three of the four roots are known and they are all real, which means the fourth root must also be real.

Because we know 3 and -1 (multiplicity 2) are both roots, the last root r is such that we can write

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There are a few ways we can go about finding r, but the easiest way would be to consider only the constant term in the expansion of the right hand side. We don't have to actually compute the expansion, because we know by properties of multiplication that the constant term will be (-3)(1)(1)(-r)=3r.

Meanwhile, on the left hand side, we see the constant term is supposed to be 9, which means we have

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Other things we could have tried that spring to mind:

- three rounds of division, dividing the quartic polynomial by (x-3), then by (x+1) twice, and noting that the remainder upon each division should be 0

- rational root theorem

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Answer:

29

Step-by-step explanation:

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