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PtichkaEL [24]
3 years ago
9

in a lecture hall at a collage, the number of seats per row increased at a constand rate. The professor counts 21 seats in row 3

and 33 seats in row 7. How many sets are there in row 18?
Mathematics
1 answer:
Allushta [10]3 years ago
7 0

Answer:

  66 seats

Step-by-step explanation:

The rate of increase is ...

  (change in seats)/(change in rows) = (33 -21)/(7 -3) = 12/4 = 3 . . . seats/row

Then row 18 will have (18-3)·3 = 45 more seats than row 3, hence ...

  21 + 45 = 66 . . . . seats in row 18

_____

An explicit formula for the number of seats can be written as ...

  s = 21 +3(n-3) = 12 +3n

For n=18, this is ...

 s = 12 + 3(18) = 12 +54 = 66 . . . seats in row 18

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Artist 52 [7]

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Answer:

  "complete the square" to put in vertex form

Step-by-step explanation:

It may be helpful to consider the square of a binomial:

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The expression x² +x +1 is in the standard form of the expression on the right above. Comparing the coefficients of x, we see ...

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That means we can write ...

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But we need x² +x +1, so we need to add 3/4 to the binomial square in order to make the expressions equal:

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_____

Another way to consider this is ...

  x² +bx +c

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  = (x +b/2)² +(c -(b/2)²)

for b=1, c=1, this becomes ...

  x² +x +1 = (x +1/2)² +(1 -(1/2)²)

  = (x +1/2)² +3/4

_____

* This process, "rewrite bx, add and subtract (b/2)²," is called "completing the square"—especially when written as (x-h)² +k, a parabola with vertex (h, k).

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3 years ago
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Is it possible it’s (-2,2)
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dsp73

Answer:

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Step-by-step explanation:

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