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Ira Lisetskai [31]
3 years ago
7

If y varies directly as x, and y is 180 when x is n and y is n when x is 5, what is the value of n?

Mathematics
2 answers:
Goshia [24]3 years ago
5 0

Answer:

EDGE 2020

Step-by-step explanation:

C) 30

trust me

defon3 years ago
3 0

For this case we have that if "y" varies directly with "x", we can propose:

y = kx

Where "k" represents the constant of proportionality.

According to the data:

180 = kn\\n = k5

We substitute the second equation in the first:

180 = k * k5\\180 = 5k ^ 2\\k ^ 2 = \frac {180} {5}\\k ^ 2 = 36

We apply root:

k = \pm \sqrt {36}\\k = \pm6

If k = 6, thenn = 6 * 5 = 30

Answer:

n = 30

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There are 22 rows of seats on a concert hall: 23 seats are in the 1st row, 27 seats on the 2nd row, 31 seats on the 3rd row, and
JulijaS [17]
We can model this situation with an arithmetic series.
we have to find the number of all the seats, so we need to sum up the number of seats in all of the 22 rows.

1st row: 23
2nd row: 27
3rd row: 31
Notice how we are adding 4 each time.

So we have an arithmetic series with a first term of 23 and a common difference of 4.

We need to find the total number of seats. To do this, we use the formula for the sum of an arithmetic series (first n terms):

Sₙ = (n/2)(t₁ + tₙ)

where n is the term numbers, t₁ is the first term, tₙ is the nth term

We want to sum up to 22 terms, so we need to find the 22nd term

Formula for general term of an arithmetic sequence:

tₙ = t₁ + (n-1)d,

where t1 is the first term, n is the term number, d is the common difference. Since first term is 23 and common difference is 4, the general term for this situation is

tₙ = 23 + (n-1)(4)

The 22nd term, which is the 22nd row, is

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There are 107 seats in the 22nd row.

So we use the sum formula to find the total number of seats:

S₂₂ = (22/2)(23 + 107) = 1430 seats

Total of 1430 seats.
If all the seats are taken, then the total sale profit is

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