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marshall27 [118]
3 years ago
8

The population of a city has increased by 26 % since it was last measured. If the current population is 44,100 , what was the pr

evious population?
Mathematics
1 answer:
postnew [5]3 years ago
5 0
44,100 × 0.26 = 11,466

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Which is the equation of a circle whose center is at the origin and that passes through the point (3, 5)?
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Answer:

x² + y² = 34

Formula:

  • (x - h)² + (y - k)² = r²                    where (h, k) is the center

<u>Here find the radius using distance formula</u>:                → origin : (0, 0)

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<u>Thus the equation of circle</u>:

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The easiest way to find the vertex is to convert this standard form equation into vertex form, which is y = a(x - h)^2 + k.

Firstly, put x^2 - 10x into parentheses: y = (x^2 - 10x) + 30

Next, we want to make what's inside the parentheses a perfect square. To do that, we need to divide the x coefficient by 2 and square it. In this case, the result is 25. Add 25 inside the parentheses and subtract 25 outside of the parentheses: y = (x^2 - 10x + 25) + 30 - 25

Next, factor what's inside the parentheses and combine like terms outside of the parentheses, and your vertex form is: y = (x - 5)^2 + 5.

Now going back to the formula of the vertex form, y = a(x - h)^2 + k, the vertex is (h,k). Using our vertex equation, we can see that the vertex is (5,5).

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