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KengaRu [80]
3 years ago
14

What is the center and radius of the circle that has the equation x+72+y-42=49? Explain.

Mathematics
1 answer:
balu736 [363]3 years ago
3 0

Answer: The center is (-7, 4) and the radius is 7.

Step-by-step explanation:

The equation for a circle usually is:

(x - a)^2 + (y - b)^2 = R^2

where R is the radius, and (a, b) is the center of the circle.

I guess that the equation in this case is:

(x + 7)^2 + (y - 4)^2 = 49

then, in this case we have:

a = -7 and b = 4, then (a, b) = (-7, 4)

this means that the center of our circle is in the point (-7, 4)

and we know that:

R^2 = 49

R = √49 = 7

Then the radius is equal to 7.

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I NEED HELP WITH THESE TWO QUESTIONS PLZ DO NOT ANSWER IF YOU CANNOT EXPLAIN THE ANSWER
Murljashka [212]

9514 1404 393

Answer:

  1. asymptotes: x=-6, x=6, y=0; zero: x=0

  2. 20 blue fish

Step-by-step explanation:

1. The vertical asymptotes are where the denominator is zero. It factors as (x-6)(x+6), so will have zeros at x=-6 and x=6.

The horizontal asymptote is at the limit when x goes to infinity. Here, the ratio of highest-degree terms is 6/x, so the value goes to zero as x gets large.

The zero is where the numerator is zero, at x=0.

In summary:

  • vertical asymptotes: x = ±6
  • horizontal asymptote: y = 0
  • zero: (0, 0)

__

2. 60% are red, so 40% are blue. The difference in percentages is 60%-40% = 20%. The percentage of blue fish (40%) is twice the difference (=2×20%), so the number of blue fish is twice the difference in numbers.

  blue fish = 2×10 = 20 fish

<em><u>Check</u></em>

There are then 20+10=30 red fish, so 20+30=50 fish total. Reds are 30/50 = 60% of the total.

<u><em>Additional comment</em></u>

I find it often works well to work with ratios, which I can often do in my head. Other folks like to see equations. Here, we could write equations like ...

  r = 60%(r + b) . . . . reds are 60% of the total

  r - b = 10 . . . . . . . . 10 more reds than blues

We want the value of b, so we can eliminate r by substituting for it:

  r = 10 + b . . . . from the second equation above

  (10 +b) = 0.60((10 +b) + b) . . . . substitute for r

  10 +b = 6 + 1.2b . . . simplify

  4 = 0.2b . . . . subtract b+6

  20 = b . . . . . . multiply by 5 (there are 20 blue fish)

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