The general form of the equation of a circle is x2 + y2 + 42x + 38y − 47 = 0. The equation of this circle in standard form is .

The center of the circle is at the point
, and its radius is
units.

The general form of the equation of a circle that has the same radius as the above circle is
.

Step-by-step explanation:

x² + y² + 42x + 38y - 47 = 0

Put the equation into standard (center-radius) form:

regroup terms

(x²+42x) + (y²+38y) = 47

complete the squares:

(x²+42x+21²) + (y²+38y+19²) = 47 + 21² + 19²

(x+21)² + (y+19)² = 849

center at (-21,-19)

radius = √849 units

The general form of the equation for a circle with radius √849 units is:

(x-h)² + (y-k)² = 849

where the (h,k) is the center.

every 5 customers that walk in, only 2 buy popcorn.

step-by-step explanation:

basically 2/5.

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