Find the center and the radius of the circle with the equation x^2+6x+y^2+4y+12=0
1 answer:
Answer:
(x + 3)² + (y+ 2)² = 1²
Step-by-step explanation:
The <em>standard form</em> for the equation of a circle with centre (a, b) and radius r is
(x - a)² + (y - b)² = r²
x² + 6x + y² + 4y + 12 = 0
<em>Step 1.</em> Subtract the constant from each side
x² + 6x + y² + 4y = -12
<em>Step 2.</em> Complete the squares for x and y
Square half the coefficients of x and y
(x² + 6x + 3²) + (y² + 4y + 2²) = -12 + 3² + 2²
<em>Step 3</em>. Write the lhs as squares of binomials
(x + 3)² + (y+ 2)² = -12 + 3² + 2²
Step 4. Convert the rhs to a square
(x + 3)² + (y+ 2)² = -12 + 9 + 4
(x + 3)² + (y+ 2)² = 1
(x + 3)² + (y+ 2)² = 1²
The graph below shows that this is the equation for a circle with
centre (-3, -2) and radius 1.
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Step-by-step explanation:
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The means is defined as the quotient between the sum of all elements and the total number.
Mathematically, it would be defined as
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Then, we solve for
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For example, if the sum of all elements is 700, the total number of apples would be
Therefore, the expression that represents the total number of apples is