The equation form of a circle is (x - a)² + (y - b)² = r²
Equation 1:
x² - 4x + y² + 12y - 20 = 0 ⇒ use the completing the square method for x² - 4x and y² + 12y
x² - 4x = (x - 2)² - 4
y² + 12y = (y + 6)² - 36
Put them back together, we have
(x - 2)² - 4 + (y + 6)² - 36 - 20 = 0
(x - 2)² + (y + 6)² -4 - 36 - 20 = 0
(x - 2)² + (y + 6)² - 60 = 0
(x - 2)² + (y + 6)² = 60
Equation 2:
x² + y² + 6x - 8y - 10 = 0
(x² + 6x) + (y² - 8y) -10 = 0
(x + 3)² - 9 + (y - 4)² -16 - 10 = 0
(x + 3)² + (y - 4)² - 9 - 16 - 10 = 0
(x + 3)² + (y - 4)² - 35 = 0
(x + 3)² + (y - 4)² = 35
Equation 3:
3x² + 12x + 3y² +18y - 15 = 0
3 [x² + 4x + y² + 6y - 5] = 0
x² + 4x + y² + 6y - 5 = 0
(x² + 4x) + (y² + 6y) - 5 = 0
(x + 2)² - 4 + (y + 3)² - 9 - 5 = 0
(x + 2)² + (y + 3)² - 4 - 9 -5 = 0
(x + 2)² + (y + 3)² - 18 = 0
(x + 2)² + (y + 3)² = 18
Equation 4:
5x² + 5y² - 10x + 20y - 30 = 0
5 [x² + y² - 2x + 4y - 6] = 0
x² + y² - 2x + 4y - 6 = 0
(x² - 2x) + (y² + 4y) - 6 = 0
(x - 1)² - 2 + (y + 2)² - 4 - 6 =0
(x - 1)² + (y + 2)² - 2 - 4 - 6 = 0
(x - 1)² + (y + 2)² - 12 = 0
(x - 1)² + (y + 2)² = 12
Equation 5:
2x² + 2y² - 24x - 16y -8 = 0
2 [x² + y² - 12x - 8y - 4] = 0
x² + y² - 12x - 8y - 4 = 0
(x² - 12x) + (y² - 8y) - 4 = 0
(x - 6)² - 36 + (y - 4)² - 16 - 4 = 0
(x - 6)² + (y - 4)² -36 - 16 - 4 = 0
(x - 6)² + (y - 4)² - 56 = 0
(x - 6)² + (y - 4)² = 56
Equation 6:
x² + y² + 2x - 12y - 9 = 0
(x² + 2x) + (y² - 12y) - 9 = 0
(x + 1)² - 1 + (y - 6)² - 36 - 9 = 0
(x + 1)² + (y - 6)² - 1 - 36 - 9 = 0
(x + 1)² + (y - 6)² - 46 = 0
(x + 1)² + (y - 6)² = 46
When a point divide a line segment A (x1,y1) B (x2,y2) into a ration of a:b, the coordinates of that point is x1+[a/(a+b)](x2-x1), y1+[a/(a+b)](y2-y1)
so x=0+(2/3)(6-0)=4
y=4+(2/3)(8-4)=6&2/3 (mixed number 6 and 2 over 3)
(4, 6&2/3) is the answer.
<em> ╭⊰✿ ♥ May Berlin ♥ ✿⊱╮</em>
<em> Answer:</em>
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<em> Step-by-step explanation:</em>
<em> Step 1: Divide both sides by x.</em>
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<em>╭⊰✿ ♥ Hope this helped you! ♥ ✿⊱╮</em>
Answer:
each row has 20 seats. write and solve an equation to find the number xx of rows in the theater. an equation that represents this problem is =1200=1200
