Question 252283: Find the distance between the two points of intersection of y = x^2 -x and
y = 3x+5
a. √10 b. 6 c. 6√10 d. 8 e. 2√130
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Find the distance between the two points of intersection of y = x^2 -x and
y = 3x+5
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Find the 2 points of intersection:
y = x^2 -x and
y = 3x+5
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Since they both = y, the equal each other
x^2 - x = 3x + 5
x^2 - 4x - 5 = 0
(x-5)*(x+1) = 0
x = -1, y = 2 --> (-1,2)
x = 5, y = 20 --> (5,20)
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Find the distance:
s^2 = diffy^2 + diffx^2 = 6^2 + 18^2
s^2 = 36 + 324 = 360
x = sqrt(360) = 6sqrt(10)
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