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For the lines represented by the equation 5x^2 + 6xy + 5y^2 = 0, what is the sum
For the lines represented by the equation 5x^2 + 6xy + 5y^2 = 0, what is the sum of the slopes?
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Practice Questions
1 question
Q1
For the lines represented by the equation 5x^2 + 6xy + 5y^2 = 0, what is the sum of the slopes?
-6/5
0
6/5
1
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The sum of the slopes is given by - (coefficient of xy)/(coefficient of x^2) = -6/5.
Questions & Step-by-step Solutions
1 item
Q
Q: For the lines represented by the equation 5x^2 + 6xy + 5y^2 = 0, what is the sum of the slopes?
Solution:
The sum of the slopes is given by - (coefficient of xy)/(coefficient of x^2) = -6/5.
Steps: 7
Show Steps
Step 1: Identify the equation given, which is 5x^2 + 6xy + 5y^2 = 0.
Step 2: Recognize that this is a quadratic equation in two variables (x and y).
Step 3: Identify the coefficients in the equation: the coefficient of x^2 is 5, the coefficient of xy is 6.
Step 4: Use the formula for the sum of the slopes of the lines represented by the equation, which is - (coefficient of xy) / (coefficient of x^2).
Step 5: Substitute the values into the formula: - (6) / (5).
Step 6: Simplify the expression to get -6/5.
Step 7: Conclude that the sum of the slopes is -6/5.
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