Q1. What is the value of x in the equation x^2 - 9 = 0?
Solution:
Step 1: Factor the equation: (x - 3)(x + 3) = 0. Step 2: Set each factor to zero: x - 3 = 0 or x + 3 = 0. Step 3: Solutions are x = 3 and x = -3.
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Q2. What is the solution to the equation 3(x - 1) = 12?
Solution:
Step 1: Divide both sides by 3: x - 1 = 4. Step 2: Add 1 to both sides: x = 5.
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Q3. What is the vertex of the parabola represented by the equation y = x^2 - 4x + 3?
Solution:
Step 1: Use the vertex formula x = -b/2a: x = 4/2 = 2. Step 2: Substitute x back into the equation: y = 2^2 - 4(2) + 3 = -1. Vertex is (2, -1).
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Q4. What is the solution to the equation 3(x - 2) = 9?
Solution:
Step 1: Divide both sides by 3: x - 2 = 3. Step 2: Add 2 to both sides: x = 5.
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Q5. Which of the following is a factor of the polynomial x^2 - 5x + 6?
Solution:
Step 1: Factor the polynomial: (x - 2)(x - 3). Step 2: The factors are (x - 2) and (x - 3).
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Q6. What is the slope of the line represented by the equation 2y = 4x + 6?
Solution:
Step 1: Rewrite in slope-intercept form: y = 2x + 3. Step 2: The slope (m) is 2.
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Q7. What is the vertex of the quadratic function y = x^2 - 4x + 3?
Solution:
Step 1: Use the vertex formula x = -b/2a. Here, a = 1, b = -4. Step 2: x = 4/2 = 2. Step 3: Substitute x back: y = 2^2 - 4*2 + 3 = -1. Vertex is (2, -1).
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Q8. Which of the following is the correct factorization of x^2 - 9?
Solution:
Step 1: Recognize it as a difference of squares: a^2 - b^2 = (a - b)(a + b). Step 2: Here, a = x, b = 3. So, (x - 3)(x + 3).
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Q9. What is the solution to the equation 4x - 7 = 5?
Solution:
Step 1: Add 7 to both sides: 4x = 12. Step 2: Divide both sides by 4: x = 3.
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Q10. What is the solution to the quadratic equation x^2 + 4x + 4 = 0?
Solution:
Step 1: Factor the equation: (x + 2)(x + 2) = 0. Step 2: Set the factor to zero: x + 2 = 0. Solution is x = -2.
