Q. What is the value of x in the inequality 2x + 1 > 7?
A.
x < 3
B.
x > 3
C.
x < 4
D.
x > 4
Show solution
Solution
Subtract 1 from both sides: 2x > 6. Then divide by 2: x > 3.
Correct Answer:
B
— x > 3
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Q. What is the value of x in the inequality 3x - 4 < 5?
A.
x < 3
B.
x < 2
C.
x > 3
D.
x > 2
Show solution
Solution
Step 1: Add 4 to both sides: 3x < 9. Step 2: Divide both sides by 3: x < 3.
Correct Answer:
B
— x < 2
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Q. What is the value of x in the inequality 3x - 7 < 2?
A.
x < 3
B.
x < 2
C.
x > 3
D.
x > 2
Show solution
Solution
Step 1: Add 7 to both sides: 3x < 9. Step 2: Divide by 3: x < 3.
Correct Answer:
A
— x < 3
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Q. What is the value of x in the polynomial equation 3x^2 + 12x = 0?
A.
x = 0, -4
B.
x = 0, 4
C.
x = -3, -4
D.
x = 3, 4
Show solution
Solution
Step 1: Factor out 3x: 3x(x + 4) = 0. Step 2: Set each factor to zero: 3x = 0 or x + 4 = 0. Step 3: Solutions are x = 0 and x = -4.
Correct Answer:
A
— x = 0, -4
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Q. What is the value of x in the polynomial equation 3x^2 - 12 = 0?
A.
x = 2
B.
x = -2
C.
x = 4
D.
x = -4
Show solution
Solution
Add 12 to both sides: 3x^2 = 12. Divide by 3: x^2 = 4. Take the square root: x = ±4.
Correct Answer:
C
— x = 4
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Q. What is the value of x in the polynomial equation x^3 - 4x = 0?
A.
x = 0, 2, -2
B.
x = 1, -1, 0
C.
x = 4, -4, 0
D.
x = 3, -3, 0
Show solution
Solution
Factor out x: x(x^2 - 4) = 0. Thus, x = 0 or x^2 - 4 = 0, giving x = 2 or x = -2.
Correct Answer:
A
— x = 0, 2, -2
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Q. What is the value of x in the polynomial equation x^3 - 4x^2 + 4x = 0?
A.
x = 0, 2
B.
x = 1, 3
C.
x = 2, 4
D.
x = -1, 5
Show solution
Solution
Factor out x: x(x^2 - 4x + 4) = 0. This gives x = 0 or (x - 2)^2 = 0, so x = 2.
Correct Answer:
A
— x = 0, 2
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Q. What is the value of x in the polynomial equation x^3 - 4x^2 + x = 0?
A.
x = 0, 1, 4
B.
x = 0, 2, 3
C.
x = 1, 2, 3
D.
x = 0, -1, -4
Show solution
Solution
Factor out x: x(x^2 - 4x + 1) = 0. Thus, x = 0 or solve x^2 - 4x + 1 = 0.
Correct Answer:
A
— x = 0, 1, 4
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Q. What is the value of x in the quadratic equation x^2 - 5x + 6 = 0?
A.
x = 1 or x = 6
B.
x = 2 or x = 3
C.
x = 3 or x = 2
D.
x = 0 or x = 5
Show solution
Solution
Factor the equation: (x - 2)(x - 3) = 0. Thus, x = 2 or x = 3.
Correct Answer:
B
— x = 2 or x = 3
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Q. What is the vertex of the parabola given by the equation y = x^2 - 4x + 3?
A.
(2, -1)
B.
(2, 1)
C.
(1, 2)
D.
(3, 0)
Show solution
Solution
Step 1: Use the vertex formula x = -b/(2a): x = 4/(2*1) = 2. Step 2: Substitute x back into the equation: y = (2)^2 - 4(2) + 3 = 4 - 8 + 3 = -1. Step 3: Vertex is (2, -1).
Correct Answer:
A
— (2, -1)
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Q. What is the vertex of the parabola represented by the equation y = x^2 - 4x + 1?
A.
(2, -3)
B.
(2, -4)
C.
(4, 1)
D.
(1, 4)
Show solution
Solution
Use the vertex formula x = -b/2a: x = 4/2 = 2. Substitute x back to find y: y = 2^2 - 4(2) + 1 = -3. Vertex is (2, -3).
Correct Answer:
A
— (2, -3)
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Q. What is the vertex of the parabola represented by the equation y = x^2 - 4x + 3?
A.
(2, -1)
B.
(2, 1)
C.
(1, 2)
D.
(3, 0)
Show solution
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).
Correct Answer:
A
— (2, -1)
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Q. What is the vertex of the parabola represented by the equation y = x^2 - 4x + 4?
A.
(2, 0)
B.
(0, 4)
C.
(4, 0)
D.
(2, 4)
Show solution
Solution
The vertex can be found using the formula x = -b/(2a). Here, a = 1, b = -4, so x = 2. Substitute x back to find y: y = 0.
Correct Answer:
A
— (2, 0)
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Q. What is the vertex of the parabola represented by y = x^2 - 4x + 3?
A.
(2, -1)
B.
(2, 1)
C.
(1, 2)
D.
(3, 0)
Show solution
Solution
The vertex can be found using the formula x = -b/(2a). Here, a = 1, b = -4. Thus, x = 2. Plugging x back into the equation gives y = 1. So, the vertex is (2, 1).
Correct Answer:
A
— (2, -1)
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Q. What is the vertex of the quadratic equation y = x^2 - 4x + 3?
A.
(2, -1)
B.
(2, 1)
C.
(1, 2)
D.
(3, 0)
Show solution
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).
Correct Answer:
A
— (2, -1)
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Q. What is the vertex of the quadratic function y = 2x^2 - 8x + 5?
A.
(2, -3)
B.
(4, -3)
C.
(2, 5)
D.
(4, 5)
Show solution
Solution
The vertex can be found using the formula x = -b/(2a). Here, a = 2 and b = -8, so x = 8/4 = 2. Plugging x = 2 into the equation gives y = 2(2)^2 - 8(2) + 5 = -3. Thus, the vertex is (2, -3).
Correct Answer:
A
— (2, -3)
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Q. What is the vertex of the quadratic function y = x^2 - 4x + 3?
A.
(2, -1)
B.
(2, -4)
C.
(1, 2)
D.
(3, 0)
Show solution
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).
Correct Answer:
A
— (2, -1)
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Q. What is the vertical asymptote of y = tan(x)?
A.
x = 0
B.
x = π/2
C.
x = π
D.
x = 2π
Show solution
Solution
The vertical asymptotes of the tangent function occur at x = π/2 + nπ, where n is an integer.
Correct Answer:
B
— x = π/2
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Q. What is the vertical shift of the function y = 5sin(x) + 2?
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Solution
The vertical shift of the function y = Asin(Bx) + D is D. Here, D = 2, so the vertical shift is 2 units up.
Correct Answer:
B
— 2
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Q. What is the vertical shift of the function y = tan(x) + 2?
Show solution
Solution
The vertical shift is determined by the constant added to the function, which is +2.
Correct Answer:
C
— 2
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Q. What is the volume of a cube with a side length of 2 units?
A.
4 cubic units
B.
6 cubic units
C.
8 cubic units
D.
10 cubic units
Show solution
Solution
The volume V of a cube is given by V = side³. Here, V = 2³ = 8 cubic units.
Correct Answer:
C
— 8 cubic units
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Q. What is the volume of a cylinder with a radius of 2 units and a height of 5 units?
A.
20π
B.
10π
C.
15π
D.
25π
Show solution
Solution
The volume of a cylinder is calculated using the formula V = πr²h. Here, V = π(2)²(5) = π(4)(5) = 20π.
Correct Answer:
A
— 20π
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Q. What is the volume of a cylinder with a radius of 3 cm and a height of 5 cm?
A.
45π cm³
B.
30π cm³
C.
60π cm³
D.
15π cm³
Show solution
Solution
Volume = πr²h = π * 3² * 5 = 45π cm³.
Correct Answer:
A
— 45π cm³
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Q. What is the volume of a cylinder with a radius of 3 cm and a height of 5 cm? (Use π ≈ 3.14)
A.
141.3 cm³
B.
113.1 cm³
C.
94.2 cm³
D.
78.5 cm³
Show solution
Solution
Volume = π * (radius)² * height = 3.14 * (3)² * 5 = 141.3 cm³.
Correct Answer:
A
— 141.3 cm³
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Q. What is the volume of a cylinder with a radius of 3 units and a height of 5 units?
A.
45π
B.
30π
C.
15π
D.
60π
Show solution
Solution
The volume of a cylinder is given by V = πr²h. For r = 3 and h = 5, V = π(3)²(5) = π(9)(5) = 45π.
Correct Answer:
A
— 45π
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Q. What is the volume of a cylinder with a radius of 3 units and a height of 7 units?
A.
63π
B.
27π
C.
21π
D.
9π
Show solution
Solution
The volume V of a cylinder is given by V = πr²h. Here, V = π(3)²(7) = π(9)(7) = 63π.
Correct Answer:
A
— 63π
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Q. What is the x-intercept of the function y = cos(x) - 1?
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Solution
The x-intercept occurs when y = 0, which happens at x = 0 for cos(x) - 1.
Correct Answer:
A
— 0
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Q. What is the x-intercept of the function y = cos(x) in the interval [0, 2π]?
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Solution
The cosine function equals zero at x = π/2 and x = 3π/2. The x-intercepts in [0, 2π] are π/2 and 3π/2.
Correct Answer:
C
— π
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Q. What is the x-intercept of the line given by the equation 4x - 2y = 8?
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Solution
To find the x-intercept, set y = 0.\n1. 4x - 2(0) = 8\n2. 4x = 8\n3. x = 2.\nThe x-intercept is 2.
Correct Answer:
C
— 4
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Q. What is the y-intercept of the line given by the equation 3x + 2y = 6?
Show solution
Solution
Convert to slope-intercept form (y = mx + b).\n1. 2y = -3x + 6\n2. y = -1.5x + 3.\nThe y-intercept is 3.
Correct Answer:
B
— 3
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