Which of the following is equivalent to the expression 2x + 5y - 3x - 7y?

1. -x - 2y
2. -x + 2y
3. x - 2y
4. x + 2y
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Answer: A
Explanation:
• Explanation: 2x - 3x = -x, and 5y - 7y = -2y. Therefore, the expression simplifies to -x - 2y.
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If x + 2y = 10 and x - y = 2, what is the value of y?

1. 4
2. 3
3. 2
4. 1
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Answer: B
Explanation:
• Explanation: Add the equations x + 2y = 10 and x - y = 2 to eliminate x:(x + 2y) + (x - y) = 10 + 2 3y = 12 y = 4
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Which of the following is the equation of a line that passes through the point (2, 4) and has a slope of -3?

1. y = -3x
2. y = -3x + 4
3. y = -3x - 2
4. y = -3x + 10
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Answer: C
Explanation:
• Explanation: The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. The point (2, 4) is on the line, so we can use it to solve for b:4 = -3(2) + b b = 10 Therefore, the equation of the line is y = -3x + 10.
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Which of the following is the equation of a circle with center (3, -2) and radius 5?

1. (x - 3)^2 + (y - 2)^2 = 5
2. (x + 3)^2 + (y + 2)^2 = 5
3. (x - 3)^2 + (y + 2)^2 = 25
4. (x + 3)^2 + (y - 2)^2 = 25
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Answer: C
Explanation:
• Explanation: The equation of a circle with center (h, k) and radius r is (x - h)^2 + (y - k)^2 = r^2. Therefore, the equation of the circle with center (3, -2) and radius 5 is (x - 3)^2 + (y + 2)^2 = 25.
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If a rectangular prism has a length of 8, a width of 5, and a height of 3, what is its volume?

1. 40
2. 60
3. 80
4. 120
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Answer: B
Explanation:
• Explanation: The volume of a rectangular prism is found by multiplying its length, width, and height. Therefore, the volume of the prism is 8 x 5 x 3 = 60.
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If the square root of x is equal to y, what is the value of x?

1. `y^2`
2. y/2
3. y
4. 2y
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Answer: A
Explanation:
• N/A
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What is the slope of the line that passes through the points (2, 4) and (6, 8)?

1. 2-Jan
2. 1
3. 2
4. 4
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Answer: A
Explanation:
• Explanation: The formula for slope is (y₂ - y₁) / (x₂ - x₁). Plugging in the values, we get (8 - 4) / (6 - 2) = 4 / 4 = 1. Therefore, the slope of the line is 1.
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What is the value of x in the equation 2x + 7 = 15?

1. 4
2. 6
3. 8
4. 9
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Answer: B
Explanation:
• Explanation: Subtract 7 from both sides of the equation to get 2x = 8. Then divide both sides by 2 to get x = 4.
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What is the value of f(2) for the function f(x) = x² + 3x - 4?

1. -1
2. 0
3. 4
4. 8
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Answer: C
Explanation:
• Explanation: Substitute x = 2 into the function f(x) = x² + 3x - 4 to get f(2) = 2² + 3(2) - 4 = 4 + 6 - 4 = 6.
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What is the equation of a line that is perpendicular to y = 2x + 3 and passes through the point (1, 4)?

1. y = -1/2x + 9/2
2. y = -2x + 6
3. y = 1/2x + 7/2
4. y = 2x + 2
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Answer: A
Explanation:
• Explanation: The slope of a line perpendicular to y = 2x + 3 is -1/2 (since the slopes of perpendicular lines are negative reciprocals of each other). Using the point-slope formula, the equation of the line is y - 4 = -1/2(x - 1), which simplifies to y = -1/2x + 9/2.
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