Q. What are the roots of the quadratic equation x^2 - 4 = 0?
A.
-2, 2
B.
0, 4
C.
1, -1
D.
2, -2
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Solution
Step 1: Factor the equation: (x - 2)(x + 2) = 0. Step 2: Set each factor to zero: x - 2 = 0 or x + 2 = 0. Step 3: Roots are x = -2 and x = 2.
Correct Answer:
A
— -2, 2
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Q. What are the roots of the quadratic equation x^2 - 4x - 5 = 0?
A.
-1, 5
B.
1, -5
C.
5, -1
D.
5, 1
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Solution
Step 1: Factor the equation: (x - 5)(x + 1) = 0. Step 2: Set each factor to zero: x - 5 = 0 or x + 1 = 0. Step 3: Roots are x = 5 and x = -1.
Correct Answer:
A
— -1, 5
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Q. What are the roots of the quadratic equation x^2 - 5x + 6 = 0?
A.
x = 1, 6
B.
x = 2, 3
C.
x = -2, -3
D.
x = 0, 6
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Solution
Step 1: Factor the equation: (x - 2)(x - 3) = 0. Step 2: Set each factor to zero: x - 2 = 0 or x - 3 = 0. Step 3: Solutions are x = 2 and x = 3.
Correct Answer:
B
— x = 2, 3
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Q. What are the roots of the quadratic equation: x^2 + 6x + 9 = 0?
A.
-3, -3
B.
3, 3
C.
0, 9
D.
1, -1
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Solution
Factor the equation as (x + 3)(x + 3) = 0. Thus, the root is x = -3 (a double root).
Correct Answer:
A
— -3, -3
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Q. What are the solutions to the equation x^2 - 10x + 21 = 0?
A.
x = 3, 7
B.
x = -3, -7
C.
x = 1, 21
D.
x = 0, 10
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Solution
Factoring gives (x - 3)(x - 7) = 0. Thus, the solutions are x = 3 and x = 7.
Correct Answer:
A
— x = 3, 7
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Q. What are the solutions to the equation x^2 - 10x + 25 = 0?
A.
x = 5
B.
x = 0, 5
C.
x = 10
D.
x = 2, 3
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Solution
The equation can be factored as (x - 5)(x - 5) = 0. Thus, the solution is x = 5 (a repeated root).
Correct Answer:
A
— x = 5
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Q. What are the solutions to the equation x^2 - 4 = 0?
A.
x = 2, -2
B.
x = 4, -4
C.
x = 0, 4
D.
x = 0, -4
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Solution
Factoring gives (x - 2)(x + 2) = 0. Thus, the solutions are x = 2 and x = -2.
Correct Answer:
A
— x = 2, -2
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Q. What are the solutions to the equation x^2 - 6x + 9 = 0?
A.
x = 3, 3
B.
x = -3, -3
C.
x = 6, 0
D.
x = 0, 6
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Solution
The equation can be factored as (x - 3)(x - 3) = 0. Thus, the solution is x = 3 with multiplicity 2.
Correct Answer:
A
— x = 3, 3
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Q. What are the solutions to the equation x^2 - 9 = 0?
A.
x = 3, -3
B.
x = 0, 9
C.
x = 1, -1
D.
x = 2, -2
Show solution
Solution
Factoring gives (x - 3)(x + 3) = 0. Thus, the solutions are x = 3 and x = -3.
Correct Answer:
A
— x = 3, -3
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Q. What are the solutions to the quadratic equation x^2 + 4x + 4 = 0?
A.
x = -2, -2
B.
x = 2, 2
C.
x = -4, 0
D.
x = 0, 4
Show solution
Solution
Step 1: Factor the equation: (x + 2)(x + 2) = 0. Step 2: Set the factor to zero: x + 2 = 0. Step 3: Solution is x = -2 (double root).
Correct Answer:
A
— x = -2, -2
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Q. What can be concluded if two angles are supplementary and one of them is 90 degrees?
A.
Both angles are acute.
B.
Both angles are right angles.
C.
The other angle is 90 degrees.
D.
The other angle is obtuse.
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Solution
If two angles are supplementary, their sum is 180 degrees. If one angle is 90 degrees, the other must also be 90 degrees.
Correct Answer:
C
— The other angle is 90 degrees.
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Q. What can be concluded if two angles are supplementary and one of them is an exterior angle formed by a transversal intersecting two parallel lines?
A.
They are both acute.
B.
They are both obtuse.
C.
One is an interior angle.
D.
They are equal.
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Solution
If one angle is an exterior angle formed by a transversal intersecting two parallel lines, the other angle must be an interior angle, as they are supplementary.
Correct Answer:
C
— One is an interior angle.
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Q. What can be concluded if two lines are cut by a transversal and the alternate exterior angles are equal?
A.
The lines are parallel.
B.
The lines are perpendicular.
C.
The lines intersect.
D.
No conclusion can be made.
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Solution
If the alternate exterior angles are equal, by the Alternate Exterior Angles Theorem, the lines are parallel.
Correct Answer:
A
— The lines are parallel.
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Q. What can be concluded if two lines are cut by a transversal and the alternate interior angles are equal?
A.
The lines are parallel.
B.
The lines are perpendicular.
C.
The lines intersect.
D.
The angles are complementary.
Show solution
Solution
If the alternate interior angles are equal, it can be concluded that the two lines are parallel.
Correct Answer:
A
— The lines are parallel.
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A.
0.90
B.
1.00
C.
1.25
D.
1.50
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Solution
0.25 + 0.75 = 1.00
Correct Answer:
B
— 1.00
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A.
0.6
B.
0.7
C.
0.8
D.
0.9
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A.
0.8
B.
0.9
C.
1.0
D.
1.1
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Solution
0.4 + 0.6 = 1.0
Correct Answer:
A
— 0.8
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A.
1.0
B.
1.5
C.
2.0
D.
2.5
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A.
0.6
B.
0.7
C.
0.8
D.
0.9
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Solution
0.5 + 0.3 = 0.8
Correct Answer:
B
— 0.7
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A.
0.8
B.
1.0
C.
1.2
D.
1.4
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Solution
0.6 + 0.4 = 1.0
Correct Answer:
B
— 1.0
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A.
2.5
B.
3.0
C.
3.5
D.
4.0
Show solution
A.
1.0
B.
1.2
C.
1.4
D.
1.6
Show solution
A.
1.0
B.
0.5
C.
1.5
D.
0.75
Show solution
Solution
0.75 + 0.25 = 1.0
Correct Answer:
A
— 1.0
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A.
3.0
B.
3.5
C.
4.0
D.
4.5
Show solution
A.
0.8
B.
0.9
C.
1.0
D.
1.1
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Solution
0.9 + 0.1 = 1.0
Correct Answer:
C
— 1.0
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A.
0.5
B.
0.6
C.
0.7
D.
0.8
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Solution
0.9 - 0.2 = 0.7
Correct Answer:
B
— 0.6
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A.
4.0
B.
5.0
C.
6.0
D.
7.0
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Solution
1.0 ÷ 0.2 = 5.0
Correct Answer:
A
— 4.0
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A.
1.8
B.
2.0
C.
2.2
D.
2.4
Show solution
Solution
1.2 + 0.8 = 2.0
Correct Answer:
A
— 1.8
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A.
2.8
B.
3.0
C.
3.2
D.
3.4
Show solution
Solution
1.2 + 1.8 = 3.0
Correct Answer:
A
— 2.8
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