Q. If two triangles are similar, and the lengths of the sides of the first triangle are 3, 4, and 5, what are the lengths of the corresponding sides of the second triangle if the ratio is 2:3?
A.
4, 5, 6
B.
6, 8, 10
C.
2, 3, 4
D.
1.5, 2, 2.5
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Solution
If the ratio is 2:3, then the sides of the second triangle are (3 * 3/2), (4 * 3/2), (5 * 3/2) = 4.5, 6, 7.5. The closest whole numbers are 6, 8, 10.
Correct Answer:
B
— 6, 8, 10
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Q. If two triangles are similar, and the lengths of the sides of the first triangle are 3 cm, 4 cm, and 5 cm, what are the lengths of the corresponding sides of the second triangle if the ratio of similarity is 2:1?
A.
6 cm, 8 cm, 10 cm
B.
3 cm, 4 cm, 5 cm
C.
1.5 cm, 2 cm, 2.5 cm
D.
4 cm, 5 cm, 6 cm
Show solution
Solution
If the ratio is 2:1, then the sides of the second triangle are 3*2, 4*2, and 5*2, which gives 6 cm, 8 cm, and 10 cm.
Correct Answer:
A
— 6 cm, 8 cm, 10 cm
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Q. If two triangles are similar, and the lengths of the sides of the first triangle are 3, 4, and 5, what are the lengths of the corresponding sides of the second triangle if the shortest side is 6?
A.
6, 8, 10
B.
9, 12, 15
C.
12, 16, 20
D.
15, 20, 25
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Solution
The ratio of the sides of similar triangles is constant. If the shortest side of the first triangle (3) corresponds to 6, then the sides are scaled by a factor of 2. Thus, the other sides are 4*2=8 and 5*2=10.
Correct Answer:
A
— 6, 8, 10
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Q. If two triangles are similar, what can be said about their areas?
A.
They are equal
B.
They are proportional to the square of the ratio of their corresponding sides
C.
They are proportional to the ratio of their corresponding sides
D.
They cannot be compared
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Solution
The areas of similar triangles are proportional to the square of the ratio of their corresponding sides.
Correct Answer:
B
— They are proportional to the square of the ratio of their corresponding sides
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Q. If two triangles are similar, what can be said about their corresponding angles?
A.
They are equal
B.
They are supplementary
C.
They are complementary
D.
They are unequal
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Solution
In similar triangles, corresponding angles are equal.
Correct Answer:
A
— They are equal
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Q. If two triangles are similar, what can be said about their corresponding sides?
A.
They are equal.
B.
They are proportional.
C.
They are congruent.
D.
They are not related.
Show solution
Solution
In similar triangles, the corresponding sides are proportional.
Correct Answer:
B
— They are proportional.
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Q. If two triangles are similar, what is the ratio of their areas if the ratio of their corresponding sides is 3:5?
A.
3:5
B.
9:25
C.
15:25
D.
6:10
Show solution
Solution
The ratio of the areas of similar triangles is the square of the ratio of their corresponding sides. Thus, (3/5)² = 9/25.
Correct Answer:
B
— 9:25
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Q. If two triangles are similar, what is the ratio of their areas if the ratio of their corresponding sides is 3:4?
A.
3:4
B.
9:16
C.
12:16
D.
1:1
Show solution
Solution
The ratio of the areas of similar triangles is the square of the ratio of their corresponding sides. Therefore, (3/4)² = 9/16.
Correct Answer:
B
— 9:16
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Q. If two triangles are similar, what is the ratio of their corresponding sides if the ratio of their areas is 9:16?
A.
3:4
B.
2:3
C.
4:3
D.
1:2
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Solution
The ratio of the sides of similar triangles is the square root of the ratio of their areas. sqrt(9:16) = 3:4.
Correct Answer:
A
— 3:4
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Q. If two triangles are similar, what is true about their corresponding angles?
A.
They are equal
B.
They are supplementary
C.
They are complementary
D.
They are different
Show solution
Solution
In similar triangles, corresponding angles are equal.
Correct Answer:
A
— They are equal
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Q. If two triangles are similar, what is true about their corresponding sides?
A.
They are equal in length
B.
They are proportional
C.
They are perpendicular
D.
They are congruent
Show solution
Solution
In similar triangles, the lengths of corresponding sides are proportional.
Correct Answer:
B
— They are proportional
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Q. If two triangles are similar, which of the following is true about their corresponding sides?
A.
They are equal
B.
They are proportional
C.
They are congruent
D.
They are perpendicular
Show solution
Solution
In similar triangles, the corresponding sides are proportional to each other.
Correct Answer:
B
— They are proportional
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Q. If two triangles have sides in the ratio 3:4, what can be said about their areas?
A.
The areas are in the ratio 3:4.
B.
The areas are in the ratio 9:16.
C.
The areas are equal.
D.
The areas are not related.
Show solution
Solution
The areas of similar triangles are in the ratio of the squares of their corresponding sides. Therefore, (3:4)² = 9:16.
Correct Answer:
B
— The areas are in the ratio 9:16.
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Q. If two triangles have sides in the ratio 3:4, what is the ratio of their areas?
A.
3:4
B.
9:16
C.
12:16
D.
6:8
Show solution
Solution
The ratio of the areas of two similar triangles is the square of the ratio of their corresponding sides. Therefore, (3:4)² = 9:16.
Correct Answer:
B
— 9:16
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Q. If two triangles have sides in the ratio 3:4:5, what can be said about their similarity?
A.
They are similar
B.
They are congruent
C.
They are not similar
D.
Not enough information
Show solution
Solution
Triangles with sides in the same ratio are similar.
Correct Answer:
A
— They are similar
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Q. If two triangles have sides in the ratio 3:4:5, what type of triangle are they?
A.
Equilateral
B.
Isosceles
C.
Right
D.
Scalene
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Solution
A triangle with sides in the ratio 3:4:5 is a right triangle, as it satisfies the Pythagorean theorem.
Correct Answer:
C
— Right
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Q. If x^2 + 6x + 9 = 0, what are the roots?
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Solution
The polynomial can be factored as (x + 3)(x + 3) = 0, giving the root x = -3.
Correct Answer:
A
— -3
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Q. If x^2 - 4x + 4 = 0, what is the repeated root?
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Solution
Factoring gives (x - 2)(x - 2) = 0, so the repeated root is x = 2.
Correct Answer:
A
— 2
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Q. If x^2 - 4x + k has a double root, what is the value of k?
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Solution
For a double root, the discriminant must be zero: b^2 - 4ac = 0. Here, 4^2 - 4(1)(k) = 0. Thus, 16 - 4k = 0, leading to k = 4.
Correct Answer:
A
— 4
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Q. If x^2 - 6x + 9 = 0, what is the repeated root?
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Solution
The polynomial can be factored as (x - 3)(x - 3) = 0, giving a repeated root of x = 3.
Correct Answer:
A
— 3
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Q. If you divide 1/2 by 1/4, what do you get?
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Solution
1/2 ÷ 1/4 = 1/2 x 4/1 = 2.
Correct Answer:
C
— 2
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Q. If you eat 1/4 of a pizza and there are 3 pizzas, how much pizza is left?
A.
2.25
B.
2.5
C.
2
D.
1.75
Show solution
Solution
3 pizzas - (3 * 1/4) = 3 - 0.75 = 2.25 pizzas left.
Correct Answer:
B
— 2.5
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Q. If you eat 1/4 of a pizza and there are 4 slices, how many slices are left?
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Solution
4 slices - 1 slice (1/4 of 4) = 3 slices left.
Correct Answer:
A
— 3
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Q. If you eat 1/4 of a pizza and your friend eats 1/4 of the same pizza, how much of the pizza is left?
A.
1/2
B.
1/4
C.
3/4
D.
1/8
Show solution
Solution
1 - (1/4 + 1/4) = 1/2 of the pizza is left.
Correct Answer:
A
— 1/2
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Q. If you flip a fair coin three times, what is the probability of getting exactly two heads?
A.
1/8
B.
3/8
C.
3/4
D.
1/2
Show solution
Solution
The probability of getting exactly 2 heads in 3 flips = C(3,2) * (1/2)^2 * (1/2)^1 = 3/8.
Correct Answer:
B
— 3/8
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Q. If you have 0.75 of a pizza and eat 0.25, how much is left?
A.
0.25
B.
0.5
C.
0.75
D.
1.0
Show solution
Solution
0.75 - 0.25 = 0.5
Correct Answer:
B
— 0.5
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Q. If you have 0.8 of a pizza and eat 0.3, how much is left?
A.
0.3
B.
0.4
C.
0.5
D.
0.6
Show solution
Solution
0.8 - 0.3 = 0.5
Correct Answer:
B
— 0.4
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Q. If you have 1.2 liters of juice and pour out 0.2 liters, how much juice is left?
A.
0.8
B.
1.0
C.
1.2
D.
1.4
Show solution
Solution
1.2 - 0.2 = 1.0
Correct Answer:
A
— 0.8
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Q. If you have 1.2 liters of juice and pour out 0.7 liters, how much juice is left?
A.
0.3
B.
0.4
C.
0.5
D.
0.6
Show solution
Solution
1.2 - 0.7 = 0.5
Correct Answer:
D
— 0.6
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Q. If you have 1.2 liters of juice and you drink 0.5 liters, how much juice is left?
A.
0.7 liters
B.
0.6 liters
C.
0.5 liters
D.
0.8 liters
Show solution
Solution
1.2 - 0.5 = 0.7 liters
Correct Answer:
A
— 0.7 liters
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