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1. |
Daniel wants to send Jasmine flowers for her birthday. At the flower store, he can choose between roses, irises, or carnations. The salesperson tells Daniel that 50% of the customers buy roses, 30% buy carnations, and 20% buy irises. Which of the following is a valid conjecture? |
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A. |
Jasmine will be excited to receive flowers for her birthday. |
B. |
The salesperson likes carnations. |
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C. |
Daniel will buy Jasmine irises. |
D. |
More customers buy roses than carnations. |
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Hint |
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2. |
Determine if the following conjecture is true or false? Explain. Given: x2 = 4
Conjecture: x = 4 or x = -4 |
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A. |
True; two answers are always more accurate than one answer. |
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B. |
True; squaring a positive number results in a positive number and squaring a negative number results in a positive number. |
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C. |
False; the square root of a positive number is always a positive number. |
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D. |
False; the square root of 4 is 2 or -2. |
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Hint |
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3. |
Determine the contrapositive of the following if-then statement.
If three points are noncollinear, then they form a triangle. |
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A. |
If three points do not form a triangle, then they are not noncollinear. |
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B. |
If three points form a triangle, then they are noncollinear. |
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C. |
If three points do not form a triangle, then they are noncollinear. |
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D. |
If three points are not noncollinear, then they do not form a triangle. |
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Hint |
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4. |
Which statement follows from statements (1) and (2) by the Law of Syllogism? (1) If an object is a square, then it is a rhombus.
(2) If an object is a rhombus, then it is an equilateral. |
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A. |
An object is a square. |
B. |
An object is a rhombus. |
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C. |
If an object is an equilateral, then it is a square. |
D. |
If an object is a square, then it is an equilateral. |
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Hint |
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5. |
Justify step 2 in solving  |
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A. |
Subtraction Property (=) |
B. |
Division Property (=) |
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C. |
Distributive Property (=) |
D. |
Multiplication Property (=) |
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Hint |
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6. |
For the proof shown, provide statement 2. |
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A. |
AB = BC, DE = EF |
B. |
AB = DE |
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C. |
AC = DE, AB = DF |
D. |
AC = DF, BC = EF |
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Hint |
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7. |
Which statement explains why  |
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A. |
Angles adjacent to the same angle or to congruent angles are congruent. |
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B. |
Vertical angles are congruent. |
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C. |
Angles complementary to the same angle or to congruent angles are congruent. |
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D. |
All right angles are congruent. |
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Hint |
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8. |
In order to find the contrapositive of a conditional, you must first find the _____ and then find the _____ of each part. |
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A. |
hypothesis, converse |
B. |
converse, negation |
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C. |
inverse, negation |
D. |
converse, inverse |
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Hint |
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9. |
Using the following true conditional and hypothesis, which statement would follow from the Law of Detachment?A square has four right angles. WXYZ is a square. |
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A. |
If WXYZ is not a square, then it has four right angles. |
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B. |
WXYZ has four right angles. |
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C. |
If WXYZ is not a square, then it does not have four right angles. |
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D. |
If WXYZ has four right angles, then it is a square. |
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Hint |
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10. |
The starting point of a proof is the _____ of the conditional and the end is the _____ of the conditional. |
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A. |
conclusion, hypothesis |
B. |
conjecture, justification |
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C. |
hypothesis, conclusion |
D. |
statement, reason |
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Hint |
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11. |
For the proof shown, provide statement 3. |
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A. |
AB = CD |
B. |
AB = BA |
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C. |
CD = EF |
D. |
AB = EF |
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Hint |
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12. |
Which of the following is not one of the five essential parts needed to construct a good proof? |
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A. |
Assume what you are trying to prove is true. |
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B. |
State the theorem to be proved. |
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C. |
List the given information. |
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D. |
If possible, draw a diagram to illustrate the given information. |
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Hint |
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13. |
The freshman class of 63 students conducted a survey to compare how many students took Spanish as opposed to French as a foreign language. The results are shown in the Venn diagram. How many students studied both Spanish and French? |
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A. |
40 |
B. |
55 |
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C. |
1 |
D. |
15 |
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Hint |
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14. |
The freshman class of 63 students conducted a survey to compare how many students took Spanish as opposed to French as a foreign language. The results are shown in the Venn diagram. How many students studied Spanish or French? |
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A. |
25 |
B. |
63 |
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C. |
55 |
D. |
56 |
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Hint |
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15. |
If  and  lie in plane P. Which of the following postulates can be used to show that  lies in plane P? |
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A. |
Through any two points, there is exactly one line. |
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B. |
If two points lie in a plane, then the entire line containing those points lies in that plane. |
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C. |
If two planes intersect, then their intersection is a line. |
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D. |
A plane contains at least three points not on the same line. |
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Hint |
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16. |
If  and  form a linear pair and m = 72, find m. |
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A. |
18 |
B. |
144 |
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C. |
108 |
D. |
72 |
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Hint |
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