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Which numbers from the set{-63,-54, -41, 11, 13, 76, 80, 130, 132, 137} are congruent to 7 mod 13? 137 13, 130 -63, 80, 132 -54, -41, 11, 76

Which numbers from the set{-63,-54, -41, 11, 13, 76, 80, 130, 132, 137} are congruent to 7 mod 13? 137 13, 130 -63, 80, 132 -54, -41, 11, 76

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter1: Variables, Expressions, And Integers
Section1.4: Comparing And Ordering Integers
Problem 1E
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**Question:** Which numbers from the set \(\{-63, -54, -41, 11, 13, 76, 80, 130, 132, 137\}\) are congruent to 7 mod 13? **Options:** - [ ] 137 - [ ] 13, 130 - [ ] -63, 80, 132 - [ ] -54, -41, 11, 76 **Explanation:** To determine which numbers are congruent to 7 mod 13, we need to check the remainder when each number is divided by 13. If the remainder is 7, then the number is congruent to 7 mod 13. Calculate for each number: 1. **137 mod 13** doesn't yield a remainder of 7. 2. **13 mod 13 = 0**; **130 mod 13** doesn't yield 7. 3. **-63 mod 13 = 7**, **80 mod 13** doesn't yield 7, **132 mod 13** doesn't yield 7. 4. **-54 mod 13** doesn't yield 7, **-41 mod 13 = 7**, **11 mod 13 = 11**, **76 mod 13** doesn't yield 7. Thus, from the set, only **-63** and **-41** are congruent to 7 mod 13. The correct answer is: - [x] -63, -41
Transcribed Image Text:**Question:** Which numbers from the set \(\{-63, -54, -41, 11, 13, 76, 80, 130, 132, 137\}\) are congruent to 7 mod 13? **Options:** - [ ] 137 - [ ] 13, 130 - [ ] -63, 80, 132 - [ ] -54, -41, 11, 76 **Explanation:** To determine which numbers are congruent to 7 mod 13, we need to check the remainder when each number is divided by 13. If the remainder is 7, then the number is congruent to 7 mod 13. Calculate for each number: 1. **137 mod 13** doesn't yield a remainder of 7. 2. **13 mod 13 = 0**; **130 mod 13** doesn't yield 7. 3. **-63 mod 13 = 7**, **80 mod 13** doesn't yield 7, **132 mod 13** doesn't yield 7. 4. **-54 mod 13** doesn't yield 7, **-41 mod 13 = 7**, **11 mod 13 = 11**, **76 mod 13** doesn't yield 7. Thus, from the set, only **-63** and **-41** are congruent to 7 mod 13. The correct answer is: - [x] -63, -41
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