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
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter1: Variables, Expressions, And Integers
Section1.4: Comparing And Ordering Integers
Problem 1E
Related questions
Question
![**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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faf74fb9e-b533-4057-a79c-37c4b56e1189%2F186a8bff-6718-42ed-948e-d6b4b9cce615%2Fizvegj_processed.jpeg&w=3840&q=75)
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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