The sum of 𝑎 and 𝑏 is c. The number line shows 𝑎 and 𝑏.
_____________b____0_______________a_
Which statements about c are true?
□ |𝑎| < |𝑐|
□ |𝑎| = |𝑐|
□ |𝑎| > |𝑐|
□ 𝑐 < 0
□ 𝑐 = 0
□ 𝑐 > 0
Looks like #3,6 to me
since |a| > |b| and b<0, c is positive and between b and a.
Based on the given number line and the fact that the sum of 𝑎 and 𝑏 is 𝑐:
□ 𝑎 < 𝑐. Since 𝑎 is located to the left of 𝑐 on the number line, 𝑎 is less than 𝑐.
□ 𝟘 < 𝑏. Since 𝟘 is located to the left of 𝑏 on the number line, 𝟘 is less than 𝑏.
□ 𝑎 + 𝑏 = 𝑐.
□ 𝑐 > 𝟘. Since 𝑐 is located to the right of 𝟘 on the number line, 𝑐 is greater than 𝟘.
Therefore, the correct statements about 𝑐 are:
□ |𝑎| < |𝑐|
□ 𝑐 > 0
To determine which statements about c are true, we need to consider the positions of a, b, and 0 on the number line.
- The fact that a is to the right of b on the number line indicates that a > b.
- The sum of a and b is c. Since a > b, c will be to the right of a on the number line.
- Considering the above information, we can deduce that c > a.
Now, let's evaluate each statement:
□ |𝑎| < |𝑐|: This statement is not true because a is to the right of c on the number line, indicating that |a| > |c|.
□ |𝑎| = |𝑐|: This statement is not true because a is to the right of c on the number line, indicating that |a| > |c|.
□ |𝑎| > |𝑐|: This statement is true. Since a is to the right of c on the number line, |a| > |c|.
□ 𝑐 < 0: This statement is not true because c is to the right of a and b on the number line, indicating that c > 0.
□ 𝑐 = 0: This statement is not true because c is to the right of a and b on the number line, indicating that c > 0.
□ 𝑐 > 0: This statement is true. Since c is to the right of a and b on the number line, c > 0.
Therefore, the true statements are:
- □ |𝑎| > |𝑐|
- □ 𝑐 > 0