To determine which situations could be represented by the numeric expression [tex]\(-8 + 10\)[/tex], let's carefully analyze each option provided.
Option A:
An atom has a positive charge because it contains 8 electrons that each have a charge of [tex]\(-1\)[/tex] and 10 protons that each have a charge of [tex]\(+1\)[/tex].
- Electrons carry a negative charge, so 8 electrons contribute a total charge of [tex]\(8 \times -1 = -8\)[/tex].
- Protons carry a positive charge, so 10 protons contribute a total charge of [tex]\(10 \times +1 = +10\)[/tex].
- The net charge of the atom is [tex]\(-8 + 10 = 2\)[/tex].
Hence, this situation could be represented by the expression [tex]\(-8 + 10\)[/tex].
Option B:
Janice sold 8 goldfish for a total of \[tex]$10. Therefore, she made a profit of \$[/tex]2.
- Selling goldfish for a total of \$10 does not clearly correlate with the addition of negative and positive values. The expression [tex]\(-8 + 10\)[/tex] suggests a combination of negative and positive changes, not a straightforward profit calculation.
- This situation is not directly represented by the expression [tex]\(-8 + 10\)[/tex].
Option C:
At a bus stop, 8 people got off the bus and 10 people got on. This means that the number of passengers increased by 2.
- 8 people getting off the bus can be represented as [tex]\(-8\)[/tex] (a decrease).
- 10 people getting on the bus can be represented as [tex]\(+10\)[/tex] (an increase).
- The change in the number of passengers is [tex]\(-8 + 10 = 2\)[/tex].
Hence, this situation could be represented by the expression [tex]\(-8 + 10\)[/tex].
Option D:
The temperature dropped 8 degrees and then another 10 degrees. The temperature is now [tex]\(-18\)[/tex] degrees.
- Dropping temperatures would be represented by negative changes. A drop of 8 degrees is [tex]\(-8\)[/tex] and another drop of 10 degrees is [tex]\(-10\)[/tex].
- The resulting temperature change would be [tex]\(-8 + -10 = -18\)[/tex].
However, the temperature change described here does not match the numeric expression [tex]\(-8 + 10\)[/tex], since it results in [tex]\(-18\)[/tex], not [tex]\(2\)[/tex].
In conclusion, the situations that can be represented by the numeric expression [tex]\(-8 + 10\)[/tex] are:
- Option A
- Option C
