Answer :
To solve the equation [tex]\(\frac{50}{5} + \frac{c}{5} = \frac{36}{5}\)[/tex], follow these steps:
1. Simplify the fractions:
- [tex]\(\frac{50}{5}\)[/tex] simplifies to [tex]\(10\)[/tex].
- [tex]\(\frac{36}{5}\)[/tex] stays as [tex]\(\frac{36}{5}\)[/tex] since it can't be simplified further.
So the equation becomes:
[tex]\[
10 + \frac{c}{5} = \frac{36}{5}
\][/tex]
2. Eliminate the fraction: To clear the fractions, multiply the entire equation by 5:
[tex]\[
5 \times 10 + 5 \times \frac{c}{5} = 5 \times \frac{36}{5}
\][/tex]
This simplifies to:
[tex]\[
50 + c = 36
\][/tex]
3. Solve for [tex]\(c\)[/tex]: Subtract 50 from both sides of the equation to isolate [tex]\(c\)[/tex]:
[tex]\[
c = 36 - 50
\][/tex]
4. Calculate:
[tex]\[
c = -14
\][/tex]
Therefore, the solution is [tex]\(c = -14\)[/tex].
Now, regarding the situations that can be modeled by linear equations:
- Situation A: The Barton family is driving at a constant speed (62 miles per hour). This is a linear situation because distance increases steadily over time.
- Situation B: The money grows at a constant rate of 4% per year. This is not linear; it's exponential because the growth rate applies to the increasing total over time.
- Situation C: A tree grows a consistent amount each year (2 feet per year). This is linear because its height increases by a fixed amount each year.
- Situation D: The coin is falling at a rate of 9.8 meters per second squared, indicating acceleration. This is not linear, as it's related to the quadratic relationship of acceleration.
- Situation E: The number of people decreases by a percentage every 10 minutes. This is exponential decay, not linear.
Thus, the situations that can be modeled by a linear equation are A and C.
1. Simplify the fractions:
- [tex]\(\frac{50}{5}\)[/tex] simplifies to [tex]\(10\)[/tex].
- [tex]\(\frac{36}{5}\)[/tex] stays as [tex]\(\frac{36}{5}\)[/tex] since it can't be simplified further.
So the equation becomes:
[tex]\[
10 + \frac{c}{5} = \frac{36}{5}
\][/tex]
2. Eliminate the fraction: To clear the fractions, multiply the entire equation by 5:
[tex]\[
5 \times 10 + 5 \times \frac{c}{5} = 5 \times \frac{36}{5}
\][/tex]
This simplifies to:
[tex]\[
50 + c = 36
\][/tex]
3. Solve for [tex]\(c\)[/tex]: Subtract 50 from both sides of the equation to isolate [tex]\(c\)[/tex]:
[tex]\[
c = 36 - 50
\][/tex]
4. Calculate:
[tex]\[
c = -14
\][/tex]
Therefore, the solution is [tex]\(c = -14\)[/tex].
Now, regarding the situations that can be modeled by linear equations:
- Situation A: The Barton family is driving at a constant speed (62 miles per hour). This is a linear situation because distance increases steadily over time.
- Situation B: The money grows at a constant rate of 4% per year. This is not linear; it's exponential because the growth rate applies to the increasing total over time.
- Situation C: A tree grows a consistent amount each year (2 feet per year). This is linear because its height increases by a fixed amount each year.
- Situation D: The coin is falling at a rate of 9.8 meters per second squared, indicating acceleration. This is not linear, as it's related to the quadratic relationship of acceleration.
- Situation E: The number of people decreases by a percentage every 10 minutes. This is exponential decay, not linear.
Thus, the situations that can be modeled by a linear equation are A and C.