Question
The Celsius to Fahrenheit formula F=9/5C+32
Solve this formula for C. Check all answers that are true.
(4 points)
A. First step is to multiply by 9 on each side.
B. First step is to add 32 on both sides.
C. The next step from F-32=9/5 C, could be to multiply both sides by 5.
D. The next step from F-32=9/5 C, could be to divide both sides by 5.
E. Solution: 5/9-32 = C
F. To solve this equation for C, you would have to distribute at some point.
Solve this formula for C. Check all answers that are true.
(4 points)
A. First step is to multiply by 9 on each side.
B. First step is to add 32 on both sides.
C. The next step from F-32=9/5 C, could be to multiply both sides by 5.
D. The next step from F-32=9/5 C, could be to divide both sides by 5.
E. Solution: 5/9-32 = C
F. To solve this equation for C, you would have to distribute at some point.
Answers
GPT-4o mini
Let's solve the formula \( F = \frac{9}{5}C + 32 \) for C step by step and evaluate the provided statements.
1. **Start with the original equation**:
\[
F = \frac{9}{5}C + 32
\]
2. **First step**: Subtract 32 from both sides.
\[
F - 32 = \frac{9}{5}C
\]
3. **Next step**: Multiply both sides by \( \frac{5}{9} \) to isolate \( C \):
\[
C = \frac{5}{9}(F - 32)
\]
Now let's evaluate each option:
- **A. First step is to multiply by 9 on each side.**
- **False**. The first step was to subtract 32 from both sides.
- **B. First step is to add 32 on both sides.**
- **False**. The first step was to subtract 32, not add.
- **C. The next step from \( F - 32 = \frac{9}{5}C \) could be to multiply both sides by 5.**
- **False**. We actually multiply both sides by \( \frac{5}{9} \) to isolate \( C \).
- **D. The next step from \( F - 32 = \frac{9}{5}C \) could be to divide both sides by 5.**
- **False**. We should multiply by \( \frac{5}{9} \), not divide by 5.
- **E. Solution: \( \frac{5}{9}-32 = C \)**
- **False**. The correct expression is \( C = \frac{5}{9}(F - 32) \).
- **F. To solve this equation for C, you would have to distribute at some point.**
- **True**. After multiplying by \( \frac{5}{9} \), you would distribute it to both \( F \) and \( -32 \).
So, the only true statement is **F**.
1. **Start with the original equation**:
\[
F = \frac{9}{5}C + 32
\]
2. **First step**: Subtract 32 from both sides.
\[
F - 32 = \frac{9}{5}C
\]
3. **Next step**: Multiply both sides by \( \frac{5}{9} \) to isolate \( C \):
\[
C = \frac{5}{9}(F - 32)
\]
Now let's evaluate each option:
- **A. First step is to multiply by 9 on each side.**
- **False**. The first step was to subtract 32 from both sides.
- **B. First step is to add 32 on both sides.**
- **False**. The first step was to subtract 32, not add.
- **C. The next step from \( F - 32 = \frac{9}{5}C \) could be to multiply both sides by 5.**
- **False**. We actually multiply both sides by \( \frac{5}{9} \) to isolate \( C \).
- **D. The next step from \( F - 32 = \frac{9}{5}C \) could be to divide both sides by 5.**
- **False**. We should multiply by \( \frac{5}{9} \), not divide by 5.
- **E. Solution: \( \frac{5}{9}-32 = C \)**
- **False**. The correct expression is \( C = \frac{5}{9}(F - 32) \).
- **F. To solve this equation for C, you would have to distribute at some point.**
- **True**. After multiplying by \( \frac{5}{9} \), you would distribute it to both \( F \) and \( -32 \).
So, the only true statement is **F**.
AYD3N
what are the other the other 3 answers?
GPT-4o mini
Let’s analyze the statements again in a more detailed way, considering both correct and incorrect reasoning based on the steps to solve for \(C\) in the equation \(F = \frac{9}{5}C + 32\).
- **A. First step is to multiply by 9 on each side.**
**False**. The first step to isolate \(C\) involves subtracting 32 from both sides, not multiplying.
- **B. First step is to add 32 on both sides.**
**False**. The first step is to subtract 32 from both sides, not add.
- **C. The next step from \(F - 32 = \frac{9}{5}C\) could be to multiply both sides by 5.**
**False**. The correct procedure immediately after this step would involve multiplying both sides by \(\frac{5}{9}\) to isolate \(C\).
- **D. The next step from \(F - 32 = \frac{9}{5}C\) could be to divide both sides by 5.**
**False**. While it's possible to divide both sides by 5, it is not a sensible or useful step in this context. The better approach would be to multiply by \(\frac{5}{9}\) in order to eliminate the fraction.
- **E. Solution: \(\frac{5}{9}-32 = C\)**
**False**. This expression is not correctly formatted; rather, the result should state that \(C = \frac{5}{9}(F - 32)\).
- **F. To solve this equation for C, you would have to distribute at some point.**
**True**. After multiplying by \(\frac{5}{9}\), you will indeed distribute this factor across \(F - 32\).
Thus, there are **no other true answers** apart from **F**. All others (A, B, C, D, and E) are false.
- **A. First step is to multiply by 9 on each side.**
**False**. The first step to isolate \(C\) involves subtracting 32 from both sides, not multiplying.
- **B. First step is to add 32 on both sides.**
**False**. The first step is to subtract 32 from both sides, not add.
- **C. The next step from \(F - 32 = \frac{9}{5}C\) could be to multiply both sides by 5.**
**False**. The correct procedure immediately after this step would involve multiplying both sides by \(\frac{5}{9}\) to isolate \(C\).
- **D. The next step from \(F - 32 = \frac{9}{5}C\) could be to divide both sides by 5.**
**False**. While it's possible to divide both sides by 5, it is not a sensible or useful step in this context. The better approach would be to multiply by \(\frac{5}{9}\) in order to eliminate the fraction.
- **E. Solution: \(\frac{5}{9}-32 = C\)**
**False**. This expression is not correctly formatted; rather, the result should state that \(C = \frac{5}{9}(F - 32)\).
- **F. To solve this equation for C, you would have to distribute at some point.**
**True**. After multiplying by \(\frac{5}{9}\), you will indeed distribute this factor across \(F - 32\).
Thus, there are **no other true answers** apart from **F**. All others (A, B, C, D, and E) are false.
AYD3N
Solve the following for a: ax-5>18(1 point)
1. a>13/x
2. a=23/x
3. a=23+x
4. a>23/x
1. a>13/x
2. a=23/x
3. a=23+x
4. a>23/x
GPT-4o mini
To solve the inequality \( ax - 5 > 18 \) for \( a \), follow these steps:
1. **Add 5 to both sides**:
\[
ax > 18 + 5
\]
\[
ax > 23
\]
2. **Divide by \( x \) (assuming \( x \neq 0 \))**:
\[
a > \frac{23}{x}
\]
This shows that the solution is:
**1. \( a > \frac{23}{x} \)**
Now, let's evaluate the provided options:
1. **\( a > \frac{13}{x} \)** — **False**, the correct threshold is \( \frac{23}{x} \).
2. **\( a = \frac{23}{x} \)** — **False**, the inequality indicates a "greater than" relationship, not equality.
3. **\( a = 23 + x \)** — **False**, this is not derived from the original inequality.
4. **\( a > \frac{23}{x} \)** — **True**, this matches our derived inequality.
**Thus, the true statement corresponding to the solution is option 4: \( a > \frac{23}{x} \)**.
1. **Add 5 to both sides**:
\[
ax > 18 + 5
\]
\[
ax > 23
\]
2. **Divide by \( x \) (assuming \( x \neq 0 \))**:
\[
a > \frac{23}{x}
\]
This shows that the solution is:
**1. \( a > \frac{23}{x} \)**
Now, let's evaluate the provided options:
1. **\( a > \frac{13}{x} \)** — **False**, the correct threshold is \( \frac{23}{x} \).
2. **\( a = \frac{23}{x} \)** — **False**, the inequality indicates a "greater than" relationship, not equality.
3. **\( a = 23 + x \)** — **False**, this is not derived from the original inequality.
4. **\( a > \frac{23}{x} \)** — **True**, this matches our derived inequality.
**Thus, the true statement corresponding to the solution is option 4: \( a > \frac{23}{x} \)**.