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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.

5 answers

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.

what are the other the other 3 answers?

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.

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

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: \( a > \frac{23}{x} \).