Consider the formula S = 12lp + B which is used to find the surface area of a square-based pyramid. Which of the following correctly rearranges the formula for the quantity of interest p?(1 point) Responses p = S − B −l2 p equals upper S minus upper B minus Start Fraction l over 2 End Fraction p = 2S − Bl p equals Start Fraction 2 upper S minus upper B over l End Fraction p = 2(S − B)l p equals Start Fraction 2 left parenthesis upper S minus upper B right parenthesis over l End Fraction p = l2S − 2B p equals Start Fraction l over upper 2 S minus 2 upper B End Fraction

Answer 1

To rearrange the formula \( S = 12lp + B \) for the variable \( p \), let's follow these steps:

1. Start with the original equation: \[ S = 12lp + B \]

2. Subtract \( B \) from both sides: \[ S - B = 12lp \]

3. Divide both sides by \( 12l \): \[ p = \frac{S - B}{12l} \]

Now, we can see that none of the options provided match this answer directly. Based on your question, it appears there's a slight misunderstanding in the options given.

However, based on this manipulation: The form we have shows that \( p \) can be expressed in terms of \( S - B \) divided by \( 12l \), which is not represented in any of the listed options accurately.

If the options are to express \( p \) in other ways, we can derive:

• Commonly transferred variables or expressions like \( 2(S − B)l \), but that wouldn't apply here unless we multiplied/divided further.

Given that there seems to be a potential miscommunication, it might help to look for an option where you can factor out terms correctly if further simplified. But as per the clean rearrangement here, \( p = \frac{S - B}{12l} \) captures the sought rearrangement accurately.