Consider the formula S = 1/2lp + 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)Responsesp = 2(S − B)lp equals Start Fraction 2 left parenthesis upper S minus upper B right parenthesis over l End Fractionp = l2S − 2Bp equals Start Fraction l over upper 2 S minus 2 upper B End Fractionp = S − B −l2p equals upper S minus upper B minus Start Fraction l over 2 End Fractionp = 2S − Bl

Answer 1

To rearrange the formula \( S = \frac{1}{2}lp + B \) for the quantity of interest \( p \), we will isolate \( p \) on one side of the equation.

Here are the steps for rearranging the formula:

1. Start with the original formula: \[ S = \frac{1}{2}lp + B \]

2. Subtract \( B \) from both sides: \[ S - B = \frac{1}{2}lp \]

3. Multiply both sides by \( 2 \) to eliminate the fraction: \[ 2(S - B) = lp \]

4. Finally, divide both sides by \( l \): \[ p = \frac{2(S - B)}{l} \]

The correct rearrangement of the formula for \( p \) is: \[ p = \frac{2(S - B)}{l} \]

So, the correct answer is: \( p = \frac{2(S - B)}{l} \)