Question

Which of the following shows the equation A=12(b1+b2)h correctly rearranged for the quantity of interest b1 ?(1 point) Responses b1 =h−b22A b subscript 1 baseline equals Start Fraction h minus b subscript 2 baseline over 2 upper A End Fraction b1 = h2A − b2 b subscript 1 baseline equals Start Fraction h over 2 upper A End Fraction minus b subscript 2 baseline b1=2Ah−b2 b subscript 1 baseline equals Start Fraction 2 upper A over h End Fraction minus b subscript 2 baseline b1 =2A−b2h

Answer 1

Let's start with the original equation you provided:

\[ A = \frac{1}{2}(b_1 + b_2) h \]

To rearrange this equation for \( b_1 \), we can follow these steps:

1. Multiply both sides by 2 to eliminate the fraction:
\[ 2A = (b_1 + b_2)h \]

2. Divide both sides by \( h \):
\[ \frac{2A}{h} = b_1 + b_2 \]

3. Finally, isolate \( b_1 \) by subtracting \( b_2 \) from both sides:
\[ b_1 = \frac{2A}{h} - b_2 \]

Now, comparing this with the provided response options, we find that:

- **b1 = 2A/h - b2** (This matches our rearrangement)

So, the correct choice is:

**b1 = 2A/h - b2**.