Which of the following shows the equation A=12(b1+b2)h correctly rearranged for the quantity of interest b1 ?(1 point)

Question

Responses

b1 =2A−b2h
b subscript 1 baseline equals Start Fraction upper A minus b subscript 2 baseline over h End Fraction

b1 =h−b22A
b subscript 1 baseline equals Start Fraction h minus b subscript 2 baseline over 2 upper A End Fraction

b1=2Ah−b2
b subscript 1 baseline equals Start Fraction 2 upper A over h End Fraction minus b subscript 2 baseline

b1 = h2A − b2

Answer 1

To rearrange the equation \( A = \frac{1}{2}(b_1 + b_2)h \) for \( b_1 \), we need to isolate \( b_1 \) step by step.

Starting with the original equation:

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

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

3. Finally, subtract \( b_2 \) from both sides to solve for \( b_1 \): \[ b_1 = \frac{2A}{h} - b_2 \]

Thus, the correct rearrangement of the equation for \( b_1 \) is: \[ b_1 = \frac{2A}{h} - b_2 \]

This matches with the option:

b1 = 2Ah − b2

So, the correct response is: b1 = 2Ah − b2.