Answered

Solve the equation [tex]A=\frac{h\left(b_1+b_2\right)}{2}[/tex] for [tex]b_1[/tex].

A. [tex]b_1 = \frac{2A}{h} - b_2[/tex]
B. [tex]b_1 = \frac{A}{h} - 2b_2[/tex]
C. [tex]b_1 = \frac{2h}{A} - 2b_2[/tex]
D. [tex]b_1 = \frac{A}{h} - b_2[/tex]



Answer :

GinnyAnswer
To solve the equation [tex]\( A = \frac{h(b_1 + b_2)}{2} \)[/tex] for [tex]\( b_1 \)[/tex], follow these steps:

1. Start with the given equation:
[tex]\[ A = \frac{h(b_1 + b_2)}{2} \][/tex]

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

3. Distribute [tex]\( h \)[/tex] on the right side:
[tex]\[ 2A = h b_1 + h b_2 \][/tex]

4. Isolate [tex]\( h b_1 \)[/tex] by subtracting [tex]\( h b_2 \)[/tex] from both sides:
[tex]\[ 2A - h b_2 = h b_1 \][/tex]

5. Solve for [tex]\( b_1 \)[/tex] by dividing both sides by [tex]\( h \)[/tex]:
[tex]\[ b_1 = \frac{2A - h b_2}{h} \][/tex]

6. Simplify the fraction:
[tex]\[ b_1 = \frac{2A}{h} - b_2 \][/tex]

Hence, the solution to the equation for [tex]\( b_1 \)[/tex] is:
[tex]\[ b_1 = \frac{2A}{h} - b_2 \][/tex]

Among the provided options, the correct one is:
[tex]\[ b_1 = \frac{2A}{h} - b_2 \][/tex]

So the correct answer is:
[tex]\[ b_1 = \frac{2A}{h} - b_2 \][/tex]

Other Questions