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Solve [tex]$w = t\left(r_1 + r_2\right)$[/tex] for [tex]$t$[/tex].
A. [tex]$t = w\left(r_1 + r_2\right)$[/tex] B. [tex]$t = \frac{w}{\left(r_1 + r_2\right)}$[/tex] C. [tex][tex]$t = w - \left(r_1 + r_2\right)$[/tex][/tex]
To solve the equation [tex]\( w = t(r_1 + r_2) \)[/tex] for [tex]\( t \)[/tex], we need to isolate [tex]\( t \)[/tex] on one side of the equation. Let's go through the steps in detail:
1. Start with the given equation: [tex]\[
w = t(r_1 + r_2)
\][/tex]
2. Isolate [tex]\( t \)[/tex] by dividing both sides of the equation by [tex]\( (r_1 + r_2) \)[/tex]: [tex]\[
\frac{w}{r_1 + r_2} = \frac{t(r_1 + r_2)}{r_1 + r_2}
\][/tex]
3. Simplify the right side of the equation: Since [tex]\( (r_1 + r_2) \)[/tex] appears in both the numerator and the denominator on the right side, they cancel out: [tex]\[
\frac{w}{r_1 + r_2} = t
\][/tex]
4. Thus, the solution for [tex]\( t \)[/tex] is: [tex]\[
t = \frac{w}{r_1 + r_2}
\][/tex]
Therefore, the correct formulation solving for [tex]\( t \)[/tex] is: [tex]\[
t = \frac{w}{r_1 + r_2}
\][/tex]
This is the correct solution for the given equation [tex]\( w = t(r_1 + r_2) \)[/tex].
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