Problem 47
Question
Solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? \(A=\frac{1}{2} h(a+b)\) for \(a\)
Step-by-Step Solution
Verified Answer
The solution for the equation for \(a\) is \(a = \frac{2A}{h} - b\).
1Step 1: Isolate terms with \(a\)
To solve the equation for \(a\), isolate the terms containing \(a\). Multiply both sides of the equation by 2 to eliminate the fraction: \(2A = h(a+b)\).
2Step 2: Divide by \(h\)
Next, the term on the right-hand side, \(h(a+b)\), can be deconstructed. To do this, divide both sides of the equation by \(h\): \(\frac{2A}{h} = a+b\).
3Step 3: Solve for \(a\)
Finally, isolate the variable \(a\) on one side of the equation. Subtract \(b\) from both sides: \(a = \frac{2A}{h} - b\).
Other exercises in this chapter
Problem 47
Solve equation by completing the square. $$ x^{2}+6 x=7 $$
View solution Problem 47
Solve each equation in Exercises 41–60 by making an appropriate substitution. $$x^{-2}-x^{-1}-20=0$$
View solution Problem 47
Contain rational equations with variables in denominators. For each equation, a. write the value or values of the variable that make a denominator zero. These a
View solution Problem 47
Perform the indicated operation(s) and write the result in standard form. $$ (2+i)^{2}-(3-i)^{2} $$
View solution