/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 65 Solve each formula for the speci... [FREE SOLUTION] | 91影视

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Chapter 1: Problem 65

Solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? $$A=\frac{1}{2} h(a+b) \text { for } a$$

Short Answer

Expert verified
The formula \(a = \frac{2A - bh}{h}\) represents the length of one base of a trapezoid given the area, the length of the other base, and the height.

Step by step solution

01

Identify the current formula and what it represents

The given formula \(A=\frac{1}{2} h(a+b)\) represents the area of a trapezoid. The goal is to rearrange this formula to isolate \(a\).
02

Multiply both sides by 2

To remove the fraction from the equation, multiply both sides of the equation by 2. This results in \(2A = h(a + b)\).
03

Distribute h

Distribute \(h\) to both \(a\) and \(b\) to get \(2A = ah + bh\).
04

Isolate a

To isolate \(a\), subtract \(bh\) from both sides, which results in the equation \(a = \frac{2A - bh}{h}\).

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Most popular questions from this chapter

In Exercises \(127-130,\) solve each equation by the method of your choice. $$ \sqrt{3} x^{2}+6 x+7 \sqrt{3}=0 $$

Will help you prepare for the material covered in the next section. $$\text { Simplify: } \sqrt{18}-\sqrt{8}$$

Solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? $$V=\frac{1}{3} B h \text { for } B$$

Describe the relationship between the real solutions of \(a x^{2}+b x+c=0\) and the graph of \(y=a x^{2}+b x+c\).

If you are given a quadratic equation, how do you determine which method to use to solve it?
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