Table of contents

0. Review of Algebra4h 18m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 22m
10. Combinatorics & Probability1h 45m

1. Equations & Inequalities

Linear Equations

College Algebra

1. Equations & Inequalities

Linear Equations

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1:19 minutes

Problem 37

Textbook Question

In Exercises 35–54, solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe?A = (1/2)bh for b

Verified step by step guidance

Start with the given formula: $ A = \frac{1}{2}bh $.

To solve for $ b $, first eliminate the fraction by multiplying both sides of the equation by 2: $ 2A = bh $.

Next, isolate $ b $ by dividing both sides of the equation by $ h $: $ b = \frac{2A}{h} $.

Recognize that this formula is the area of a triangle, where $ A $ is the area, $ b $ is the base, and $ h $ is the height.

The formula describes how to find the base $ b $ of a triangle when you know its area $ A $ and height $ h $.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Algebraic Manipulation

Algebraic manipulation involves rearranging equations to isolate a specific variable. This process includes operations such as addition, subtraction, multiplication, and division applied to both sides of the equation. Understanding how to manipulate formulas is essential for solving for a variable, as it allows one to express the variable in terms of others.

Area of a Triangle

The formula A = (1/2)bh represents the area of a triangle, where 'A' is the area, 'b' is the base, and 'h' is the height. This formula is derived from the concept that the area of a triangle is half the product of its base and height. Recognizing this formula helps in understanding the geometric context of the problem and the significance of the variables involved.

Solving for a Variable

Solving for a variable means finding an expression that represents that variable in terms of others. In this case, we need to isolate 'b' in the equation A = (1/2)bh. This involves reversing the operations applied to 'b' and may require multiplying or dividing by other terms in the equation, which is a fundamental skill in algebra.