/*! 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 43 Solve each formula for the indic... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 43

Solve each formula for the indicated letter. $$ A=a t+b t, \text { for } t $$

Short Answer

Expert verified
\[ t = \frac{A}{a + b} \]

Step by step solution

01

- Combine like terms

The formula given is \[ A = at + bt \]. Notice that both terms on the right-hand side have a common variable, \( t \). Combine these like terms: \[ A = (a + b)t \].
02

- Isolate variable t

To solve for \( t \), divide both sides of the equation by \( a + b \): \[ t = \frac{A}{a + b} \].

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

combine like terms
Combining like terms is an essential step in simplifying algebraic expressions. When we say 'like terms', we refer to terms in an equation that have the same variable raised to the same power. For example, in the equation \( A = at + bt \), both \(at\) and \(bt\) are like terms because they both have the variable \(t\).

To combine them, simply add their coefficients together. In this problem, the coefficients are \(a\) and \(b\). So, combining like terms gives us:
\[ A = (a + b)t \]
This operation simplifies the equation, making it easier to manipulate and solve in subsequent steps.
isolate variable
Isolating the variable means getting the variable you're solving for alone on one side of the equation. After combining like terms, we have: \[ A = (a + b)t \]

Let's isolate \(t\) by performing the same operation on both sides of the equation. Since \(t\) is multiplied by \(a + b\), do the opposite (divide) to both sides of the equation:
\[ \frac{A}{a + b} = t \]
Now \(t\) is isolated. This technique is useful whenever you need to solve for a specific variable in an equation.
solve for variable
Solving for the variable means finding the value of the variable in terms of the other quantities in the equation. After isolating \(t \) in the equation:

\[ t = \frac{A}{a + b} \]
You've now solved for \(t\). This expresses \(t\) as a fraction where the numerator is \(A \) and the denominator is the sum of \(a \) and \(b \).

This solution method is widely applicable in algebra. Whether you're dealing with simple linear equations or more complex ones, these steps can help you find the solution.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Solve using the addition and multiplication principles. $$ \frac{2}{3}\left(\frac{7}{8}-4 x\right)-\frac{5}{8}<\frac{3}{8} $$

Match the sentence with one of the following: $$ a

Use an inequality and the five-step process to solve each problem. Aiden can be paid for his masonry work in one of two ways: Plan \(A: \quad \$ 300\) plus \(\$ 9.00\) per hour Plan \(B:\) Straight \(\$ 12.50\) per hour. Suppose that the job takes \(n\) hours. For what values of \(n\) is plan B better for Aiden?

Use an inequality and the five-step process to solve each problem. Reduced Fat Oreo " cookies contain 4.5 of fat per serving. In order for a food to be labeled "reduced fat," it must have at least \(25 \%\) less fat than the regular item. What can you conclude about the number of grams of fat in a serving of the regular Oreo cookies?

Use an inequality and the five-step process to solve each problem. Following the guidelines of the Food and Drug Administration, Dale tries to eat at least 5 servings of fruits or vegetables each day. For the first \(\operatorname{six}\) days of one week, she had \(4,6,7,4,6,\) and 4 servings. How many servings of fruits or vegetables should Dale eat on Saturday, in order to average at least 5 servings per day for the week?
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.