/*! 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 72 In Exercises 69 and 70, identify... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 72

In Exercises 69 and 70, identify the variable(s) in the expression. $$ \frac{6}{t}-22 $$

Short Answer

Expert verified
The variable in the expression \( \frac{6}{t}-22 \) is 't'.

Step by step solution

01

Identify the Expression

Look at the given expression: \( \frac{6}{t}-22 \).
02

Identify the Variable

In the given expression \( \frac{6}{t}-22 \), the letter 't' is unknown, hence it is treated as a variable.
03

Describe the Variable

The variable in the expression \( \frac{6}{t}-22 \) is 't'. It represents an unknown quantity that we could try to solve or use in further calculations.

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.

Identifying Variables
In algebraic expressions, **variables** are symbols or letters that represent unknown quantities. These are essential in mathematics because they allow us to create general formulas or solve problems using different values. In the expression \( \frac{6}{t}-22 \), the letter 't' is a variable.
When identifying a variable in an expression:
  • Look for any letters or symbols which are not numbers.
  • See how the variable is used in the expression (it might be part of a fraction, an exponent, a product, etc.).
  • Understand that each variable can vary, meaning that it can take on different numerical values.
The context or the problem statement usually gives meaning to these symbols. Once a variable is identified, it becomes a tool for representing real-world situations or mathematical relationships.
Algebraic Expressions
An **algebraic expression** is a combination of numbers, operations, and variables. Expressions can include:
  • Constants: Fixed numerical values (like 6 or 22 in the expression \( \frac{6}{t}-22 \)).
  • Variables: Symbols that can change (such as 't' in this case).
  • Operators: Mathematical symbols that denote operations (e.g., plus, minus, multiply, divide).
  • Terms: Individual parts of the expression separated by plus or minus signs.
For the expression \( \frac{6}{t}-22 \):
  • The term \( \frac{6}{t} \) involves a variable in a division operation.
  • "-22" is a constant term being subtracted from \( \frac{6}{t} \).
Algebraic expressions play a crucial role in developing equations and functions, offering a way to model problems and make predictions.
Unknown Quantities
In mathematics, **unknown quantities** are values that need to be found or solved. They are often denoted by variables like 't' in the expression \( \frac{6}{t}-22 \). Understanding unknown quantities is vital as they form the basis of problems in algebra.
When dealing with unknown quantities, remember:
  • They represent specific numbers that solve an equation or make a statement true.
  • You often work to "solve for" these quantities, which means finding the values of the variables that make the expression or equation valid.
  • In practical applications, these values often represent measurable items, such as time, distance, or quantities in a recipe.
Unknown quantities in expressions like \( \frac{6}{t}-22 \) allow us to pose and solve a wide variety of mathematical questions, helping us tackle challenging or real-world problems by finding what these variables could possibly stand for.

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

In Exercises \(63-68\), simplify the expression. $$ t^{2} \cdot t^{5} $$

In Exercises 51-54, determine whether each value of \(x\) is a solution of the equation. \(\frac{5}{x-1}+\frac{1}{x}=5\) (a) \(x=3\) (b) \(x=\frac{1}{6}\)

Determine which verbal phrase(s) is (are) equivalent to the expression \(n+4\). (a) 4 more than \(n\) (b) the sum of \(n\) and 4 (c) \(n\) less than 4 (d) the ratio of \(n\) to 4 (e) the total of 4 and \(n\)

Determine which equations are equivalent to \(14=x+8\). (a) \(x+8=14\) (b) \(8 x=14\) (c) \(x-8=14\) (d) \(8+x=14\) (e) \(2(x+4)-x=14\) (f) \(3(x+6)-2 x+5=14\)

In Exercises 33-38, justify each step of the equation. Then identify any properties of equality used to solve the equation. $$ \begin{aligned} x+4 &=16 \\ x+4-4 &=16-4 \\ x &=12 \end{aligned} $$
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Decision Maths

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Pure Maths

Read Explanation

Logic and Functions

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.