/*! 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 7 Give the numerical coefficient a... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 7

Give the numerical coefficient and the degree of each term. $$ \frac{t}{6} $$

Short Answer

Expert verified
Numerical coefficient: \( \frac{1}{6} \), Degree: 1.

Step by step solution

01

Identify the Numerical Coefficient

The numerical coefficient is the number that multiplies the variable. In the term \(\frac{t}{6}\), the variable \(t\) is divided by 6. This can be rewritten as \(\frac{1}{6}t\). Therefore, the numerical coefficient is \(\frac{1}{6}\).
02

Determine the Degree of the Term

The degree of a term is the exponent of the variable. In \(\frac{t}{6} = \frac{1}{6}t\), the variable \(t\) is to the power of 1. Therefore, the degree of the term is 1.

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.

degree of a term
The degree of a term is a measure of the power of the variable in that term.
It tells us how many times the variable is multiplied by itself.
For example, in the term \(x^3\), the variable \(x\) is raised to the 3rd power. Thus, the degree is 3.
In the original exercise with the term \(\frac{t}{6}\), the term can be rewritten as \(\frac{1}{6}t\). Here, the \(t\) is raised to the power of 1, making the degree of the term 1.Understanding the degree of a term is important in algebra because:
  • It helps in classifying terms and polynomials.
  • It is crucial for solving equations and inequalities.
  • High-degree terms have more significant impacts on the graph of a polynomial function.
Next time you see a term, just check the power of the variable to find its degree!
algebraic expressions
Algebraic expressions are combinations of variables, numbers, and operations (like addition or multiplication).
They can be as simple as \(3x\) or as complex as \(5xy + 2x - 7\).
They are a fundamental part of algebra and appear in almost every math problem.
In the given exercise, the term \(\frac{t}{6}\) is an algebraic expression.
Its components are:
  • \(t\) - the variable
  • \(\frac{1}{6}\) - the numerical coefficient
Algebraic expressions are used to represent real-world situations.
For example, if \(t\) were the amount of time you spend studying, \(\frac{1}{6}t\) could represent the fraction of that time spent on math homework.Remember:
  • Terms in algebraic expressions are separated by plus or minus signs.
  • Each term can have a coefficient, a variable, and an exponent.
variable exponent
A variable exponent refers to the power to which a variable is raised in a term.
For instance, in \(x^2\), the exponent is 2, making \(x\) squared.
Exponents tell you how many times to multiply the variable by itself.
  • In the term \(\frac{t}{6}\), we can rewrite it as \(\frac{1}{6} t\), where \(t\) has an exponent of 1.
Exponents are essential because:
  • They play a significant role in determining the degree of a term.
  • They affect the slope and curvature of graphs in algebraic functions.
  • They are used in rules of exponents for simplifying expressions.
So, in any algebraic term, always look for the exponent to determine the influence of the variable.

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

Simplify each expression so that no negative exponents appear in the final result. Assume that all variables represent nonzero real numbers. $$ a^{-3} a^{2} a^{-4} $$

Evaluate. Express answers in standard notation. $$ \frac{840,000 \times 0.03}{0.00021 \times 600} $$

Simplify each expression so that no negative exponents appear in the final result. Assume that all variables represent nonzero real numbers. $$ \left(\frac{8 x^{-6} y^{3}}{x^{4} y^{-4}}\right)^{-2} $$

Find each product. $$ (m-5 p)\left(m^{2}-2 m p+3 p^{2}\right) $$

Write each number in standard notation. $$ 8.91 \times 10^{2} $$
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation

Geometry

Read Explanation

Mechanics Maths

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.