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Chapter 1: Problem 34

In each term, give the numerical coefficient. 15

Short Answer

Expert verified
The numerical coefficient is 15.

Step by step solution

01

Identify the term

First, identify the term which needs to be evaluated. In this case, the term is simply '15'.
02

Recognize the structure of the term

Notice that the term '15' is a standalone number without any variables attached to it. It can be considered as a constant term.
03

Identify the numerical coefficient

The numerical coefficient of a term that is a standalone number (constant term) is the number itself. Therefore, the numerical coefficient of '15' is '15'.

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Key Concepts

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

constant term
In algebra, a constant term is a term that has a fixed value, meaning it does not change.
It does not have any variables attached to it.
For instance, in the term '15' from our exercise, '15' is a number that stands alone.
It is constant whether you are solving an equation or simply evaluating the term.

Here are some key points to remember about constant terms:
  • Constant terms do not change regardless of the values of the variables in an expression
  • They can be positive, negative, or zero
  • They are simply numbers
Understanding the concept of constant terms can help simplify many algebraic expressions and make problem-solving easier.
algebraic terms
Algebraic terms are parts of algebraic expressions that are separated by addition or subtraction.
A term can be a single number, a variable, or numbers and variables multiplied together.
For example, in the expression \(3x + 5y - 7\), there are three terms: '3x', '5y', and '-7'.
Each term has its own part:
  • Numerical coefficient: The number part of the term, like '3' in '3x'
  • Variable: The letter part, like 'x' in '3x'
  • Constant term: If the term is a standalone number, it is considered a constant, like '-7'
Recognizing these parts is essential for simplifying and solving algebraic expressions.
evaluating expressions
Evaluating expressions means finding the value of an algebraic expression when the variables are known.
Here is how you can evaluate a simple expression:
  • Substitute the known values of the variables into the expression
  • Perform the arithmetic operations following the proper order of operations (PEMDAS/BODMAS)
  • Simplify the expression to find the numerical result
For example, if you have the expression \(2x + 3\) and know that \(x = 4\), you substitute \(4\) for \(x\):
\(2(4) + 3 = 8 + 3 = 11\).
This way, evaluating expressions helps in finding specific values and understanding the relationships between different parts of the expression.

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Most popular questions from this chapter

Solve each problem. In \(2006,\) bachelor's degree recipients from private four-year institutions had an average of \(\$ 18,800\) in total student debt. This average increased \(\$ 1400\) by 2011 and then dropped \(\$ 300\) by \(2016 .\) What was the average amount of total student debt in \(2016 ?\) (Data from The College Board.)

Evaluate each expression for \(x=6, y=-4,\) and \(a=3\) \(\left(\frac{1}{3} x-\frac{4}{5} y\right)\left(-\frac{1}{5} a\right)\)

Write each sentence as an equation, using \(x\) as the variable. Then find the solution of the equation from the set of integers between -12 and \(12,\) inclusive. An integer is divisible by 9 if the sum of its digits is divisible by \(9,\) and not otherwise. (a) Is 2,287,321 divisible by \(9 ?\) (b) Is 4,114,107 divisible by \(9 ?\)

Write each sentence as an equation, using \(x\) as the variable. Then find the solution of the equation from the set of integers between -12 and \(12,\) inclusive. An integer is divisible by 8 if its last three digits form a number divisible by \(8,\) and not otherwise. (a) Is 2,923,296 divisible by \(8 ?\) (b) Is 7,291,623 divisible by \(8 ?\)

Write each sentence as an equation, using \(x\) as the variable. Then find the solution of the equation from the set of integers between -12 and \(12,\) inclusive. An integer is divisible by 2 if its last digit is divisible by \(2,\) and not otherwise. (a) Is 3,473,986 divisible by \(2 ?\) (b) Is 4,336,879 divisible by \(2 ?\)
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