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Chapter 7: Problem 25

Fill in the blanks. A \(____\) is a letter that represents a number.

Short Answer

Expert verified
The completed sentence is: 'A variable is a letter that represents a number.'

Step by step solution

01

Understanding the Definition

First, think about what in mathematics is a letter that represents a number. In algebraic expressions, this is commonly done.
02

Fill in the blank

The answer should be 'variable'. So the complete sentence becomes: 'A variable is a letter that represents a number.'

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Key Concepts

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

Variables
Variables are like placeholders in algebra that help us work with unknown or changing values. They are usually represented by letters like \(x\), \(y\), or \(z\). Here鈥檚 why variables are important and how they work:
  • **Representation:** They allow us to generalize mathematical problems and express relationships between numbers.
  • **Flexibility:** By using variables, we can form equations and formulas that apply to many instances, not just specific numbers.
  • **Problem Solving:** Variables help to set up equations that can be solved to find unknown values. This is essential in areas like physics, engineering, and everyday problem-solving.
Remember, whenever you encounter a variable, it鈥檚 just a symbol that can take on different values depending on the problem or context.
Algebraic Expressions
An algebraic expression is a combination of numbers, variables, and operations (like addition or multiplication). These expressions form the foundation of algebra. Here鈥檚 what you need to know:
  • **Components:** Typically includes numbers (constants), variables, and arithmetic operations. Example: \(3x + 4\).
  • **Simplification:** These expressions can often be simplified by combining like terms or using other arithmetic rules.
  • **Equations:** When you set algebraic expressions equal to each other, you create equations, which can be solved to find the value of variables.
Algebraic expressions allow us to model real-world situations mathematically, making them essential for solving everyday problems.
Mathematics Definitions
Understanding the language of mathematics is crucial. Definitions help us grasp concepts and solve problems accurately. Here鈥檚 a look at the role of definitions in math:
  • **Clarity:** Definitions ensure that we have a clear understanding of terms and concepts, avoiding misunderstandings.
  • **Consistency:** They provide a consistent framework for discussing mathematical ideas, which is crucial for learning and communication.
  • **Foundation:** Many complex concepts build on basic definitions, so having a solid grasp on them is essential to progressing in math.
When studying math, always pay attention to definitions, as they are the building blocks of your understanding.

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Most popular questions from this chapter

Use two equations in two variables to solve each application. One catcher's mitt and ten outfielder's gloves cost $$ 239.50 .\( How much does each cost if one catcher's mitt and five outfielder's gloves cost $$ 134.50 ?\)

Graph each inequality for nonnegative values of \(x\) and \(y\). Then give some ordered pairs that satisfy the inequality. SEE EXAMPLE \(5 .\) (OBJECTIVE 3) It costs a bakery \(3\)dollar to make a cake and \(4\)dollar to make a pie. Production costs cannot exceed \(120\)dollar per day. Find an inequality that shows the possible combinations of cakes, \(x,\) and pies, \(y,\) that can be made, and graph it in the illustration.

Solve each system using any method. $$\left\\{\begin{array}{l}2(2 x+3 y)=5 \\\8 x=3(1+3 y)\end{array}\right.$$

Graph the solution. $$\left\\{\begin{array}{l}2 x-4 y>-6 \\\3 x+y \geq 5\end{array}\right.$$

Graph the solution. $$4 x+3 y \leq 12$$
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