What word describes the "4" in the expression [tex]$4 x-10$[/tex]?
A) Sum
B) Product
C) Coefficient
D) Term
Answer (1)
The problem asks to identify the term that describes the '4' in the expression 4 x − 10 .
Define the terms: Sum, Product, Coefficient, and Term.
Recognize that '4' is multiplied by the variable 'x'.
Conclude that '4' is the coefficient of 'x', so the answer is C .
Explanation
Understanding the Expression The expression given is 4 x − 10 . We need to identify what the '4' is called in this expression from the given options.
Defining the Options Let's define each of the options:
Sum: The result of adding two or more numbers.
Product: The result of multiplying two or more numbers.
Coefficient: A number multiplied by a variable.
Term: A single number or variable, or numbers and variables multiplied together. Terms are separated by + or - signs in an expression.
Identifying the Correct Term In the expression 4 x − 10 , '4' is multiplied by the variable 'x'. Therefore, '4' is the coefficient of 'x'.
Final Answer Therefore, the correct answer is C) Coefficient.
Examples
Understanding coefficients is crucial in many real-world applications. For example, in physics, the equation F = ma (Force = mass × acceleration) shows that mass ( m ) is the coefficient of acceleration ( a ). Similarly, in economics, if you have a cost function C = 5 q + 20 , where C is the total cost and q is the quantity of goods produced, the number 5 is the coefficient of q , representing the variable cost per unit. Identifying coefficients helps in understanding the relationships between variables and their impact on the overall outcome.
