Three times a nuber subtracted fro the product of fifteen and the reciprocal of a number
a
15x^(-1)-3x
b
(2+x^3)/2
c
(5x-7)+9x
d
Linear
e
Nonlinear
The expression "Three times a number subtracted from the product of fifteen and the reciprocal of a number" can be represented as:
15/x - 3x
Therefore, the correct option is a)
To determine whether each expression is linear or nonlinear, we need to consider the power (exponent) of the variable.
a) 15x^(-1) - 3x:
This expression is nonlinear because the variable x is raised to a negative power (-1).
b) (2+x^3)/2:
This expression is nonlinear because the variable x is raised to the power of 3.
c) (5x-7) + 9x:
This expression is linear because the variable x is only raised to the power of 1.
d) Linear:
The term "Linear" by itself does not represent an expression. If you have a specific expression in mind, please provide it so I can determine its linearity.
e) Nonlinear:
The term "Nonlinear" by itself does not represent an expression. If you have a specific expression in mind, please provide it so I can determine its linearity.
To determine which of the given expressions represents a linear equation, we need to understand what a linear equation is.
A linear equation is an equation in which the variable(s) are raised to the first power and are not multiplied or divided by each other. Additionally, the coefficients of the variable(s) are either constants or variables raised to the power of 1 (i.e., not raised to any higher power).
Let's analyze each option to identify the linear equation:
a) 15x^(-1) - 3x: This expression contains x raised to the power of -1, which means it is the reciprocal of x. Since the variable appears with a negative exponent, this expression is not linear.
b) (2+x^3)/2: This expression contains x raised to the power of 3, which is a higher power than 1. Therefore, this expression is not linear.
c) (5x-7) + 9x: This expression contains x raised to the first power and is not multiplied or divided by any other variable, so it represents a linear equation.
d) Linear: This option indicates that the equation is linear. However, we need a specific equation to determine if it is linear or not.
e) Nonlinear: This option implies that the equation is not linear, but we still need a specific equation to determine if it is nonlinear or not.
Based on the given options, option c, (5x-7) + 9x, represents a linear equation.