Half of the sum of two and a number multiplied by itself three times
a
15x^(-1)-3x
b
(2+x^3)/2
c
(5x-7)+9x
d
Linear
e
Nonlinear
The answer is e) Nonlinear.
In a nonlinear equation, the variable is raised to a power other than 1 (such as x^2, x^3, etc.) or multiplied/divided by itself multiple times.
In this case, the equation is "Half of the sum of two and a number multiplied by itself three times." This can be represented as (2 + a)^3/2, where "a" is the number. The variable "a" is raised to the power of 3, which makes it nonlinear.
To determine which of the given expressions is half of the sum of two and a number multiplied by itself three times, we need to simplify each expression and apply the given condition. Let's go through each option:
a) The expression is a. To simplify it, we can rewrite it as:
a = 15x^(-1) - 3x
= 15/x - 3x
This expression does not match the given condition, so it is not the correct answer.
b) The expression is (2 + x^3)/2. We can simplify it:
b = (2 + x^3)/2
This expression also does not match the given condition, so it is not the correct answer.
c) The expression is (5x - 7) + 9x. Let's simplify it:
c = (5x - 7) + 9x
= 5x + 9x - 7
= 14x - 7
This expression does not match the given condition, so it is not the correct answer.
d) The expression is Linear. Linear expressions have the form y = mx + b, where x is the variable, m is the slope, and b is the y-intercept. This is not the correct answer since it does not match the given condition.
e) The expression is Nonlinear. Nonlinear expressions do not have a constant rate of change. This is also not the correct answer since it does not match the given condition.
None of the given options match the condition of being half of the sum of two and a number multiplied by itself three times.
To determine whether each given expression is linear or nonlinear, we need to look at the power (exponent) of the variable(s) involved in the expression.
a) Half of the sum of two and a number multiplied by itself three times:
To express this algebraically, let's assume the number is represented by 'x'.
The expression can be written as: (x^3 + 2) / 2.
The variable 'x' is raised to the power of 3, which means that the expression is nonlinear.
Answer: e) Nonlinear.
b) (2 + x^3) / 2:
Here, the variable 'x' is raised to the power of 3, but the highest power is 3, which is still a polynomial with the variable raised to a whole number power. Therefore, it is considered a linear expression.
Answer: d) Linear.
c) (5x - 7) + 9x:
This expression represents a combination of two linear terms: 5x and 9x. The variable 'x' is raised to the power of 1, which is a linear power. Therefore, the expression is linear.
Answer: d) Linear.
In summary:
a) Nonlinear
b) Linear
c) Linear