Answer:
a) x < 0 excluding zero.
b) y ≥ 0
Explanation:
a)
"x is negative": This means that x is less than zero. Negative numbers are any numbers less than zero, so this statement implies that x is a negative number. For example, x could be -1, -2, -3, and so on.
so answer is x < 0 excluding zero.
- "x > 0": This means that x is greater than zero. Positive numbers are any numbers greater than zero, so this statement implies that x is a positive number. For example, x could be 1, 2, 3, and so on.
- "x ≤ 0": This means that x is less than or equal to zero. Non-positive numbers are any numbers less than or equal to zero, so this statement implies that x could be zero or any negative number. For example, x could be -1, -2, -3, or 0.
- "x < 0": This means that x is strictly less than zero. This statement implies that x is a negative number, but it does not include zero. For example, x could be -1, -2, -3, and so on, but not 0.
- "X < 20": This means that x is less than 20. Any number less than 20 satisfies this statement, so x could be any negative number, zero, or any positive number less than 20.
- "x = 0": This means that x is exactly equal to zero. The value of x is not positive or negative, but zero
The inequality that expresses the statement "x is less than 0" using the expression "5a^2" would be:
5a^2 > 0 and x < 0
Here, the expression "5a^2 > 0" means that the value of "5a^2" is positive for any non-zero value of "a". Therefore, the expression "5a^2 > 0" is true for all non-zero values of "a". The inequality "x < 0" means that "x" is negative, or less than zero.
So, combining the two expressions, we get the inequality:
5a^2 > 0 and x < 0
b)
The statement "y is nonnegative" means that y is greater than or equal to zero. Therefore, the valid options for y are:
- "y ≥ 0": This means that y is greater than or equal to zero. Any non-negative number satisfies this statement, so y could be 0, 1, 2, and so on.
- "y > 0": This means that y is strictly greater than zero. Any positive number satisfies this statement, so y could be 1, 2, and so on, but not 0.
- "y ≤ 0": This means that y is less than or equal to zero. The only value that satisfies this statement is y = 0.
- "y < 0": This means that y is strictly less than zero. No non-negative number satisfies this statement, so there are no valid options for y in this case.
- "y = 0": This means that y is exactly equal to zero. This statement is true because zero is nonnegative.
Therefore, the valid option for y is y ≥ 0.
As the given statement "y is nonnegative" cannot be expressed as an inequality involving the expression "5a^2". The expression "5a^2" is a polynomial in the variable "a", and it is not related to the variable "y" in the statement.
The inequality that expresses the statements "x is less than 0" and "y is non-negative" using the expression "5a^2" would be:
5a^2 > 0 and y ≥ 0 and x < 0
Here, the expression "5a^2 > 0" means that the value of "5a^2" is positive for any non-zero value of "a". Therefore, the expression "5a^2 > 0" is true for all non-zero values of "a".
The inequality "y ≥ 0" means that "y" is non-negative, or greater than or equal to zero.
The inequality "x < 0" means that "x" is negative, or less than zero.
So, combining the three expressions, we get the inequality:
5a^2 > 0 and y ≥ 0 and x < 0
I hope this helps!