Yes.
They are the positive and negative even numbers.
The expression -x² is always negative for any nonzero value of x because squaring a nonzero number (whether positive or negative) results in a positive value. Thus, when you take the negative of that positive value, you end up with a negative result. For example, if x = 2, then -x² = -4, and if x = -2, then -x² = -4 as well. In both cases, -x² is negative.
To evaluate a nonzero number with a negative integer exponent, you can use the rule that states ( a^{-n} = \frac{1}{a^n} ), where ( a ) is the nonzero number and ( n ) is the positive integer. For example, ( 2^{-3} ) can be evaluated as ( \frac{1}{2^3} = \frac{1}{8} ). This method effectively converts the negative exponent into a positive one by taking the reciprocal of the base raised to the corresponding positive exponent.
A mathematical element that when added to another numeral makes the same numeral
Not if the original number is positive, otherwise yes.
The absolute value of a nonzero number is defined as the distance of that number from zero on the number line, regardless of direction. Since distance cannot be negative, the absolute value is always a positive quantity. For example, both -5 and 5 have an absolute value of 5, illustrating that absolute values are inherently non-negative. Thus, any nonzero number, whether positive or negative, will have a positive absolute value.
It means that the number is an integer, AND that it is not zero.
In division by three, possible nonzero remainders are 1 and 2.
The equation can be expressed as ( 15x^2 = 15x ), where ( x ) is the nonzero number. Dividing both sides by 15 (since 15 is nonzero) simplifies to ( x^2 = x ). This implies ( x(x - 1) = 0 ), giving solutions ( x = 0 ) or ( x = 1 ). Since we are looking for a nonzero number, the solution is ( x = 1 ).
That sounds like a nonzero whole number, which could be either negative or positive, so -57, 896, 52, -99 etc., and infinitely many more, would qualify.
The absolute value of a number is its distance from zero on the number line, so it is always non-negative. When you multiply two nonzero absolute values, you are essentially multiplying two non-negative numbers together. In multiplication, a positive number multiplied by a positive number always results in a positive number, hence the product of two nonzero absolute values is always positive.
The quotient of two nonzero integers is the definition of a rational number. There are nonzero numbers other than integers (imaginary, rational non-integers) that the quotient of would not be a rational number. If the two nonzero numbers are rational themselves, then the quotient will be rational. (For example, 4 divided by 2 is 2: all of those numbers are rational).