Determine whether the statement is true, false, or sometimes true.
1) If x and y are both integers, 1)
then (-x)3 = -x3
A) Sometimes true B) True C) False
If you mean
(-x)3 = -x3
yes, that is always true
As a matter of fact, it is true for all odd exponents of n for
(-x)n = -xn
and false for all even numbers of n.
e.g. (-3)^3 = (-3)(-3)(-3) = -27
-3^3 = -(3)^3 = -(3)(3)(3) = -27
but
(-3)^4 = (-3)(-3)(-3)(-3) = +81
and -3^4 = -(3)(3)(3)(3) = -81
Let's try that again
If you mean
(-x)3 = -x3
yes, that is always true
As a matter of fact, it is true for all odd exponents of n for
(-x)n = -xn
and false for all even numbers of n.
e.g. (-3)^3 = (-3)(-3)(-3) = -27
-3^3 = -(3)^3 = -(3)(3)(3) = -27
but
(-3)^4 = (-3)(-3)(-3)(-3) = +81
and -3^4 = -(3)(3)(3)(3) = -81
Determine the nature of the solutions of the equations. 2t²-6t=0
To determine whether the statement is true, false, or sometimes true, we need to analyze the given expression and evaluate it for different values of x and y.
The given expression is (-x)3 = -x3.
Let's consider some possible values for x and y and evaluate the expression:
1) If x = 2, y = 3:
(-2)3 = (-2) x (-2) x (-2) = -8
-23 = -2 x -2 x -2 = -8
In this case, the expression holds true.
2) If x = -5, y = 1:
(-(-5))3 = (-(-5)) x (-(-5)) x (-(-5)) = -125
-(-5)3 = -(-5) x -(-5) x -(-5) = -(-125) = 125
In this case, the expression does not hold true.
Since the expression holds true for some values of x and y (such as x = 2, y = 3), but does not hold true for other values (such as x = -5, y = 1), we can conclude that the statement is sometimes true (Option A).