You should post your attempts to each question.
Take out a common factor of z.
By difference of 2 squares
I wasn't sure whether this belonged in this section or the algebra section. Anyway, I'm studying for the math portion of the ACT and I can't remember how to solve certain problems. Like this one:
Which of the following is NOT a factor of z^5 - 16z ?
A. z^2 - 1
B. z^2 - 4
C. z + 2
D. z
E. z - 2
Now I'm aware the answer is A but I have no idea why. If someone could provide an explanation for how to solve that would be great.
Another One: If (2x - y) / (x + y) = 2/3, then x/y = ?
(2x - y is the numerator, x + y is the denominator)
F. 1/2
G. 2/3
H. 5/4
J. 5/3
K. 5
One more: For all nonzero x, y, and z such that x = yz, which of the following must be equivalent to xy?
A. z/x
B. yz^2
C. yz
D. x^2/z
E. x/y
I'm sorry if I posted in the wrong place. Thanks in advance.
Multiplying on both sides by 3(x+y), 3(2x-y)= 2(x+y) so 6x- 3y= 2x+ 2y. Adding 3y and subtracting 2x from both sides, 4x= 5y. Now, what is x/y?
The obvious first step is to multiply on both sides by y to get . But that isn't any of the given answers so lets try eliminating some: if y= 2 and z= 1, then x= (2)(1)= 2 and xy= 4. z/x= 2/1= 2, not 4 so it can't be that. so that is not it. yz= 2(1)= 2 so that is not it. so that might be it! x/y= 2/2= 1 so that is not it.One more: For all nonzero x, y, and z such that x = yz, which of the following must be equivalent to xy?
A. z/x
B. yz^2
C. yz
D. x^2/z
E. x/y
I'm sorry if I posted in the wrong place. Thanks in advance.
If this were a multiple choice test where I did not have much time, I think I could, with confidence, mark "D" and go on. But, of course, just showing it is correct for one chosen value of y and z doesn't mean it is always true. How can we get from x=yz to ? As before, multiplying both sides of x= yz by y gives . Now that I see the "correct" answer has only x and z in it, I can argue that x= yz is equivalent to y= x/z (divide both sides by z) and so . Then as claimed.