Answer:
B
Step-by-step explanation:
The volume of a rectangular prism is the length times width times height.
V = LWH
V = (4√3)(3√6)W
V = 12√18 W
V = 36√2 W
If the volume is irrational, then W cannot have a radical that is half of a perfect square, because when multiplied by √2, that would yield a rational volume. For example, √18 × √2 = √36 = 6.
Therefore, the answer must be B, because 12 is not half of a perfect square.
V = 36√2 (4√12)
V = 144√24
V = 288√6
<h3>
Answer: False</h3>
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Explanation:
I'm assuming you meant to type out
(y-2)^2 = y^2-6y+4
This equation is not true for all real numbers because the left hand side expands out like so
(y-2)^2
(y-2)(y-2)
x(y-2) .... let x = y-2
xy-2x
y(x)-2(x)
y(y-2)-2(y-2) ... replace x with y-2
y^2-2y-2y+4
y^2-4y+4
So if the claim was (y-2)^2 = y^2-4y+4, then the claim would be true. However, the right hand side we're given doesn't match up with y^2-4y+4
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Another approach is to pick some y value such as y = 2 to find that
(y-2)^2 = y^2-6y+4
(2-2)^2 = 2^2 - 6(2) + 4 .... plug in y = 2
0^2 = 2^2 - 6(2) + 4
0 = 4 - 6(2) + 4
0 = 4 - 12 + 4
0 = -4
We get a false statement. This is one counterexample showing the given equation is not true for all values of y.
Answer is 20 by plugging the 4 in the equation it equals 20
