Answer: 1- 2:3
2- 4:7
3- draw 5 of something, then one of something else
4- same as 3
5- 10, 3, and 20
6- 14, 21, and 4
Step-by-step explanation:
3x^3 - 12x has a greatest common factor of 3x.
3x(x^2 - 4) is one other way to write it. It was created by factoring out the GCF of 3x.
3x(x+2)(x-2) is another form which is created by factoring the (x^2 - 4) from the last form.
Answer:
y = √55
Step-by-step explanation:
All the triangles are similar, so the ratio of short side to hypotenuse is the same for all:
5/y = y/(5+6)
y^2 = 55
y = √55
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<em>Comment on the geometry</em>
There are three "geometric mean" relationships that apply to this geometry.
- the altitude BD is the geometric mean of BC and BA (√30)
- the long side of the large triangle is the geometric mean of the longer segment of the hypotenuse and the whole hypotenuse (x = √66)
- the short side of the large triangle is the geometric mean of the shorter segment of the hypotenuse and the whole hypotenuse (y = √55)
If you were aware of the last of these relationships, you could write down the answer without any "work."
y = √(5(5 +6)) = √55
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The geometric mean is the n-th root of the product of n numbers. When there are 2 numbers, it is the square root of their product.
X> 1000/997
Alternate form is
x> 10 30/997, 1000/997 = 10.03009 , x {10000/997 , + infinity}
Regardless of the sign of
, we have
(never negative). But multiplying by -1 makes it negative.
On the other hand,
which can never be negative for real
.
