Fifteen divided by three is 18
Answer:
(C) 2√15
Step-by-step explanation:
Recognize that all the triangles are right triangles, so are similar to each other. In these similar triangles, the ratio of the short side to the long side is the same for all.
... CB/CA = CT/CB
... CB² = CA·CT = 10·6 = 60 . . . . . . . . . . multiply by CA·CB; substitute values
... CB = √60 = 2√15 . . . . . . . take the square root; simplify
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<em>Comment on this solution</em>
The altitude to the hypotenuse of a right triangle (CB in this case) divides the hypotenuse into lengths such that the altitude is their geometric mean. That is ...
... CB = √(AC·CT) . . . . as above
This is true for any right triangle — another fact of geometry to put in your list of geometry facts.
Answer:
Step-by-step explanation:
The posssible factors are
x^2 + 4x - 32
(x+8)(x-4)
x^2+ 14x - 32
(x+16)(x-2)
(x+32)(x-1)
x^2+31x-32
There are 2001 items in that set.
So n(A) = 2001
We can individually count them all out, which is very slow and tedious, or we can use the formula
n-m+1
where,
m = starting value
n = ending value
In this case,
m = 0
n = 2000
So,
n-m+1 = 2000-0+1 = 2001
This formula only works if we increase the number by 1 each time (eg: 6, 7, 8, etc)
