Let

be an integer. Suppose there is a triangle with legs of length 16 and

. Then by the Pythagorean theorem, the length of the hypotenuse should be

The formulas for Pythagorean triples say that if the legs are integers, then so must be the hypotenuse, because if

and

are integers, then so are

,

, and

.
However,

is not a perfect square trinomial, which means for any integer

, the length of the hypotenuse is not an integer, so such a triangle doesn't exist.
Answer:
The answer to this question can be defined as follows:
In option 1, She buys 4 memory cards.
In option 2, The cost of memory is $40
Step-by-step explanation:
Given:
Available space is = 105 GB
required space = 1000 GB
256 GB memory cost $10.
Find needed memory:
= 1000 GB - 105 GB
= 895 GB
∴ the available memory is 256 GB.
∵ 256 × 4 = 1024 GB
The total memory she have = 1024 + 105 = 1129 GB
And she needs to buy 4 memory cards.
The cost of the four memory cards is= 4 ×10 = $40.
Step-by-step explanation:
481/26%=1850
crosscheck: 1850×26%=481
so the answer is $1850
Any tangent line to the curve has a slope given by
.


Since
, the denominator ranges from 3 to 5, so the range of slopes is
.