1) x=9, because we can use the Pythagorean theorem, x^2 + 144 = 225, x^2 = 81
2) 
, because 6^2 +6^2 = 72, 
3) 
, because 
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Solution. To check whether the vectors are linearly independent, we must answer the following question: if a linear combination of the vectors is the zero vector, is it necessarily true that all the coefficients are zeros?
Suppose that
x 1 ⃗v 1 + x 2 ⃗v 2 + x 3 ( ⃗v 1 + ⃗v 2 + ⃗v 3 ) = ⃗0
(a linear combination of the vectors is the zero vector). Is it necessarily true that x1 =x2 =x3 =0?
We have
x1⃗v1 + x2⃗v2 + x3(⃗v1 + ⃗v2 + ⃗v3) = x1⃗v1 + x2⃗v2 + x3⃗v1 + x3⃗v2 + x3⃗v3
=(x1 + x3)⃗v1 + (x2 + x3)⃗v2 + x3⃗v3 = ⃗0.
Since ⃗v1, ⃗v2, and ⃗v3 are linearly independent, we must have the coeffi-
cients of the linear combination equal to 0, that is, we must have
x1 + x3 = 0 x2 + x3 = 0 ,
x3 = 0
from which it follows that we must have x1 = x2 = x3 = 0. Hence the
vectors ⃗v1, ⃗v2, and ⃗v1 + ⃗v2 + ⃗v3 are linearly independent.
Answer. The vectors ⃗v1, ⃗v2, and ⃗v1 + ⃗v2 + ⃗v3 are linearly independent.
Answer: The correct answer is D. None of the above
Explanation:
Although the first three alternatives may eventually contribute, none of them is a prerequisite for a successful marriage.
Living together before the wedding is meant to get to know each other better, but there is no indication that it will make the marriage last any longer. Likewise, religious and premarital counseling can help the couple, but without any guarantee. What makes the marriage successful is the couple's complicity, love, and tolerance for the defects they both have.
Answer:
read below
Explanation:
The answers are close so, #1 would not make much sense. Coasts are exactly where land and water meet so... #2 I guess that would also make sense since water deposits sediments and it's where land meets water. #3, um, coasts won't be exactly flat if sediments from water are brought and it's where water and land meet, so it can't be #3. It won't be #4 since the coasts are not very steep.
I would say #2 because sediments from the shelf are what keep the coast complete. You could say #3 but i honestly don't know what else to say.
