Answer:
See proof below
Step-by-step explanation:
Assume that V is a vector space over the field F (take F=R,C if you prefer).
Let
. Then, we can write x as a linear combination of elements of s1, that is, there exist
and
such that
. Now,
then for all
we have that
. In particular, taking
with
we have that
. Then, x is a linear combination of vectors in S2, therefore
. We conclude that
.
If, additionally
then reversing the roles of S1 and S2 in the previous proof,
. Then
, therefore
.
Answer:
x=2.66
Step-by-step explanation:
6x=60-10y-8z
x=(60-10*2-8*3)÷6
x=(60-20-24)/6=16/6=2.66
Work backwards. If there were 14 at the end, then multiply this by 3/2 because 2/3 of the marbles were given to Sam. so 14 times 3/2 is 21. There were 28 total because if you add 1/3 to 1/6 you get 1/2. So they they lost 1/2 of the marbles and got 1/4 of the original amount back, which was 21.
So the original number was 28. Hope this helps!
<h3>
Answer:</h3>

<h3>
Step-by-step explanation:</h3>
In this question, we're trying to find how much Hermione spent on plums.
We know that:
- Hermione bought 9/10 of a pound of plums
- Plums cost $1.30 <em>per pound</em>
With the information above, we can solve the question.
Since we know that plums cost $1.30 per pound and Hermione bought 9/10 of a pound, we would multiply 1.30 by 0.90 in order to get the price Hermione bought the plums for. Hermione is pretty much paying 90% of the cost of a pound.

When you multiply, you should get 1.17
This means that Hermione spent $1.17 on 9/10 pound of plums.
<h3>I hope this helped you out.</h3><h3>Good luck on your academics.</h3><h3>Have a fantastic day!</h3>