Why are the triangles congruent?
2 answers:
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Answer:
a) No
b) No
c) No
d) No
Step-by-step explanation:
Remember, a set V wit the operations addition and scalar product is a vector space if the following conditions are valid for all u, v, w∈V and for all scalars c and d:
1. u+v∈V
2. u+v=v+u
3. (u+v)+w=u+(v+w).
4. Exist 0∈V such that u+0=u
5. For each u∈V exist −u∈V such that u+(−u)=0.
6. if c is an escalar and u∈V, then cu∈V
7. c(u+v)=cu+cv
8. (c+d)u=cu+du
9. c(du)=(cd)u
10. 1u=u
let's check each of the properties for the respective operations:
Let
Observe that
1. u+v∈V
2. u+v=v+u, because the adittion of reals is conmutative
3. (u+v)+w=u+(v+w). because the adittion of reals is associative
4.
5.
then regardless of the escalar product, the first five properties are met for a), b), c) and d). Now let's verify that properties 6-10 are met.
a)
6.
7.
8.
Since 8 isn't satify then V is not a vector space with the addition as in R^3 and the scalar product
b) 6.
7.
8.
9.
10
Since 10 isn't satify then V is not a vector space with the addition as in R^3 and the scalar product
c) Observe that
Since 10 isn't satify then V is not a vector space with the addition as in R^3 and the scalar product .
d) Observe that
Since 10 isn't satify then V is not a vector space with the addition as in R^3 and the scalar product .
<h2>Hello!</h2>
The answer is: The point (0,0) is part of the solution.
<h2>Why?</h2>To find which point is part of the solution of the inequality, we need to evaluate each of the given points. If the inequality is satisfied, then the point is part of the solution, otherwise, if the inequality is not satisfied, the point is not part of the solution.
We are given the inequality:
So, evaluating we have:
- First point (-2,1)
Now, since 1 is not less or equal to -1, the point (-2,1) is not part of the solution.
- Second point (1,3)
Now, since 3 is not less or equal to 2, the point (1,3) is not part of the solution.
- Third point (-4,2)
Now, since 2 is not less or equal to -3, the point (-4,2) is not part of the solution.
- Fourth point (0,0)
Now, since 0 is less than 1, the point (0,0) is part of the solution.
Hence, we have that the point (0,0) is part of the solution.
Have a nice day!