Solve algebraically 8x + 10y = -4 -4x = 2 + 5y
1 answer:
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Answer:
The graph is attached below.
Step-by-step explanation:
The volume of the box containing the coffee mugs is,
Then the function representing the side length, in inches, for the box is:
Now, it is provided that the company decides to double the volume of the box.
That is, the new volume will be:
Then the side length, in inches, for the box will be:
Then the graph representing the function, formed using the following points is:
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 .