Answer:
<em>The employees will work for 1 hour, will earn $5 per hour and will be paid $5</em>
Step-by-step explanation:
<u>System of Equations</u>
The number of hours the employees work is x.
And the hourly wage that they are paid is y. The store manager is willing to pay the employees a wage given by the equation
10y-30x=20
The business owner states that the employees should be paid a wage given by the equation
6y+30x=60
Adding both equations we have:
16y = 80
Dividing by 16:
y = 80/16 = 5
Substituting into the first equation:
10*5-30x=20
Operating and simplifying:
50-30x=20
50 - 20 = 30x
30x = 30
x = 30/30 = 1
Thus, the employees will work for 1 hour, will earn $5 per hour and will be paid $5
They are more atoms in a body, only 75,000,000,000,000,000,000 grains of sand
and
7,000,000,000,000,000,000,000,000,000
atoms in a body, at the end , the number of atoms seem longer and larger.
X equals 7.1 if you round to the nearest tenth
Answer:
True. See the explanation and proof below.
Step-by-step explanation:
For this case we need to remeber the definition of linear transformation.
Let A and B be vector spaces with same scalars. A map defined as T: A >B is called a linear transformation from A to B if satisfy these two conditions:
1) T(x+y) = T(x) + T(y)
2) T(cv) = cT(v)
For all vectors 
and for all scalars 
. And A is called the domain and B the codomain of T.
Proof
For this case the tranformation proposed is t: 
Where 
For this case we have the following assumption:
1) The transpose of an nxm matrix is an nxm matrix
And the following conditions:
2) 
And we can express like this 
3) If 
and then we have this:
And since we have all the conditions satisfied, we can conclude that T is a linear transformation on this case.
