Answer:
The average velocity the entire trip was 43.25 mi/h
Step-by-step explanation:
In this case we have to calculate an average based on the miles traveled. First we have to calculate the total of miles traveled, then calculate the portion of the total travel of each and with this calculate the average speed during the trip. First the total miles traveled:

Now the percentages:
At 57 mi/h were 
At 44 mi/h were 
At 37.8 mi/h were 
Now multiplying the speed by the portion and summing them we can have the average velocity:

The average velocity the entire trip was 43.25 mi/h
Answer:
d
Step-by-step explanation:
cannot be a or c cause it has a negative sign in front of it causing it to reflect over y axis. Cannot be B cause it doesn't have two coefficients with X. I also graphed it.
Answer:
(A) Set A is linearly independent and spans
. Set is a basis for
.
Step-by-Step Explanation
<u>Definition (Linear Independence)</u>
A set of vectors is said to be linearly independent if at least one of the vectors can be written as a linear combination of the others. The identity matrix is linearly independent.
<u>Definition (Span of a Set of Vectors)</u>
The Span of a set of vectors is the set of all linear combinations of the vectors.
<u>Definition (A Basis of a Subspace).</u>
A subset B of a vector space V is called a basis if: (1)B is linearly independent, and; (2) B is a spanning set of V.
Given the set of vectors
, we are to decide which of the given statements is true:
In Matrix
, the circled numbers are the pivots. There are 3 pivots in this case. By the theorem that The Row Rank=Column Rank of a Matrix, the column rank of A is 3. Thus there are 3 linearly independent columns of A and one linearly dependent column.
has a dimension of 3, thus any 3 linearly independent vectors will span it. We conclude thus that the columns of A spans
.
Therefore Set A is linearly independent and spans
. Thus it is basis for
.
Inversely variation means xy = c, where c is a constant
Since when y = 12 x = 5, then c = 12*5 = 60
So xy = 60
Now when x = 3, y = 60/3 = 20