I suppose
The vectors that span 
form a basis for 
if they are (1) linearly independent and (2) any vector in can be expressed as a linear combination of those vectors (i.e. they span ).
Compute the Wronskian determinant:
The determinant is non-zero, so the vectors are linearly independent. For this reason, we also know the dimension of is 3.
Write an arbitrary vector in as 
. Then the given vectors span if there is always a choice of scalars 
such that
which is equivalent to the system
The coefficient matrix is non-singular, so it has an inverse. Multiplying both sides by that inverse gives
so the vectors do span .
The vectors comprising form a basis for it because they are linearly independent.
Answer:
B. y = -0.58x^2 -0.43x +15.75
Step-by-step explanation:
The data has a shape roughly that of a parabola opening downward. So, you'll be looking for a 2nd-degree equation with a negative coefficient of x^2. There is only one of those, and its y-intercept (15.75) is in about the right place.
The second choice is appropriate.
_____
The other choices are ...
A. a parabola opening upward
C. an exponential function decaying toward zero on the right and tending toward infinity on the left
D. a line with negative slope (This might be a good linear regression model, but the 2nd-degree model is a better fit.)
For this case we have a function of the form:
Where,
A: initial amount
b: growth rate (for b> 1)
x: independent variable
y: dependent variable
We then have the following function:
Using the definition, the following statements are correct:
1) The function is exponential
2) The function increases by a factor of 2.5 for each unit increase in x
3) The domain of the function is all real numbers
As you know that sum of complementary angles equal 90°
so,
7x + 11x = 90
18x = 90
x = 90/18
x =5
so,
option A is the correct one.
