Answer:
9% fund: $
210,000
13% fund: $70,000
Step-by-step explanation:
As she wants to have a $28,000 annual return for her $280,000 investment, she is expecting a return rate of 10%:
If we call x the proportion of the capital in the 9% fund, then (1-x) is the proportion of the capital in the 13% fund,and the return of the combination has to be the expected return of 10%:
Then, we know that 75% of the capital should be invested in the 9% fund and 25% in the 13% fund.
This correspond to a capital of:
9% fund: 0.75*$280,000 = $
210,000
13% fund: 0.25*$280,000 = $70,000
Answer:
63degrees
Step-by-step explanation:
I cant see the picture well but i assume that is an angle and it is right before 90 degrees
5x - 2y = 17
4x - 3y = 8
Try to change one of the equations to isolate a variable, so you can use the new equation and substitute it into the other equation.
5x - 2y = 17
-2y = 17 - 5x
y = -17/2 + 5/2x
Now plug this into the second equation
4x - 3(-17/2 + 5/2x) = 8
4x + 51/2 - 15/2x = 8
8/2x - 15/2x = 16/2 - 51/2
-7/2x = -35/2
x = 5
Plug this into either equation to find y
4x - 3y = 8
4(5) - 3y = 8
20 - 3y = 8
-3y = -12
y = 4
x = 5, y = 4
Answer:
Option C.
The distance from the point to the circle is 6 units
Step-by-step explanation:
we know that
The distance between the circle and the point will be the difference of the distance of the point from the center of circle and the radius of the circle
step 1
Find the center and radius of the circle
we have
Convert to radius center form
Complete the square
Rewrite as perfect squares
so
The center is the point (0,4)
The radius is
step 2
Find the distance of the point from the center of circle
the formula to calculate the distance between two points is equal to
we have
(6,-4) and (0,4)
substitute the values
step 3
Find the difference of the distance of the point from the center of circle and the radius of the circle
therefore
The distance from the point to the circle is 6 units
see the attached figure to better understand the problem
