Answer:
The two points solutions to the system of equations are: (2, 3) and (-1,6)
Step-by-step explanation:
These system of equations consists of a parabola and a line. We need to find the points at which they intersect:
Since we were able to factor out the quadratic expression, we can say that the x-values solution of the system are:
x = 2 and x = -1
Now, the associated y values we can get using either of the original equations for the system. We pick to use the linear equation for example:
when x = 2 then 
when x= -1 then 
Then the two points solutions to the system of equations are: (2, 3) and (-1,6)
To solve this we are going to use the future value of annuity ordinary formula:
![FV=P[ \frac{(1+ \frac{r}{n} )^{kt} -1}{ \frac{r}{n} } ]](https://tex.z-dn.net/?f=FV%3DP%5B%20%5Cfrac%7B%281%2B%20%5Cfrac%7Br%7D%7Bn%7D%20%29%5E%7Bkt%7D%20-1%7D%7B%20%5Cfrac%7Br%7D%7Bn%7D%20%7D%20%5D)
where
is the future value
is the periodic payment
is the interest rate in decimal form
is the number of times the interest is compounded per year
is the number of payments per year
is the number of years
We know for our problem that
and
. To convert the interest rate to decimal form, we are going to divide the rate by 100%:
Since the deposit is made semiannually, it is made 2 times per year, so
.
Since the type of the annuity is ordinary, payments are made at the end of each period, and we know that we have 2 periods, so
.
Lets replace the values in our formula:
![FV=6200[ \frac{(1+ \frac{0.06}{2} )^{(2)(5)} -1}{ \frac{0.06}{2} } ]](https://tex.z-dn.net/?f=FV%3D6200%5B%20%5Cfrac%7B%281%2B%20%5Cfrac%7B0.06%7D%7B2%7D%20%29%5E%7B%282%29%285%29%7D%20-1%7D%7B%20%5Cfrac%7B0.06%7D%7B2%7D%20%7D%20%5D)
We can conclude that the correct answer is <span>
$71,076.06</span>
108 divided by 3 equals 36.
I got this answer by multiplying 3 and 36, which equaled 108. Then I figured out that 108 divided by 3 equals 36!
