Answer:
0.2682 or 26.82%
Step-by-step explanation:
The monthly interest rate (r) that your friend is willing to pay is:

The following expression converts a monthly interest rate (r) into an annual interest rate (i):
![r=\sqrt[12]{1+i}-1](https://tex.z-dn.net/?f=r%3D%5Csqrt%5B12%5D%7B1%2Bi%7D-1)
For r = 0.02:
![0.02=\sqrt[12]{1+i}-1 \\1.02^{12}-1=i\\i=0.2682](https://tex.z-dn.net/?f=0.02%3D%5Csqrt%5B12%5D%7B1%2Bi%7D-1%20%5C%5C1.02%5E%7B12%7D-1%3Di%5C%5Ci%3D0.2682)
Your friend is willing to pay an annual rate of 0.2682 or 26.82%.
The nth term of any geometric sequence can be expressed as:
a(n)=ar^(n-1), a(n)=nth term, a=initial term, r=common ratio, n=term number...
We can easily see that the first term, a=-8
The common ratio is 4/-8=-2/4=1/-2=r=-1/2 so the rule is:
a(n)=-8(-1/2)^(n-1) so the tenth term is:
a(10)=-8(-1/2)^(10-1)
a(10)=-8(-1/2)^9
a(10)=1/64
Step-by-step explanation:
Proof: equidistance means at an equal distance from two points
so: Take the distance formula and then plug the values in and compare.
Answer:
Dividing by 7
Step-by-step explanation:
1. Find the common term in the fraction 7
divided all by 7
The vertex is 
Explanation:
The equation is 
To find the vertex, we need the equation in the form of 
Dividing each term by 2 in the equation 

Now, completing the square by adding and subtracting 1, we get,

The first three terms can be written as
,
![f(x)=2[(x+1)^{2}+\frac{1}{2} ]](https://tex.z-dn.net/?f=f%28x%29%3D2%5B%28x%2B1%29%5E%7B2%7D%2B%5Cfrac%7B1%7D%7B2%7D%20%20%5D)
Multiplying 2 into the bracket, we get,

This equation is of the form 
Now, we shall find the vertex 
Thus,
and 
Thus, the vertex is 