Answer:
Slope of the line segment PQ is 1/2.
Step-by-step explanation:
We are given with a line connecting two points P and Q.
The coordinates of P are (4,4) and the coordinates of Q are (-2,1).
Slope of line joining two points
and ![(x_{2},y_{2})](https://tex.z-dn.net/?f=%28x_%7B2%7D%2Cy_%7B2%7D%29)
is given by the formula ![\frac{y_{2}-y_{1}}{x_{2}-x_{1}}](https://tex.z-dn.net/?f=%5Cfrac%7By_%7B2%7D-y_%7B1%7D%7D%7Bx_%7B2%7D-x_%7B1%7D%7D)
Hence the slope of the line PQ is ![\frac{1-4}{-2-4}=\frac{-3}{-6}= \frac{1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B1-4%7D%7B-2-4%7D%3D%5Cfrac%7B-3%7D%7B-6%7D%3D%20%5Cfrac%7B1%7D%7B2%7D)
Therefore correct option is 'C' that is 1/2.
Answer:
Explicit form: ![g_n=3(\frac{1}{3})^{n-1}](https://tex.z-dn.net/?f=g_n%3D3%28%5Cfrac%7B1%7D%7B3%7D%29%5E%7Bn-1%7D)
Recursive form:
with
.
Step-by-step explanation:
The first term is 3 and we are dividing by 3 each time.
Another way to say we are dividing by 3 each time is to say we are multiplying by factors of 1/3.
If the first term is
and
is the common ratio then the geometric sequence in explicit form is:
![a_n=a(r)^{n-1}](https://tex.z-dn.net/?f=a_n%3Da%28r%29%5E%7Bn-1%7D)
![g_n=3(\frac{1}{3})^{n-1}](https://tex.z-dn.net/?f=g_n%3D3%28%5Cfrac%7B1%7D%7B3%7D%29%5E%7Bn-1%7D)
The recursive form for a geometric sequence is
with
where
is the common ratio and
is the first term.
So the recursive form for our sequence is
with
.
Answer:
10-x
Step-by-step explanation:
The difference of 10 and x is subtracting x from 10