Answer: 6/8 or 3/4 or 0.75
Step-by-step explanation:
Solution:
Given that the point P lies 1/3 along the segment RS as shown below:
To find the y coordinate of the point P, since the point P lies on 1/3 along the segment RS, we have

Using the section formula expressed as
![[\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n}]](https://tex.z-dn.net/?f=%5B%5Cfrac%7Bmx_2%2Bnx_1%7D%7Bm%2Bn%7D%2C%5Cfrac%7Bmy_2%2Bny_1%7D%7Bm%2Bn%7D%5D)
In this case,

where

Thus, by substitution, we have
![\begin{gathered} [\frac{1(2)+2(-7)}{1+2},\frac{1(4)+2(-2)}{1+2}] \\ \Rightarrow[\frac{2-14}{3},\frac{4-4}{3}] \\ =[-4,\text{ 0\rbrack} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5B%5Cfrac%7B1%282%29%2B2%28-7%29%7D%7B1%2B2%7D%2C%5Cfrac%7B1%284%29%2B2%28-2%29%7D%7B1%2B2%7D%5D%20%5C%5C%20%5CRightarrow%5B%5Cfrac%7B2-14%7D%7B3%7D%2C%5Cfrac%7B4-4%7D%7B3%7D%5D%20%5C%5C%20%3D%5B-4%2C%5Ctext%7B%200%5Crbrack%7D%20%5Cend%7Bgathered%7D)
Hence, the y-coordinate of the point P is
It is prime, it has no factors besides 1,23
Answer 10
This is the formula of an arithmetic sequence.
a
n
=
a
1
+
d
(
n
−
1
)
a
n
=
a
1
+
d
(
n
-
1
)
Substitute in the values of
a
1
=
1
a
1
=
1
and
d
=
3
d
=
3
.
a
n
=
1
+
(
3
)
(
n
−
1
)
a
n
=
1
+
(
3
)
(
n
-
1
)
Simplify each term.
a
n
=
1
+
3
n
−
3
a
n
=
1
+
3
n
-
3
Subtract
3
3
from
1
1
.
a
n
=
3
n
−
2