Answer:
Step-by-step explanation:
Using the section formula, if a point (x,y) divides the line joining the points (x
1
,y
1
) and (x
2
,y
2
) in the ratio m:n, then
(x,y)=(
m+n
mx
2
+nx
1
,
m+n
my
2
+ny
1
)
The vertices of the triangle are given to be (x
1
,y
1
),(x
2
,y
2
) and (x
3
,y
3
). Let these vertices be A,B and C respectively.
Then the coordinates of the point P that divides AB in l:k will be
(
l+k
lx
2
+kx
1
,
l+k
ly
2
+ky
1
)
The coordinates of point which divides PC in m:k+l will be
⎩
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎧
m+k+l
mx
3
+(k+l)
(l+k)
lx
2
+kx
1
,
m+k+l
my
3
+(k+l)
(l+k)
ly
2
+ky
1
⎭
⎪
⎪
⎪
⎬
⎪
⎪
⎪
⎫
⇒(
m+k+l
kx
1
+lx
2
+mx
3
,
m+k+l
ky
1
+ly
2
+my
3
)
36/27=1.3
7x1.3=9.1
The actual length is 9.1meters
Answer:
s = 15.
Step-by-step explanation:
The formula for a polygon with s sides is:
Sum of the angles = 180(s - 2) so we have:
180(s - 2) = 2340
180s - 360 = 2340
180s = 2700
s = 15
For this type of question it is easiest to think about it in terms of a simple multiplication. The way we can do this is by working out how many possibilities there are for each position on the program. This is as follows:
For the first act, there are 9 possible performers we can pick
For the second act, because we have already assigned a performer to the first act, there are only 8 possible performers
For the third act, because we have already assigned a performer to the first two acts, there are only 7 possible performers
This goes on and on until we reach the final act, where we have used all the performers except one.
Therefore we can say:
For the first act there are 9 possibilities
For the second act there are 8 possibilities
For the third act there are 7 possibilities
For the fourth act there are 6 possibilities and so on
If we want to write this mathematically we can just say that there are:
9 possibilities x 8 possibilites x 7 possibilities etc right down until we are at the final act where there is 1 possibility.
To write this out as an equation we just say:
9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = the number of different ways
In maths however, we have a much simpler way of saying this, which we call "factorial".
That whole stream of numbers up there can just be said to be "9 factorial", or if we are writing it in an equation "9!". You may find that your calculator has a button which has an "!" on it. If you put in the number of performers and then press the "!" button, it will give you the answer to your question.
Hope this helped you :)
Multiply the hours worked by the wage,
5x25=125 7x20=140,
Add the two totals,
140+125=265,
Divide total made by hours worked,
$265/12=22.08 dollars an hour.
