In how many ways can we seat 6 people around a round table if Fred and Gwen insist on sitting opposite each other? (Two seatings
are considered equivalent if one is a rotation of the other.)
1 answer:
Make a picture of the problem.
Fred and Gwen are seated opposite each other, and we name the 4 remaining seats 1, 2, 3, 4, starting from the right of Fred.
There are 4 options for seat 1,
then 3 for the seat 2, after one is seated in the 1.st seat
2 options for the seat 3,
and 1 for the seat 4.
That is, the 4 friends can sit in 4*3*2*1=24 different ways.
Answer: 24
Fred and Gwen are seated opposite each other, and we name the 4 remaining seats 1, 2, 3, 4, starting from the right of Fred.
There are 4 options for seat 1,
then 3 for the seat 2, after one is seated in the 1.st seat
2 options for the seat 3,
and 1 for the seat 4.
That is, the 4 friends can sit in 4*3*2*1=24 different ways.
Answer: 24
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Hi!
Your answer is C.
The vertex is the point where two different rays meet, forming an angle.
It can also simply be the point where 2 straight lines simply meet.
Option A is NOT correct because a vertex is not angle, it is a <em>part </em>of an angle.
Option B is NOT correct because, if there's only one segment, we cannot form a vertex.
See the image below for an example:
Answer:
Step-by-step explanation:
We need at least two points to write the equation of a straight line.
The recursive formula that Elijah wrote is:
When we substitute n=0, we get:
The points (0,30) and (1,37) lies on this line.
The equation of this line is of the form:
where b =30 is the y-intercept and m=7 is the slope.
We plug in these values to get:
Note that the slope of the line is equal to the common difference of the Arithmetic Sequence.
You could also use the two points to find the slope: