Twelve people join hands for a circle dance.In how many ways can they do this? Suppose six of these people are men, and the other six are women. In how many ways can they join hands for a circle dance, assuming they alternate in gender around the circle
Answer:
86400 ways
Step-by-step explanation:
Since the circle can be rotated, the number of ways to arrange a distinct number of n objects in a circle will be (n−1)!.
Now, if we rotate the circle with the six women, we will see that there are 5! ways with which they can be placed in the circle.
After picking the places for the women, we will now fill each gap between two women with a man.
We have 6 men. Thus, number of ways to arrange the men is 6!
Thus,number of ways they can join hands for a circle dance, assuming they alternate in gender around the circle = 5! × 6! = 86400 ways
The coordinate A(-1, 1) reflected over y-axis is (1, 1) is the coordinate of E, hence the two figures are congruent
- The given figures are quadrilaterals, in order to determine whether they are similar, we need to check if they are reflections of each other.
- For the Quadrilateral ABCD, the coordinate of A is at A(-1, 1) and for the Quadrilateral DEFG, the coordinate of E is at E(1, 1).
- Note that if an object is reflected over the y-axis the transformation is (x, y)->(-x, y)
- We need to check whether if we reflect the coordinate A over the y-axis we will get coordinate E
Since the coordinate A(-1, 1) reflected over y-axis is (1, 1) is the coordinate of E, hence the two figures are congruent
Learn more on reflections here:brainly.com/question/1908648
Answer:
Yes, ΔBAC ≅ ΔLMN
Step-by-step explanation:
BA = LM
AC = MN
BC = LN
ΔBAC ≅ ΔLMN {Side Side Side congruence}
Step-by-step explanation:
x = a + 7
y = b-a
To prove
x + y = b + 7.
- x+y= (a+7) + (b-a)
=a+7+b-a
=a-a+7+b
=0 + 7+b
= b+7
Proved ✅
