Polygon Y is a scaled copy of Polygon X using a scale factor of 1/3. Polygon Y’s area isn’t what fraction of Polygon X’s area?
1 answer:
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Firstly, we'll fix the postions where the women will be. We have
forms to do that. So, we'll obtain a row like:
The n+1 spaces represented by the underline positions will receive the men of the row. Then,
Since there is no women sitting together, we must write that . It guarantees that there is at least one man between two consecutive women. We'll do some substitutions:
The equation (i) can be rewritten as:
We obtained a linear problem of non-negative integer solutions in (ii). The number of solutions to this type of problem are known:
[I can write the proof if you want]
Now, we just have to calculate the number of forms to permute the men that are dispposed in the row:
Multiplying all results:
Answer:
18 and 40
Step-by-step explanation:
Let x be the age of Claire and y the age of her mother
Claire's mother is 4 years more than twice Claire's age
- y = 2x+4
The sum of their ages are is 58
- x+y = 58
the system is:
Multiply (y+x = 58) by -1 and then add it to (y = 2x+4) to eliminate y
- -y-x = -58
- -y-x+y = 2x+4-58
- -x -2x = -54
- -3x = -54
- x = 54/3
- x = 18
y= 58-18 = 40
so claire's mother is 40 years old and claire is 18