catmg

The path must contain 8 rights, and 2 ups in some order. 

10!/8!/2! = 45

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Edit:

My bad, I read all equations as x + y + z. :((

CPhill did a great job answering. :))

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I don't think those equations are possible.

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6x+3y-1=0

3y = -6x + 1

y = -2x + 1/3

The slope is -2, so the perpendicular slope line is the negative reciprocal, 1/2. 

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f(1) = 4

f(1+1) = f(1) + f(1) + 1*1

f(2) = 9

f(2+2) = f(2) + f(2) + 2*2

f(4) = 22

f(4+4) = f(4) + f(4) + 4*4

f(8) = 60

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-5(X-31)=11.5

x - 31 = -2.3

x = 28.7

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Nice. :))

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a/(1-r)

a = 1

r = 1/5^2

Can you take it from here?

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Rectangle

Width = w

Length = w + 5

The area of a rectangle is width*length. 

Trangle

short leg = w

long leg = 2(w+5)

The area of a right triangle is leg*otherLeg/2. 

Can you take it from here?

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w = # of women

m = # of men

Mr. Li is a man. 

He shook hands with m - 1 men. 

He shook hands with w women. 

3w = m - 1

Mrs. Li is a women. 

She shook hands with m men. 

She shook hands with w - 1 women. 

4(w-1) = m

3w = m - 1

4(w-1) = m

4w - 4 = m

3w = (4w - 4) - 1

w = 5

3(5) = m - 1

m = 16

16 + 5 = 21

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