Answer:
z = -12
Step-by-step explanation:
The given system of equations is:
xy/(x + y) = 1 ...........................(1)
xz/(x + z) = 2...........................(2)
yz/(y + z) = 3...........................(3)
From (1): x + y = xy
=> y = xy - x
y = x(y - 1)
x = y/(y - 1).......................................(4)
From (2): 2(x + z) = xz
=> 2x + 2z = xz
2x = xz - 2z
2x = z(x - 2)
z = 2x/(x - 2) ....................................(5)
From (3): 3(y + z) = yz
=> 3y + 3z = yz
3y = yz - 3z
3y = z(y - 3)
z = 3y/(y - 3)....................................(6)
Comparing (5) and (6)
2x/(x - 2) = 3y/(y - 3)
2x(y - 3) = 3y(x - 2)
2xy - 6x = 3xy - 6y
6(y - x) = xy .................................(7)
But from (1): xy = x + y
Using this in (7), we have
6(y - x) = x + y
6y - y - 6x - x = 0
5y - 7x = 0
5y = 7x
x = 5y/7................................................(8)
Using this in (4)
5y/7 = y/(y - 1)
1/(y - 1) = 5/7
(y - 1) = 7/5
y = 1 + 7/5
y = 12/5..........................................(9)
Using this in (8)
x = 5(12/5)/7 = 12/7 .......................(10)
Using (10) in (5)
z = 2x/(x - 2)
z = 2(12/7) ÷ (12/7 - 2)
= 24/7 ÷ -2/7
= 24/7 × (-7/2)
= -24/2 = -12
z = -12.
Answer:
2
Step-by-step explanation:
I think this is the anser because it went fom -5 to 5 so maybe it goes like that for the answer.
Answer:
There are 20 vegetable plants in garden.
Step-by-step explanation:
We are given the following in the question:
Percentage of flowers = 60%
Percentage of vegetable = 40%
Number of plants in garden = 50
Number of vegetables in garden =
Number of flowers in garden =
Thus, there are 20 vegetable plants in garden.
Answer:
Deal A) 90% Profit ; Deal B) 60% Profit
Step-by-step explanation:
Multiple ways of solving this problem here is one way:
100k-10k = 90k(Revenue) : Then you make this as a percent by 100k then multiply it by 100.
100*((100,000-10,000)/100,000) = 90%
The same is true for the other equation:
100*((50,000-20,000)/50,000) = 60%
