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:
5
Step-by-step explanation:
Since the difference in each term number is 5, we put 5 in the place of the star.
Formula for constant difference in a pattern: Tn= an+b
a is the difference while b is the number that comes before the 1st term. So, the equation to find the nth term is Tn=5n+4.
Hope this helps and please give a brainlist, thank you!
Answer:
there was a 16% increase since 2010 to 2012
Step-by-step explanation:
lets say the train had 100 people on it in 2010 and in 2011 it had an 8% increase which then brings you to 8 plus 100 and you get 108.
Now in 2012 there was an increase 8%, so you will add 8 to your previous answer 108 and receive 116. So now there was 16 more passengers in 2012 than in 2010. Transfer the 16 passengers into 16% and you now have your answer.
32% = 0.32
we know that 0.32 × a number = 8
we can set this number as the variable x
0.32 x = 8
÷0.32 ÷0.32
x = 8
therefore the number is 8
Answer:
The answer is 494.40$
Step-by-step explanation:
618*80=49440
49440/100=494.40
