X is twenty
2x+6x+20=180
8x=160
X=20
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.
First of all, lets get y on its own side of the equation.
This is slope intercept form, y=mx+b, where m is slope.
we can see that m=2, so the slope is 2 or 
9/16+ 1/2
= 9/16+ (1*8) / (2*8)
= 9/16+ 8/16 (common denominator is 16)
= (9+8)/16
= 17/16
= (16+1)/16
= 16/16+ 1/16
= 1+ 1/16
= 1 1/16
The final answer is 1 1/16~
Answer:
E. 10 and 10
Step-by-step explanation:
Standard Deviation is the square root of sum of square of the distance of observation from the mean.
where, 
is mean of the distribution.
Here, since standard deviation is the ratio of the distance from the mean and sample size. So for decreasing the standard deviation we should keep numerator constant and increasing the denominator.
This can be only possible in option (E).
Hence, only Option (E) is correct.
