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:
Area : 45 Perimeter : 2,025
Explanation:
Area: 5 times 9 equals 45. The 5 is the polygon’s base, the 9 is the polygon’s height.
Perimeter: 5 times 5 times 9 times 9 equals 2,025. Perimeter is base times base times height times height.
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Mean of the low is approximately 47.7 Median of the low is 45 and 50 or 47.5
<h3>
Answer: 2z^3</h3>
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Explanation:
The GCF of the coefficients {6, -42, 14} is 2 as it is the largest factor found in each of the three values.
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For the variable portions, we can
- write z^5 as z^3*z^2
- write z^4 as z^3*z^1
- write z^3 as z^3*1
Each time we see z^3 show up, so this is the largest common factor among the three variable terms.
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The two results we got were 2 and z^3
Putting the two results together, we end up with the overall GCF of 2z^3
