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.
Factor the numbers, starting from the smallest:
792=2*3*3*11*4
990=2*3*3*11*5
the greatest whole number that can be divided by both 792 and 990 is 2*3*3*11=198
the smallest whole number that can divide both 792 and 990 exactly is 2*3*3*11*4*5=3960
Not sure which one you are asked to find.
For this problem, we plug in the <em>numbers for t</em> and the <em>appropriate letters for e</em> to the equation <em>e = 300 - 10t</em>.
a) a = 300 - 10(-2)
simplify: a = 300 + 20
simplify: a = 320 ft.
But, this is not a viable point because when t≤0, she doesn't move anywhere, thus, should consistently be 300 ft.
b) b = 300 - 10(3.5)
simplify: b = 300 - 35
simplify: b = 265 ft.
c) c = 300 - 10(30)
simplify: c = 300 - 300
simplify: c = 0 ft.
Answer:
X=80°
Step-by-step explanation:
Bc it’s in the same place as angle F
