Answer:
See method below.
Step-by-step explanation:
m/n + n/3 = 2
2/m + n = 4
First eliminate the fractions by multiplying the first equation by 3n:-
3m + n^2 = 6n...........(1)
and the second equation by m:-
2 + mn = 4m..............(2)
Now we solve using substitution:-
From equation (2):-
4m - mn = 2
m = 2 / (4 - n)
Now substitute for m in equation (1):-
6/ (4 - n) + n^2 = 6n
6 + n^2(4 - n) = 6n(4 - n)
6 + 4n^2 - n^3 = 24n - 6n^2
n^3 - 10n^2 + 24n - 6 = 0
This will not factor so we could solve this using graphical software.
To find the values of the variable m we substitute the found values of n into one of the original equations and solve for m.
Answer:
4 airplanes
Step-by-step explanation:
1 = 2/3
6 = x
cross multiply
x = 6 × 2/3
therefore x = 4
Answer:
Marcus has 494 cards.
Jorge has 988 cards.
Ren has 518 cards.
Step-by-step explanation:
Let x represent Marcus's cards.
M + J + R
(x) + (2x) + (x+24) = 2000
x + 2x + x + 24 = 2000
4x +24 =2000
4x = 1976
x = 494
Answer:
4.3 km
Step-by-step explanation:
The law of cosines can be used to find the desired distance. If we call the lighthouse position point L, then we have ...
CH² = LC² +LH² -2·LC·LH·cos(L)
CH² = 2² +2.5² -2·2·2.5·cos(143°) = 10.25 -10cos(143°) ≈ 18.2364
CH ≈ √18.2364 ≈ 4.27 . . . . km
The distance CH is about 4.3 km.
Powers distribute over multiplications:
So, you have
Now, 
is simply 9.
As for 
, we have to use the rule
to get
So, the final answer is
