The value of m is equal to three times n divided by the difference of 4p and 5n. Which of the equations below is equivalent to the equation described above? (may be multiple answers)
a) p=3n-5mn/4m
b) 4mp/3-5m
c) p= 3n+5mn/4m
d) n=4mp/3+5m
e) p= 3mn+5n/4m
f) n=4mp/3m+5
The equation described above is:
m = 3n / (4p - 5n)
To determine which of the given equations are equivalent, we can simplify each option and compare it to the original equation.
a) p = 3n - 5mn / 4m
This equation is not equivalent to the original equation.
b) 4mp / 3 - 5m
This equation is not equivalent to the original equation.
c) p = 3n + 5mn / 4m
This equation is not equivalent to the original equation.
d) n = 4mp / 3 + 5m
This equation is not equivalent to the original equation.
e) p = 3mn + 5n / 4m
This equation is not equivalent to the original equation.
f) n = 4mp / 3m + 5
This equation is not equivalent to the original equation.
None of the given equations are equivalent to the original equation.
To solve this problem, we need to translate the given statement into an equation and then simplify it to match the options provided. Let's break it down step by step:
Given:
The value of m is equal to three times n divided by the difference of 4p and 5n.
Translation:
m = (3n) / (4p - 5n)
Now, let's simplify the equation to match one of the options:
Option a) p = 3n - 5mn / 4m
To check if this is equivalent, let's substitute m = (3n) / (4p - 5n) into the equation:
p = 3n - 5n(3n) / 4((3n) / (4p - 5n))
This equation doesn't match our original equation because the denominators are different.
Option b) 4mp / 3 - 5m
Substituting m = (3n) / (4p - 5n) into the equation:
(4((3n) / (4p - 5n))p) / 3 - 5m
This equation doesn't match our original equation because the terms are in a different order.
Option c) p = 3n + 5mn / 4m
Substituting m = (3n) / (4p - 5n) into the equation:
p = 3n + 5n((3n) / (4p - 5n)) / 4((3n) / (4p - 5n))
This equation doesn't match our original equation because the denominators are different.
Option d) n = 4mp / 3 + 5m
Substituting m = (3n) / (4p - 5n) into the equation:
n = 4((3n) / (4p - 5n))p / 3 + 5m
This equation doesn't match our original equation because the terms are in a different order.
Option e) p = 3mn + 5n / 4m
Substituting m = (3n) / (4p - 5n) into the equation:
p = 3n(3n) / (4p - 5n) + 5n / 4((3n) / (4p - 5n))
p = (9n^2) / (4p - 5n) + (20n^2) / (4p - 5n)
p = (9n^2 + 20n^2) / (4p - 5n)
Option f) n = 4mp / 3m + 5
Substituting m = (3n) / (4p - 5n) into the equation:
n = 4((3n) / (4p - 5n))p / 3((3n) / (4p - 5n)) + 5
n = (12n^2p) / (9n^2) + 5
n = (4p) / 3 + 5
After checking all the options, we find that option e) p = 3mn + 5n / 4m matches the original equation.
m=3n/(4p-5n)
Now your answers, I can't make sense of them. You failed in several instances to use parentheis to group terms