Answer: y=9
Step-by-step explanation:
Simplifying
7y = 3y + 36
Reorder the terms:
7y = 36 + 3y
Solving
7y = 36 + 3y
Solving for variable 'y'.
Move all terms containing y to the left, all other terms to the right.
Add '-3y' to each side of the equation.
7y + -3y = 36 + 3y + -3y
Combine like terms: 7y + -3y = 4y
4y = 36 + 3y + -3y
Combine like terms: 3y + -3y = 0
4y = 36 + 0
4y = 36
Divide each side by '4'.
y = 9
Simplifying
y = 9
Answer:
Reference angle:
is not defined.
Step-by-step explanation:
The angle
goes from the positive x-axis to the negative y-axis.
Therefore the reference angle can be calculated as following:

We know that
is:

If
then
, therefore
is not defined, because the division by 0 is not defined.
Answer:
The proof contains a simple direct proof, wrapped inside the unnecessary logical packaging of a proof by contradiction framework.
Step-by-step explanation:
The proof is rigourous and well written, so we discard the second answer.
This is not a fake proof by contradiction: it does not have any logical fallacies (circular arguments) or additional assumptions, like, for example, the "proof" of "All the horses are the same color". It is factually correct, but it can be rewritten as a direct proof.
A meaningful proof by contradiction depends strongly on the assumption that the statement to prove is false. In this argument, we only this assumption once, thus it is innecessary. Other proofs by contradiction, like the proof of "The square root of 2 is irrational" or Euclid's proof of the infinitude of primes, develop a longer argument based on the new assumption, but this proof doesn't.
To rewrite this without the superfluous framework, erase the parts "Suppose that the statement is false" and "The fact that the statement is true contradicts the assumption that the statement is false. Thus, the assumption that the statement was false must have been false. Thus, the statement is true."
3y means *three times y.* So it can be written as 3y or 3•y or written out three times the variable y.
Answer:
25%
Step-by-step explanation:
The percent of increase can be calculated using following formula:

In your case,
- Initial amount = 12 students;
- Final amount = 15 students,
then
