C :) brainiest? This is correct because I did the math lol
The amplitude of 
is the absolute value of 
. So first you need to condense the given function into one sine expression.
Recall that
so you need to choose 
and 
accordingly.
If we line up the terms of the given function with the expanded one above, we should have
Now, using the Pythagorean identity,
so the amplitude is √29.
Just for completeness, we also get
where 
is any integer.
Answer:
Step-by-step explanation:
We have the inequality:
Solve. Divide both sides by -2. Since we are dividing by a negative, we must flip the inequality sign. Thus:
Add 5 to both sides:
Therefore, our solution is all numbers greater than 11 .
This means that if we substitute any number greater than 11 into our original inequality, the inequality will be true.
1. (x , y) → (kx , ky) = Dilation ; similar image
2. (x , y) → (y , -x) = Rotation 90 counterclockwise ; congruent
3. (x , y) → (-x , y) = Reflection over y-axis ; congruent
4. (x , y) → (-x , -y) = Rotation 180 ; congruent
5. (x , y) → (x, -y) = Reflection over x-axis ; congruent
6. (x , y) → (-y , x) = Rotation 90 clockwise ; congruent
7. (x , y) → (x + a , y + b) = Translation ; congruent
Hope this helps :)
If complex coefficients are allowed, the answer is 3.
If the polynomial must have real coefficients, then each complex root comes as a pair of complex conjugate roots.
Root -5 is real, so that is 1 root, and degree 1.
Root 1 + 4i is complex, so it must come with its complex conjugate, 1 - 4i. This adds 2 roots to the polynomial, and now we're up to degree 3.
Root -4i is also complex. It also must come with its complex conjugate, 4i. That adds two more roots, and the degree is 5.
Answer: The least possible degree is 5 with real coefficients.
