ANSWER
Quotient:
Remainder:
EXPLANATION
The given functions are
and
We want to find the remainder and quotient when f(x) is divided by g(x).
We perform the long division as shown in the attachment.
The quotient is
The remainder is
X-x-2/6=x-7/3+2/3
-2/6+7/3-2/3=x
x= -2/6+5/3
x= 8/6
x= 4/3
The trig function sine, often abbreviated as "sin" (pronounced the same way as "sine"), is essentially the ratio or fraction of the opposite side and the hypotenuse. See the attached image for a reference.
The leg opposite angle B is side AC. Note how B is not present in the sequence "AC". Visually, we are as far away as possible from point B. This side is 16 units long. So AC = 16
The hypotenuse is the longest side of the right triangle. Always always always. This longest side is opposite the largest angle (90 degrees). Therefore the hypotenuse is BC = 17.46
In summary so far, we have,
opposite side = AC = 16
hypotenuse BC = 17.46
Let's use those values to compute sin(B)
sin(Angle) = opposite/hypotenuse
sin(B) = AC/BC
sin(B) = 16/17.46
sin(B) = 0.916 (this is approximate)
sin(B) =
0.92 (rounding to nearest hundredth)
This points to the
final answer of choice A) 0.92--------------------------------
Edit: Sorry nearly forgot about the reference image. I attached it just now.
Answer: When there are two of the same signs when adding and multiplying it means they are positive but two of the same are negative, which means Clara is rights.
We are looking for the hypotenuse in this right triangle. The reference angle is 41 degrees. We have that angle and the side that is opposite that angle, 22, so the trig identity that we will use that relates the side opposite to the hypotenuse is sin. Our ratio would be set up like this:
. Solving for xy we will have
, choice D from above.
