For this case we have the following functions:
We must find f (g (x)). So:
Finally we have to:
For the function to be defined the denominator must be different from 0. That is x different from -3.
Answer:
Option B
Answer: sin u = -5/13 and cos v = -15/17
Step-by-step explanation:
The nice thing about trig, a little information goes a long way. That’s because there is a lot of geometry and structure in the subject. If I have sin u = opp/hyp, then I know opp is the opposite side from u, and the hypotenuse is hyp, and the adjacent side must fit the Pythagorean equation opp^2 + adj^2 = hyp^2.
So for u: (-5)^2 + adj^2 = 13^2, so with what you gave us (Quad 3),
==> adj of u = -12 therefore cos u = -12/13
Same argument for v: adj = -15,
opp^2 + (-15)^2 = 17^2 ==> opp = -8 therefore sin v = -8/17
The cosine rule for cos (u + v) = (cos u)(cos v) - (sin u)(sin v) and now we substitute: cos (u + v) = (-12/13)(-15/17) - (-5/13)(-8/17)
I am too lazy to do the remaining arithmetic, but I think we have created a way to approach all of the similar problems.
Answer:
Both rates and ratios are a comparison of two numbers. A rate is simply a specific type of ratio. The difference is that a rate is a comparison of two numbers with different units, whereas a ratio compares two numbers with the same unit. For example, in a room full of students, there are 10 boys and 5 girls. This means the ratio of boys to girls is 10:5.
The correct answer is is y=2x
Dress: 93$ at 100-25%=75%
-> divide the marked down cost by the percentage to get the cost of a single percent and then multiply it with the markdown again to get the saved cost
93/75*25=93/3*1=31*1=31$
shoes 119$ at 100-15%=85%
119/85*15=119/17*3=7*3=21
add both savings together for the full sum: 31+21=52$
