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.
Theoretical probability (TP) is given by:
TP=[Number of favorable (desired) outcomes]/[Total number of possible outcomes]
From the information given:
Number of purple blocks=19
Total number of possible outcomes=125
thus;
TP=19/125
=0.152
One really simple way to find an equivalent fraction is just to multiply the numerator and denominator.
For example, for the first answer, 
, I simply multiplied the numerator and denominator each by 2. This gives you an equivalent fraction.
You can then continue with this process using numbers such as 3, 4, 5, and 6 as your multiplication factor.
The answer is 9
You divide by 1215 by 15 and the answer is 81
Then you find the square root of 81 and the answer is 9
I cannot see the images, but...
y = | x | + 5
consider the absolute value function. You know that for every value of x, y will be greater than or equal to 5. this means that the y-intercept will also be the bottom of the curve.
Plug a few values in for an idea of what the graph will look like:
f(-1) = 6 (-1,6)
f(1) = 6 (1, 6)
f(-2) = 7 (-2, 7)
f(2) = 7 (2, 7)
The graph will have a minimum value at (0,5), where two lines will converge. The graph will look like a pointy cone with its point at (0,5), with two lines pointing outward and upward from this point. Confirm that the graph passes through the coordinates provided above!
