Part of the value of sin(u) is cut off; I suspect it should be either sin(u) = -5/13 or sin(u) = -12/13, since (5, 12, 13) is a Pythagorean triple. I'll assume -5/13.
Expand the tan expression using the angle sum identities for sin and cos :
tan(u + v) = sin(u + v) / cos(u + v)
tan(u + v) = [sin(u) cos(v) + cos(u) sin(v)] / [cos(u) cos(v) - sin(u) sin(v)]
Since both u and v are in Quadrant III, we know that each of sin(u), cos(u), sin(v), and cos(v) are negative.
Recall that for all x,
cos²(x) + sin²(x) = 1
and it follows that
cos(u) = - √(1 - sin²(u)) = -12/13
sin(v) = - √(1 - cos²(v)) = -3/5
Then putting everything together, we have
tan(u + v)
= [(-5/13) • (-4/5) + (-12/13) • (-3/5)] / [(-12/13) • (-4/5) - (-5/13) • (-3/5)]
= 56/33
(or, if sin(u) = -12/13, then tan(u + v) = -63/16)
Answer:
The answer is B
Step-by-step explanation:
It's asking what the X values are, meaning only the (X,y) the x part of the coordinates
<h3>
Answer: 60 muffins</h3>
=========================================================
Explanation:
x = some positive whole number
2x = amount Helen baked initially
5x = amount Rebecca baked initially
Notice that the ratio 2x:5x reduces to 2:5 after dividing both parts by x.
So (2x)/(5x) = 2/5
Helen then bakes another 12 muffins, bumping the 2x up to 2x+12. The ratio is now 1:2, which means,
(amount Helen bakes)/(amount Rebecca bakes) = 1/2
(2x+12)/(5x) = 1/2
2(2x+12) = 5x*1 .... cross multiply
4x+24 = 5x
24 = 5x-4x
24 = x
x = 24
From here, we then can say,
- Helen = 2x+12 = 2*24+12 = 48+12 = 60
- Rebecca = 5x = 5*24 = 120
Helen baked 60 muffins and Rebecca baked 120 muffins. We see that 60:120 reduces to 1:2 after dividing both parts by the GCF 60.
Furthermore, note how
- 2x = 2*24 = 48
- 5x = 5*24 = 120
- 48:120 reduces to 2:5 after dividing both parts by 24
This helps confirm we have the correct answer.
Looking at the angles of the triangles
N=S
M=R
O=T
so MON would be RTS
