Answer:
0
1
Step-by-step explanation:
First question:
You are given a side, a, and its opposite angle, A. You are also given side b. Use that in the law of sines and solve for the other angle, B.




The sine function can never equal 2, so there is no triangle in this case.
Answer: no triangle
Second question:
You are given a side, b, and its opposite angle, B. You are also given side c. Use that in the law of sines and solve for the other angle, C.





One triangle exists for sure. Now we see if there is a second one.
Now we look at the supplement of angle C.
m<C = 52.5°
supplement of angle C: m<C' = 180° - 52.5° = 127.5°
We add the measures of angles B and the supplement of angle C:
m<B + m<C' = 63° + 127.5° = 190.5°
Since the sum of the measures of these two angles is already more than 180°, the supplement of angle C cannot be an angle of the triangle.
Answer: one triangle
5 liters = 5000ml
If they combine, they would have
5000 + 750 = 5750ml
one serving = 180ml
Number of serving = 5750 ÷ 180 = 31 serving with 170ml remaining
a. a=40° (alternate interior angles)
b+40°=180°( supplementary angles)
b=140°
c= d= 140°( vertically opposite angles)
d=b=140°( corresponding angles)
b. 2a+120°=180° (supplementary angles)
2a=60°
a=30°
c. a+110°=180°( supplementary angles)
a=70°
b+70°=180°( supplementary angles)
b=110°
c+110°=180°( supplementary angles)
c=70°
c=d=70( corresponding angles)
First integer = x
Second integer = x + 2
Third integer = x + 4
Since four times the first integer equals six more than the product of two and the third integer.
4x = 6 + 2(x + 4)
4x = 6 + 2x + 8
2x = 14
x = 7.
Hence,
First integer = x = 7
Second integer = x + 2 = 7 + 2 = 9
Third integer = x + 4 = 7 + 4 = 11.
hope this helps