Answer:
Step-by-step Solution:
<u>Simplify by subtracting 18 both sides</u>
- 7x + 18 > -3
- => 7x + 18 - 18 > -3 - 18
- => 7x > -21
- => x > -3
Hence, the solution to the inequality is x > -3.
Answer:
it ix 23 then 43
Step-by-step explanation:
Answer: see proof below
<u>Step-by-step explanation:</u>
Use the following Product to Sum Identities:
2 sin A sin B = cos (A - B) - cos (A + B)
2 sin A cos B = sin (A + B) + sin (A - B)
Use the Unit Circle to evaluate: cos 120 = -1/2 & sin 60 = √3/2
<u>Proof LHS → RHS</u>
LHS: sin 20 · sin 40 · sin 80
Regroup: (1/2) sin 20 · 2 sin 40 · sin 80
Product to Sum Identity: (1/2) sin 20 [cos(80-40) - cos (80+40)]
Simplify: (1/2) sin 20 [cos 40 - cos 120]
Unit Circle: (1/2) sin 20 [cos 40 + (1/2)]
Distribute: (1/2) sin 20 cos 40 + (1/4) sin 20
Product to Sum Identity: (1/4)[sin(20 + 40) + sin (20 - 40)] + (1/4) sin 20
Simplify: (1/4)[sin 60 + sin (-20)] + (1/4) sin 20
= (1/4)[sin 60 - sin 20] + (1/4) sin 20
Unit Circle: (1/4)[(√3/2) - sin 20] + (1/4) sin 20
Distribute: (√3/8) - (1/4) sin 20 + (1/4) sin 20
Simplify: √3/8
LHS = RHS: √3/8 = √3/8
When dealing with fractions, take the whole as 1.
in this case, the whole class is 1;
fraction of votes for Andrew: 1-1/2 -1/4 - 1/5
these fractions have different denominators (bottom), to continue, you have to make the denominators the same;
to do that, I usually count by the largest one. In this case, it is a 5. 5 is not divisible by 2 or 4, so I move on to 10. 10 is still not divisible by 2 and 4, so try 15, then 20.
20 works, so make all the denominators to 20. Remember 1 is 20/20:
20/20- 10/20 -5/20 -4/20 =1/20
so the fraction of votes Andrew got was 1/20.
For answer b, the whole is no longer 1. the whole is now 100.
1/2 of 100=50 for Amy
1/4 of 100=25 for Sophie
1/5 of 100=20 for Ryan
1/20 of 100=5 for Andrew
Notice the numbers add up to be exactly 100
Answer: 36
Step-by-step explanation: multiply 2 6 and 3