Answer: see proof below
<u>Step-by-step explanation:</u>
Given: A + B + C = π and cos A = cos B · cos C
scratchwork:
A + B + C = π
A = π - (B + C)
cos A = cos [π - (B + C)] Apply cos
= - cos (B + C) Simplify
= -(cos B · cos C - sin B · sin C) Sum Identity
= sin B · sin C - cos B · cos C Simplify
cos B · cos C = sin B · sin C - cos B · cos C Substitution
2cos B · cos C = sin B · sin C Addition
Division
2 = tan B · tan C
<u>Proof LHS → RHS</u>
Given: A + B + C = π
Subtraction: A = π - (B + C)
Apply tan: tan A = tan(π - (B + C))
Simplify: = - tan (B + C)
Substitution: = -(tan B + tan C)/(1 - 2)
Simplify: = -(tan B + tan C)/-1
= tan B + tan C
LHS = RHS: tan B + tan C = tan B + tan C 
Answer: The greatest number of pages Kenji can decorate = 3
Step-by-step explanation:
Given: Total heart stickers = 15
Total star stickers =12
If all the papers identical, with the same combination of heart and star stickers and no stickers left over.
Then the greatest number of pages Kenji can decorate = GCD(15,12) [GCD=greatest common divisor]
Since 15 = 3 x 5
12=2 x 2 x 3
GCD(15,12) =3
Hence, the greatest number of pages Kenji can decorate = 3
Question:
The options are;
A. The distances in the Olympic final were farther on average.
B. The distances in the Olympic final varied noticeably more than the US qualifier distances
C. The distances in the Olympic final were all greater than the US qualifier distances
D. none of the above
Answer:
The correct option is;
A. The distances in the Olympic final were farther on average.
Step-by-step explanation:
From the options given, we have
A. The distances in the Olympic final were farther on average.
This is true as the sum of the 5 points divided by 5 is more in the Olympic final
B. The distances in the Olympic final varied noticeably more than the US qualifier distances
This is not correct as the difference between the upper and lower quartile in the Olympic final is lesser than in the qualifier
C. The distances in the Olympic final were all greater than the US qualifier distances
This is not correct as the max of the qualifier is more than the lower quartile in the Olympic final
D. none of the above
We have seen a possible correct option in option A
B: answer(90) that’s your answer
