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 
You can do 4 to the second power and 4×4 equals 16
Answer:C
Step-by-step explanation:
Answer:
Y = 300 + 2X
Y( in dollars)
It is a functional relationship because a change in the value of X results in a corresponding change in the value of Y. And does not involve any uncertainty.
Step-by-step explanation:
Given:
Annual fixed due = $300
Variable cost = $2 per visit
X = number of visits in a year
Y = total yearly cost.
Y = annual cost + variable cost
Y = $300 + $2×X
Y = 300 + 2X
Y( in dollars)
It is a functional relationship because a change in the value of X results in a corresponding change in the value of Y. And does not involve any uncertainty.
C. Both options A and B will allow him to meet his goal.
Looking at Drake's situation after 4 weeks, he only has $470 saved. By
his original plan, he should have had $500 saved. So he's $30 short of
his goal and has 2 weeks until his originally planned class. If he goes
with option A and takes the later class, he will save an additional $125
which is more than enough to make up the $30 short fall. So option A
will work for him to save enough money for his class. With option B, he
will save $140 for the last 2 weeks of his plan giving him a savings of
$280 for the last 2 weeks. Adding the $470 he's already saved will give
him a total savings of $470 + $280 = $750 which is enough for him to
attend his class. So option B will also allow Drake to attend his
desired class. Both options A and B allow him to meet his goal. Hence,
the answer is "c".
