Answer:
x = 14
Step-by-step explanation:
you would first distribute the -2 with x - 2, which should give you -2x + 4, and you want to do the -3 - 21, which would give you -24, then subtract 4 from -2x + 4, then you should have -2x = -28, then divide it by -2, which should give you x = 14
Answer: Option 'C' is correct.
Step-by-step explanation:
Since we have given that
Polygon X is similar to polygon.
And Polygon X is three times the size of polygon Y.
So, it becomes,

Hence, perimeter of polygon Y is 27.
Therefore, Option 'C' is correct.
Answer:
24, 48, 72
Step-by-step explanation:
Common Multiples of 8: 8,16,24,32,40,48,56,64,72,80….
Common Multiples of 12: 12,24,36,48,60,72,………..
Hence the First 3 Least common multiple of 8 and 12= 24, 48, 72
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:
<h2>Amanda needs 72 grams of paint</h2>
Step-by-step explanation:
Notice that she already painted one face of each cube, that is, 8 faces in total, and she used 24 grams for that.
Now, there remain 3 faces per cube to be painted, which means there are 24 faces.
Then, we use the rule of three, if she used 24 grams of paint for 8 faces, how much grams of paint she would need to paint 24 faces?

Therefore, Amanda needs 72 grams of paint for the unpainted surfaces.