Which procedure justifies whether -3x(5-4)+3(x-6) is equivalent to -12x-6?
The expressions are not equivalent because -3(2)(5-4) +3(2-6)=-18 and -12(2)-6--30
The expressions are not equivalent because -3(2)(5-4)+ 3(2-6) --18 and -12(3)-6=-42
The expressions are equivalent because -3(2)(5-4)+3(2-6)=-18 and -12(-2)-6-18
The expressions are equivalent because -3(2)(5-4)+ 3(2-6)=-18 and -12(1)-6--18

Step-by-step explanation:

Equivalent Expressions

One approach that can be followed to know if two expressions are equivalent is to evaluate them for the same value of the independent value. If by chance they are equal for that value, it doesn't prove they are equivalent, but if they are not equal, then we can infer they are NOT equivalent.

Let's analyze these expressions

We'll use the value x=2:

This result matches the first option provided in the question. For the sake of completeness, we'll check the other options.

The above statement is true, but the second result is obtained for a different value of x respect to the first result. So it does not qualify as a valid proof.

We'll simplify the first expression

The result is not equivalent to  -12x-6. Thus, the two other options are false.

126.66 m²

step-by-step explanation:

the pertinent area formula is a = πr², where r is the radius.

here, a = π(6.35 m)² = 40.32π, or approximately 126.66 m²