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5f+3.6



5(1)+3.6


5+3.6


8.6


6f+2.6


6(1)+2.6


6+2.6


8.6


Which is true about the expressions?



(1 point)
Responses

The expressions are equivalent because Ella got different results when she substituted one for f.
The expressions are equivalent because Ella got different results when she substituted one for f .

The expressions are not equivalent because Ella would get the same results when substituting different numbers for f.
The expressions are not equivalent because Ella would get the same results when substituting different numbers for f.

The expressions are not equivalent because Ella would get different results when substituting different numbers for f.
The expressions are not equivalent because Ella would get different results when substituting different numbers for f.

The expressions are equivalent because Ella got the same result when she substituted one for f.
The expressions are equivalent because Ella got the same result when she substituted one for f .

1 answer

To determine the truth about the expressions given, let's analyze them.

  1. Expression 1: \[ 5f + 3.6 \] When \( f = 1 \): \[ 5(1) + 3.6 = 5 + 3.6 = 8.6 \]

  2. Expression 2: \[ 6f + 2.6 \] When \( f = 1 \): \[ 6(1) + 2.6 = 6 + 2.6 = 8.6 \]

Both expressions yield the same result (8.6) when \( f = 1 \).

To conclude whether the expressions are equivalent, we also need to see if they are equivalent for different values of \( f \).

  • For \( f = 0 \):
    • Expression 1: \[ 5(0) + 3.6 = 0 + 3.6 = 3.6 \]
    • Expression 2: \[ 6(0) + 2.6 = 0 + 2.6 = 2.6 \]

The expressions yield different results for \( f = 0 \) (3.6 vs. 2.6), showing that they are not equivalent in general.

Thus, the correct choice is:

  • The expressions are not equivalent because Ella would get different results when substituting different numbers for \( f \).

Therefore, the response is: The expressions are not equivalent because Ella would get different results when substituting different numbers for f.