Ella completed the following work to test the equivalence of two expressions.

Question

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 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 .

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

Answer 1

The correct response is:

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

This is because both expressions, when evaluated with \( f = 1 \), resulted in \( 8.6 \). However, this does not necessarily mean they are equivalent for all values of \( f \); the equivalence would need to be proven for all possible values of \( f \). Therefore, strictly speaking about the equivalence based on the given test, her substitution demonstrates they yield the same result for that particular case.

Answer 2

wrong

Answer 3

I apologize for any confusion in my previous response. Let's clarify the situation regarding the expressions based on Ella's work:

Ella simplified two expressions:

1. \(5f + 3.6\) and evaluated it at \(f = 1\):

   • \(5(1) + 3.6 = 5 + 3.6 = 8.6\)

2. \(6f + 2.6\) and evaluated it at \(f = 1\):

   • \(6(1) + 2.6 = 6 + 2.6 = 8.6\)

Both evaluations resulted in \(8.6\) when \(f = 1\). However, this does not mean that the two expressions are equivalent for all values of \(f\).

The correct choice based on this analysis should be:

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

Thank you for your patience, and I appreciate the opportunity to correct my response.