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 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 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 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 different results when substituting different numbers for f.

Answer 1

The correct response is:

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

Both expressions simplify to 8.6 when f is substituted with 1, showing that they are equivalent for that value of f. However, to fully determine if they are equivalent for all values of f, you would need to consider if they yield the same result for any other values of f as well, but based on the work Ella provided, they are equivalent when f is 1.

Answer 2

wrong

Answer 3

I apologize for any confusion in my previous response. Let's review the statements again.

Ella tested the two expressions:

1. First expression:
   \( 5f + 3.6 \)

   • Substitute \( f = 1 \): \[ 5(1) + 3.6 = 5 + 3.6 = 8.6 \]

2. Second expression:
   \( 6f + 2.6 \)

   • Substitute \( f = 1 \): \[ 6(1) + 2.6 = 6 + 2.6 = 8.6 \]

Both expressions evaluate to 8.6 when \( f = 1 \). However, if we want to determine if they are equivalent for all values of \( f \), we can compare the expressions more generally.

• The first expression simplifies to \( 5f + 3.6 \).
• The second expression simplifies to \( 6f + 2.6 \).

These are linear expressions with different coefficients for \( f \). For example, if you substitute \( f = 0 \):

• For the first expression: \( 5(0) + 3.6 = 3.6 \)
• For the second expression: \( 6(0) + 2.6 = 2.6 \)

The results are different. Therefore, while they yield the same result when substituting \( f = 1 \), they are not equivalent since they give different results for other values of \( f \).

Thus, the correct response would 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 apologize for the error in my initial response.