Ella completed the following work to test the equivalence of two expressions.5f+3.65(1)+3.65+3.68.6 6f+2.6 6(1)+2.6 6+2.6 8.6Which is true about the expressions? (1 point)ResponsesThe 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 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 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 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.

Answer 1

To determine the equivalence of the two expressions that Ella worked with, let’s first rewrite each expression clearly:

1. The first expression:
   \( 5f + 3.65(1) + 3.65 + 3.68 \)
   Simplifying this:
   \( 3.65(1) \) is just \( 3.65 \), so the expression becomes:
   \( 5f + 3.65 + 3.65 + 3.68 = 5f + 7.3 + 3.68 = 5f + 7.3 + 3.68 \).
   Therefore, it simplifies to:
   \( 5f + 7.3 + 3.68 = 5f + 11.38 \).

2. The second expression:
   \( 6f + 2.6(6) + 2.6 + 8.6 \)
   We can rewrite \( 2.6(6) \) as \( 15.6 \), so:
   \( 6f + 15.6 + 2.6 + 8.6 = 6f + 15.6 + 2.6 + 8.6 = 6f + 26.8 \).

Now we have:

• First expression: \( 5f + 11.38 \)
• Second expression: \( 6f + 26.8 \)

To establish whether they are equivalent, we can check by substituting a value for \( f \) (in this case, let's use 1):

1. For \( f = 1 \):

   • First expression:
     \( 5(1) + 11.38 = 5 + 11.38 = 16.38 \)

   • Second expression:
     \( 6(1) + 26.8 = 6 + 26.8 = 32.8 \)

Since \( 16.38 \neq 32.8 \), this shows different results for the same input value (in this case, \( f = 1 \)). Thus, we can conclude:

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

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