Ella completed the following work to test the equivalence of two expressions. 2f+3.6 2(0)+3.6 0+3.6 3.6 3f+3.6 3(0)+3.6 0+3.6 3.6 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 zero for f. The expressions are equivalent because Ella got the same result when she substituted zero for f . The expressions are equivalent because Ella got different results when she substituted zero for f. The expressions are equivalent because Ella got different results when she substituted zero 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. Skip to navigation

Answer 1

The correct response regarding the equivalence of the two expressions \(2f + 3.6\) and \(3f + 3.6\) is:

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

This is because the two expressions have different coefficients for \(f\).

To elaborate:

• The first expression \(2f + 3.6\) changes based on the value of \(f\). For example, substituting \(f = 0\) yields \(3.6\), but substituting \(f = 1\) gives \(2(1) + 3.6 = 5.6\).
• The second expression \(3f + 3.6\) also changes with \(f\). Substituting \(f = 0\) yields \(3.6\), but substituting \(f = 1\) gives \(3(1) + 3.6 = 6.6\).

Thus, since they yield different results for \(f = 1\) and have different coefficients for \(f\), they are not equivalent expressions.