Based on the provided information and evaluation process, the most accurate conclusion is the expressions are equivalent because Ella got the same result when she substituted zero for f. While substituting different numbers for f may yield different results, the provided information only focuses on the case of f = 0, where equivalence is demonstrated. Option of B is the right choice.
Analyzing the Equivalence of Two Expressions
Background:
Ella evaluated two expressions to determine their equivalence.
Expressions:
2f + 2.6
3f + 2.6
Evaluation Process:
Substitution:
For f, Ella substituted 0 in both expressions.
Calculation:
In both cases, she simplified and obtained the same result: 2.6.
Possible Conclusions:
Based on the given information, we can analyze the validity of the four options:
A. The expressions are equivalent because Ella got different results when she substituted zero for f.
This statement is incorrect.
Both expressions resulted in the same value (2.6) after substituting zero for f, contradicting the claim of different results.
B. The expressions are equivalent because Ella got the same result when she substituted zero for f.
This statement is CORRECT. Obtaining the same result for both expressions after substituting zero implies their equivalence.
C. The expressions are not equivalent because Ella would get different results when substituting different numbers for f.
This statement is partially correct. While substituting different numbers for f might lead to different results, the provided information only focuses on the case of f = 0, which demonstrated equivalence.
D. The expressions are not equivalent because Ella would get the same results when substituting different numbers for f.
This statement is incorrect. The information provided contradicts this statement. Ella actually obtained different results when using different values for f.
Option of B is the right choice.
question:
Ella completed the following work to test the equivalence of two expressions.
2 f + 2.6. 2 (0) + 2.6. 0 + 2.6. 2.6. 3 f + 2.6. 3 (0) + 2.6. 0 + 2.6. 2.6.
Which is true about the expressions?
A. The expressions are equivalent because Ella got different results when she substituted zero for f.
B. The expressions are equivalent because Ella got the same result when she substituted zero for f.
C. The expressions are not equivalent because Ella would get different results when substituting different numbers for f.
D. The expressions are not equivalent because Ella would get the same results when substituting different numbers for f.