Final answer:
The correct expression for the number of words in Dominic's essay in relation to Seema's is '3w/4 + 80', meaning three-fourths of the words in Seema's essay plus 80 more words. The variable 'w' represents the word count in Seema's essay and its domain is likely all positive integers, considering a realistic word count for an essay.
Step-by-step explanation:
Algebraic Expressions of Seema and Dominic's Essays
The algebraic expressions given for Seema's and Dominic's essays describe the number of words in their respective essays. According to the provided choices:
- b) Seema's essay consists of w words, and Dominic's essay consists of 3w/4 + 80 words. The expression 3w/4 represents three-fourths of the words in Seema's essay, and the additional 80 words are simply added to that count.
A possible domain for the variable w (the word count of Seema's essay) would be the set of all non-negative integers, as you cannot have a negative word count. However, considering the context of an essay, a more realistic domain might be the set of all positive integers greater than, say, 50 words, as very short texts might not typically be considered essays.
Now, let's look at the constructions:
- The option 'a) Seema's essay: w, Dominic's essay: 34w+80' contains a typo. It should likely be 3/4w + 80 like in option b).
- Option 'c) Seema's essay: w, Dominic's essay: w+80/4' adds one-fourth of 80 to the word count of Seema's essay for Dominic's essay, which is not the same as three-fourths of Seema's word count plus 80.
- The 'd) Seema's essay: w, Dominic's essay: 3w + 80' option is not equivalent to three-fourths; it represents a scenario where Dominic's essay would have three times as many words as Seema's, plus an additional 80 words.