Answer :
Certainly! Let’s match each description of an algebraic expression with its symbolic form step-by-step.
### Descriptions and Symbolic Forms:
1. Description:
- 2 terms
- Variables = x and y
2. Description:
- 3 terms
- Variables = x and y
- Constant = 2
3. Description:
- 3 terms
- Variables = x and y
- Constant = 3
4. Description:
- 2 terms
- Variable = x
- Constant = 4.5
### Symbolic Expressions:
1. [tex]\(4.5 y - 2 x\)[/tex]
2. [tex]\(4.5 x + 2 - 3 y\)[/tex]
3. [tex]\(4.5 - 2 x\)[/tex]
### Matching Process:
1. Description 1: 2 terms; variables = x and y
- Expression needs to contain exactly 2 terms.
- Both terms should contain [tex]\(x\)[/tex] and [tex]\(y\)[/tex].
- The expression [tex]\(4.5 y - 2 x\)[/tex] fits this description because it has two terms, one in [tex]\(y\)[/tex] and the other in [tex]\(x\)[/tex].
Match: [tex]\(4.5 y - 2 x\)[/tex]
2. Description 2: 3 terms; variables = x and y; constant = 2
- Expression needs to have exactly 3 terms.
- It should include both [tex]\(x\)[/tex] and [tex]\(y\)[/tex] variables, and a constant term of 2.
- The expression [tex]\(4.5 x + 2 - 3 y\)[/tex] fits this description because it has three terms: one term with [tex]\(x\)[/tex], one constant term equal to 2, and one term with [tex]\(y\)[/tex].
Match: [tex]\(4.5 x + 2 - 3 y\)[/tex]
3. Description 3: 3 terms; variables = x and y; constant = 3
- Expression needs to have exactly 3 terms.
- It should include both [tex]\(x\)[/tex] and [tex]\(y\)[/tex] variables, and a constant term of 3.
- None of the given expressions have a constant term of 3.
Match: None
4. Description 4: 2 terms; variable = x; constant = 4.5
- Expression needs to have exactly 2 terms.
- One term should be a constant of 4.5 and the other term should contain [tex]\(x\)[/tex].
- The expression [tex]\(4.5 - 2 x\)[/tex] fits this description, as it has a constant term of 4.5 and another term containing [tex]\(x\)[/tex].
Match: [tex]\(4.5 - 2 x\)[/tex]
### Final Matches:
- Description 1: [tex]\(4.5 y - 2 x\)[/tex]
- Description 2: [tex]\(4.5 x + 2 - 3 y\)[/tex]
- Description 3: None
- Description 4: [tex]\(4.5 - 2 x\)[/tex]
Thus, the matched expressions are:
1. [tex]\(4.5 y - 2 x\)[/tex]
2. [tex]\(4.5 x + 2 - 3 y\)[/tex]
3. None
4. [tex]\(4.5 - 2 x\)[/tex]
### Descriptions and Symbolic Forms:
1. Description:
- 2 terms
- Variables = x and y
2. Description:
- 3 terms
- Variables = x and y
- Constant = 2
3. Description:
- 3 terms
- Variables = x and y
- Constant = 3
4. Description:
- 2 terms
- Variable = x
- Constant = 4.5
### Symbolic Expressions:
1. [tex]\(4.5 y - 2 x\)[/tex]
2. [tex]\(4.5 x + 2 - 3 y\)[/tex]
3. [tex]\(4.5 - 2 x\)[/tex]
### Matching Process:
1. Description 1: 2 terms; variables = x and y
- Expression needs to contain exactly 2 terms.
- Both terms should contain [tex]\(x\)[/tex] and [tex]\(y\)[/tex].
- The expression [tex]\(4.5 y - 2 x\)[/tex] fits this description because it has two terms, one in [tex]\(y\)[/tex] and the other in [tex]\(x\)[/tex].
Match: [tex]\(4.5 y - 2 x\)[/tex]
2. Description 2: 3 terms; variables = x and y; constant = 2
- Expression needs to have exactly 3 terms.
- It should include both [tex]\(x\)[/tex] and [tex]\(y\)[/tex] variables, and a constant term of 2.
- The expression [tex]\(4.5 x + 2 - 3 y\)[/tex] fits this description because it has three terms: one term with [tex]\(x\)[/tex], one constant term equal to 2, and one term with [tex]\(y\)[/tex].
Match: [tex]\(4.5 x + 2 - 3 y\)[/tex]
3. Description 3: 3 terms; variables = x and y; constant = 3
- Expression needs to have exactly 3 terms.
- It should include both [tex]\(x\)[/tex] and [tex]\(y\)[/tex] variables, and a constant term of 3.
- None of the given expressions have a constant term of 3.
Match: None
4. Description 4: 2 terms; variable = x; constant = 4.5
- Expression needs to have exactly 2 terms.
- One term should be a constant of 4.5 and the other term should contain [tex]\(x\)[/tex].
- The expression [tex]\(4.5 - 2 x\)[/tex] fits this description, as it has a constant term of 4.5 and another term containing [tex]\(x\)[/tex].
Match: [tex]\(4.5 - 2 x\)[/tex]
### Final Matches:
- Description 1: [tex]\(4.5 y - 2 x\)[/tex]
- Description 2: [tex]\(4.5 x + 2 - 3 y\)[/tex]
- Description 3: None
- Description 4: [tex]\(4.5 - 2 x\)[/tex]
Thus, the matched expressions are:
1. [tex]\(4.5 y - 2 x\)[/tex]
2. [tex]\(4.5 x + 2 - 3 y\)[/tex]
3. None
4. [tex]\(4.5 - 2 x\)[/tex]
