Answer :
Sure, let's match each algebraic expression to its correct description step by step:
### Step 1: Understand the Descriptions and Expressions
Descriptions:
1. Description 1: 3 terms; variables [tex]\(=x\)[/tex] and [tex]\(y\)[/tex] : constant [tex]\(=2\)[/tex]
2. Description 2: 2 terms; variable [tex]\(=x\)[/tex], constant [tex]\(=4.5\)[/tex]
3. Description 3: 2 terms; variables [tex]\(=x\)[/tex] and [tex]\(y\)[/tex]
4. Description 4: 3 terms; variables [tex]\(=x\)[/tex] and [tex]\(y\)[/tex] : constant [tex]\(=3\)[/tex]
Expressions:
1. Expression 1: [tex]\(4.5x + 2 - 3y\)[/tex]
2. Expression 2: [tex]\(x - 2y + 3\)[/tex]
3. Expression 3: [tex]\(4.5 - 2x\)[/tex]
4. Expression 4: [tex]\(4.5y - 2x\)[/tex]
### Step 2: Match the Descriptions to Expressions
1. Expression 1: [tex]\(4.5x + 2 - 3y\)[/tex]
- This expression has 3 terms: [tex]\(4.5x\)[/tex], [tex]\(2\)[/tex], and [tex]\(-3y\)[/tex].
- The variables are [tex]\(x\)[/tex] and [tex]\(y\)[/tex].
- The constant is [tex]\(2\)[/tex].
- Matching Description 1: 3 terms; variables [tex]\(=x\)[/tex] and [tex]\(y\)[/tex] : constant [tex]\(=2\)[/tex]
2. Expression 2: [tex]\(x - 2y + 3\)[/tex]
- This expression has 3 terms: [tex]\(x\)[/tex], [tex]\(-2y\)[/tex], and [tex]\(3\)[/tex].
- The variables are [tex]\(x\)[/tex] and [tex]\(y\)[/tex].
- The constant is [tex]\(3\)[/tex].
- Matching Description 4: 3 terms; variables [tex]\(=x\)[/tex] and [tex]\(y\)[/tex] : constant [tex]\(=3\)[/tex]
3. Expression 3: [tex]\(4.5 - 2x\)[/tex]
- This expression has 2 terms: [tex]\(4.5\)[/tex] and [tex]\(-2x\)[/tex].
- The variable is [tex]\(x\)[/tex].
- The constant is [tex]\(4.5\)[/tex].
- Matching Description 2: 2 terms; variable [tex]\(=x\)[/tex], constant [tex]\(=4.5\)[/tex]
4. Expression 4: [tex]\(4.5y - 2x\)[/tex]
- This expression has 2 terms: [tex]\(4.5y\)[/tex] and [tex]\(-2x\)[/tex].
- The variables are [tex]\(x\)[/tex] and [tex]\(y\)[/tex].
- There is no constant term.
- Matching Description 3: 2 terms; variables [tex]\(=x\)[/tex] and [tex]\(y\)[/tex]
### Final Matching:
- [tex]\(4.5x + 2 - 3y\)[/tex]: 3 terms; variables [tex]\(=x\)[/tex] and [tex]\(y\)[/tex] : constant [tex]\(=2\)[/tex]
- [tex]\(x - 2y + 3\)[/tex]: 3 terms; variables [tex]\(=x\)[/tex] and [tex]\(y\)[/tex] : constant [tex]\(=3\)[/tex]
- [tex]\(4.5 - 2x\)[/tex]: 2 terms; variable [tex]\(=x\)[/tex], constant [tex]\(=4.5\)[/tex]
- [tex]\(4.5y - 2x\)[/tex]: 2 terms; variables [tex]\(=x\)[/tex] and [tex]\(y\)[/tex]
So the matched pairs are:
1. [tex]\(4.5x + 2 - 3y\)[/tex] matches with "3 terms; variables [tex]\(=x\)[/tex] and [tex]\(y\)[/tex] : constant [tex]\(=2\)[/tex]".
2. [tex]\(x - 2y + 3\)[/tex] matches with "3 terms; variables [tex]\(=x\)[/tex] and [tex]\(y\)[/tex] : constant [tex]\(=3\)[/tex]".
3. [tex]\(4.5 - 2x\)[/tex] matches with "2 terms; variable [tex]\(=x\)[/tex], constant [tex]\(=4.5\)[/tex]".
4. [tex]\(4.5y - 2x\)[/tex] matches with "2 terms; variables [tex]\(=x\)[/tex] and [tex]\(y\)[/tex]".
### Step 1: Understand the Descriptions and Expressions
Descriptions:
1. Description 1: 3 terms; variables [tex]\(=x\)[/tex] and [tex]\(y\)[/tex] : constant [tex]\(=2\)[/tex]
2. Description 2: 2 terms; variable [tex]\(=x\)[/tex], constant [tex]\(=4.5\)[/tex]
3. Description 3: 2 terms; variables [tex]\(=x\)[/tex] and [tex]\(y\)[/tex]
4. Description 4: 3 terms; variables [tex]\(=x\)[/tex] and [tex]\(y\)[/tex] : constant [tex]\(=3\)[/tex]
Expressions:
1. Expression 1: [tex]\(4.5x + 2 - 3y\)[/tex]
2. Expression 2: [tex]\(x - 2y + 3\)[/tex]
3. Expression 3: [tex]\(4.5 - 2x\)[/tex]
4. Expression 4: [tex]\(4.5y - 2x\)[/tex]
### Step 2: Match the Descriptions to Expressions
1. Expression 1: [tex]\(4.5x + 2 - 3y\)[/tex]
- This expression has 3 terms: [tex]\(4.5x\)[/tex], [tex]\(2\)[/tex], and [tex]\(-3y\)[/tex].
- The variables are [tex]\(x\)[/tex] and [tex]\(y\)[/tex].
- The constant is [tex]\(2\)[/tex].
- Matching Description 1: 3 terms; variables [tex]\(=x\)[/tex] and [tex]\(y\)[/tex] : constant [tex]\(=2\)[/tex]
2. Expression 2: [tex]\(x - 2y + 3\)[/tex]
- This expression has 3 terms: [tex]\(x\)[/tex], [tex]\(-2y\)[/tex], and [tex]\(3\)[/tex].
- The variables are [tex]\(x\)[/tex] and [tex]\(y\)[/tex].
- The constant is [tex]\(3\)[/tex].
- Matching Description 4: 3 terms; variables [tex]\(=x\)[/tex] and [tex]\(y\)[/tex] : constant [tex]\(=3\)[/tex]
3. Expression 3: [tex]\(4.5 - 2x\)[/tex]
- This expression has 2 terms: [tex]\(4.5\)[/tex] and [tex]\(-2x\)[/tex].
- The variable is [tex]\(x\)[/tex].
- The constant is [tex]\(4.5\)[/tex].
- Matching Description 2: 2 terms; variable [tex]\(=x\)[/tex], constant [tex]\(=4.5\)[/tex]
4. Expression 4: [tex]\(4.5y - 2x\)[/tex]
- This expression has 2 terms: [tex]\(4.5y\)[/tex] and [tex]\(-2x\)[/tex].
- The variables are [tex]\(x\)[/tex] and [tex]\(y\)[/tex].
- There is no constant term.
- Matching Description 3: 2 terms; variables [tex]\(=x\)[/tex] and [tex]\(y\)[/tex]
### Final Matching:
- [tex]\(4.5x + 2 - 3y\)[/tex]: 3 terms; variables [tex]\(=x\)[/tex] and [tex]\(y\)[/tex] : constant [tex]\(=2\)[/tex]
- [tex]\(x - 2y + 3\)[/tex]: 3 terms; variables [tex]\(=x\)[/tex] and [tex]\(y\)[/tex] : constant [tex]\(=3\)[/tex]
- [tex]\(4.5 - 2x\)[/tex]: 2 terms; variable [tex]\(=x\)[/tex], constant [tex]\(=4.5\)[/tex]
- [tex]\(4.5y - 2x\)[/tex]: 2 terms; variables [tex]\(=x\)[/tex] and [tex]\(y\)[/tex]
So the matched pairs are:
1. [tex]\(4.5x + 2 - 3y\)[/tex] matches with "3 terms; variables [tex]\(=x\)[/tex] and [tex]\(y\)[/tex] : constant [tex]\(=2\)[/tex]".
2. [tex]\(x - 2y + 3\)[/tex] matches with "3 terms; variables [tex]\(=x\)[/tex] and [tex]\(y\)[/tex] : constant [tex]\(=3\)[/tex]".
3. [tex]\(4.5 - 2x\)[/tex] matches with "2 terms; variable [tex]\(=x\)[/tex], constant [tex]\(=4.5\)[/tex]".
4. [tex]\(4.5y - 2x\)[/tex] matches with "2 terms; variables [tex]\(=x\)[/tex] and [tex]\(y\)[/tex]".
