Question

After simplifying, which expressions are equivalent? Check the three that apply.(3 points) Responses −0.4b+(6b−5.9a)−0.4b+(6b−5.9a)negative 0 point 4 b plus open paren 6 b minus 5 point 9 A close paren (3.4a−1.7b)+(2.5a−3.9b)(3.4a−1.7b)+(2.5a−3.9b)open paren 3 point 4 A minus 1 point 7 b close paren plus open paren 2 point 5 A minus 3 point 9 b close paren 5.9a−5.6b5.9a−5.6b5 point 9 A minus 5 point 6 b (2.5a+1.6b)+(3.4a+4b)(2.5a+1.6b)+(3.4a+4b)open paren 2 point 5 A plus 1 point 6 b close paren plus open paren 3 point 4 A plus 4 b close paren (−3.9b+a)+(−1.7b+4.9a)

Answer 1

To determine which expressions are equivalent after simplification, let's simplify each expression one by one.

1. **Expression 1: −0.4b + (6b − 5.9a)**
\[
= -0.4b + 6b - 5.9a
= (6b - 0.4b) - 5.9a
= 5.6b - 5.9a
\]

2. **Expression 2: (3.4a − 1.7b) + (2.5a − 3.9b)**
\[
= 3.4a - 1.7b + 2.5a - 3.9b
= (3.4a + 2.5a) + (-1.7b - 3.9b)
= 5.9a - 5.6b
\]

3. **Expression 3: 5.9a − 5.6b**
- This is already simplified and is the same as the result from Expression 1 and Expression 2.

4. **Expression 4: (2.5a + 1.6b) + (3.4a + 4b)**
\[
= 2.5a + 1.6b + 3.4a + 4b
= (2.5a + 3.4a) + (1.6b + 4b)
= 5.9a + 5.6b
\]

5. **Expression 5: (−3.9b + a) + (−1.7b + 4.9a)**
\[
= -3.9b + a - 1.7b + 4.9a
= (a + 4.9a) + (-3.9b - 1.7b)
= 5.9a - 5.6b
\]

Now we can summarize:

- **Expression 1** simplifies to **5.6b - 5.9a**
- **Expression 2** simplifies to **5.9a - 5.6b**
- **Expression 3** is **5.9a - 5.6b**
- **Expression 4** simplifies to **5.9a + 5.6b**
- **Expression 5** simplifies to **5.9a - 5.6b**

The equivalent expressions are:

- Expression 2: **5.9a - 5.6b**
- Expression 3: **5.9a - 5.6b**
- Expression 5: **5.9a - 5.6b**

So the three equivalent expressions are **2, 3, and 5**.