Question

After simplifying, which expressions are equivalent?%C2%A0Check the%C2%A0three that apply.(3 points) Responses (−3.9b+a)+(−1.7b+4.9a) open paren negative 3 point 9 b plus A close paren plus open paren negative 1 point 7 b plus 4 point 9 A close paren (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 −0.4b+(6b−5.9a) negative 0 point 4 b plus open paren 6 b minus 5 point 9 A close paren 5.9a−5.6b 5 point 9 A minus 5 point 6 b (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

Answer 1

To determine which expressions are equivalent, we will simplify each expression step by step.

1. **Expression:** \((-3.9b + a) + (-1.7b + 4.9a)\)

**Simplification:**
\[
= -3.9b - 1.7b + a + 4.9a
= (-3.9 - 1.7)b + (1 + 4.9)a
= -5.6b + 5.9a
\]

2. **Expression:** \((3.4a - 1.7b) + (2.5a - 3.9b)\)

**Simplification:**
\[
= 3.4a + 2.5a - 1.7b - 3.9b
= (3.4 + 2.5)a + (-1.7 - 3.9)b
= 5.9a - 5.6b
\]

3. **Expression:** \(-0.4b + (6b - 5.9a)\)

**Simplification:**
\[
= -0.4b + 6b - 5.9a
= (-0.4 + 6)b - 5.9a
= 5.6b - 5.9a
\]

4. **Expression:** \(5.9a - 5.6b\)

This expression is already in simplest form.

5. **Expression:** \((2.5a + 1.6b) + (3.4a + 4b)\)

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

Now, we can compare the results of the simplifications:

- Expression 1: \(-5.6b + 5.9a\) (which is equivalent to \(5.9a - 5.6b\))
- Expression 2: \(5.9a - 5.6b\)
- Expression 3: \(5.6b - 5.9a\) (this is not equivalent)
- Expression 4: \(5.9a - 5.6b\)
- Expression 5: \(5.9a + 5.6b\) (this is not equivalent)

From the simplifications, the equivalent expressions are:

1. \((-3.9b + a) + (-1.7b + 4.9a)\)
2. \((3.4a - 1.7b) + (2.5a - 3.9b)\)
3. \(5.9a - 5.6b\)

Thus, the expressions that are equivalent are:

- \((-3.9b + a) + (-1.7b + 4.9a)\)
- \((3.4a - 1.7b) + (2.5a - 3.9b)\)
- \(5.9a - 5.6b\)

These can be summarized as options 1, 2, and 4 from the original list.