Question

After simplifying, which expressions are equivalent? Check the three that apply.(3 points) Responses (4.3a−7.1b)+(5.2a−9.3b) open paren 4 point 3 A minus 7 point 1 b close paren plus open paren 5 point 2 A minus 9 point 3 b close paren −0.4b+(6b−9.5a) negative 0 point 4 b plus open paren 6 b minus 9 point 5 A close paren (5.2a+6.1b)+(4.3a+4b) open paren 5 point 2 A plus 6 point 1 b close paren plus open paren 4 point 3 A plus 4 b close paren 9.5a−16.4b 9 point 5 A minus 16 point 4 b (−9.3b+a)+(−7.1b+8.5a) open paren negative 9 point 3 b plus A close paren plus open paren negative 7 point 1 b plus 8 point 5 A close paren

Answer 1

To determine which expressions are equivalent after simplification, let's simplify each of the given expressions step-by-step.

1. **Expression 1**: \((4.3a - 7.1b) + (5.2a - 9.3b)\)

Combine like terms:
\[
(4.3a + 5.2a) + (-7.1b - 9.3b) = 9.5a - 16.4b
\]

2. **Expression 2**: \(-0.4b + (6b - 9.5a)\)

Combine like terms:
\[
6b - 0.4b - 9.5a = (6 - 0.4)b - 9.5a = 5.6b - 9.5a
\]
Thus, it does not simplify to \(9.5a - 16.4b\).

3. **Expression 3**: \((5.2a + 6.1b) + (4.3a + 4b)\)

Combine like terms:
\[
(5.2a + 4.3a) + (6.1b + 4b) = 9.5a + 10.1b
\]
This is also not equivalent to the previous expressions \(9.5a - 16.4b\).

4. **Expression 4**: \(9.5a - 16.4b\)

This is already simplified; it matches the result of Expression 1.

5. **Expression 5**: \((-9.3b + a) + (-7.1b + 8.5a)\)

Combine like terms:
\[
(a + 8.5a) + (-9.3b - 7.1b) = 9.5a - 16.4b
\]

Now, let's summarize:

- **Expression 1** simplifies to \(9.5a - 16.4b\).
- **Expression 4** is \(9.5a - 16.4b\).
- **Expression 5** also simplifies to \(9.5a - 16.4b\).
- **Expression 2** is \(5.6b - 9.5a\) which is not equivalent.
- **Expression 3** is \(9.5a + 10.1b\) which is also not equivalent.

The equivalent expressions are:

- Expression 1
- Expression 4
- Expression 5

Thus, the three expressions that apply are:
- (4.3a−7.1b)+(5.2a−9.3b)
- 9.5a−16.4b
- (−9.3b+a)+(−7.1b+8.5a)