After simplifying, which expressions are equivalent? Check the three 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 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 (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)

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

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

   • Combine like terms: \[ a + 4.9a - 3.9b - 1.7b = (1 + 4.9)a + (-3.9 - 1.7)b = 5.9a - 5.6b \]

2. Expression 2: \(5.9a - 5.6b\)

   • This is already simplified.

3. Expression 3: \((2.5a + 1.6b) + (3.4a + 4b)\)

   • Combine like terms: \[ 2.5a + 3.4a + 1.6b + 4b = (2.5 + 3.4)a + (1.6 + 4)b = 5.9a + 5.6b \]

4. Expression 4: \((3.4a - 1.7b) + (2.5a - 3.9b)\)

   • Combine like terms: \[ 3.4a + 2.5a - 1.7b - 3.9b = (3.4 + 2.5)a + (-1.7 - 3.9)b = 5.9a - 5.6b \]

5. Expression 5: \(-0.4b + (6b - 5.9a)\)

   • Simplify it: \[ -0.4b + 6b - 5.9a = (6 - 0.4)b - 5.9a = 5.6b - 5.9a \]
   • Rearranging gives: \[ -5.9a + 5.6b \]

Now let's check for equivalency:

• Expression 1 simplifies to \(5.9a - 5.6b\).
• Expression 2 is \(5.9a - 5.6b\).
• Expression 3 simplifies to \(5.9a + 5.6b\).
• Expression 4 simplifies to \(5.9a - 5.6b\).
• Expression 5 simplifies to \(-5.9a + 5.6b\) (which is equivalent to \(5.6b - 5.9a\), i.e., the negative).

The expressions that are equivalent are:

• Expression 1: \(5.9a - 5.6b\)
• Expression 2: \(5.9a - 5.6b\)
• Expression 4: \(5.9a - 5.6b\)

Thus, the three that apply are:

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