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.