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)
Which expression is equivalent to 30(1/2x−2)+40(3/4y−4) (1 point) Responses 15x+30y−22015x+30y−22015 x plus 30 y minus 220 15x+30y−6415x+30y−6415 x plus 30 y minus 64 15x−30y−22015x−30y−22015 x minus 30 y minus 220 45xy−220
What value correctly fills in the blank so that the expressions are equivalent? 32+72= ? (4+9)
13
12
4
8

Answer 1

Let's break down each part of your question step by step.

### Part 1: Equivalent Expressions
**Expressions to check:**
1. \(-0.4b + (6b - 5.9a)\)
2. \((3.4a - 1.7b) + (2.5a - 3.9b)\)
3. \(5.9a - 5.6b\)
4. \((2.5a + 1.6b) + (3.4a + 4b)\)
5. \((-3.9b + a) + (-1.7b + 4.9a)\)

**To simplify each expression:**

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

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

3. **Expression 3:**
It is already \(5.9a - 5.6b\).

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

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

**Equivalent expressions are:**
- Expression 1: \(5.6b - 5.9a\)
- Expression 2: \(5.9a - 5.6b\)
- Expression 3: \(5.9a - 5.6b\)
- Expression 5: \(5.9a - 5.6b\)

So, the equivalent expressions are **1, 2, 3,** and **5**.

### Part 2: Expression Equivalent to \(30(1/2x - 2) + 40(3/4y - 4)\)
**Simplifying:**
- Distributing the constants:
\[
30 \left( \frac{1}{2}x - 2 \right) = 15x - 60
\]
\[
40 \left( \frac{3}{4}y - 4 \right) = 30y - 160
\]

- Combining these gives:
\[
15x - 60 + 30y - 160 = 15x + 30y - 220
\]

So, the expression that is equivalent is **15x + 30y - 220**.

### Part 3: Value that Fills in The Blank
The equation is \(32 + 72 = ? (4 + 9)\).

First, calculate \(4 + 9\):
\[
4 + 9 = 13
\]

Now calculate \(32 + 72\):
\[
32 + 72 = 104
\]

To find the value that fills in the blank, we need:
\[
? \cdot 13 = 104
\]

Dividing both sides by 13 gives:
\[
? = \frac{104}{13} = 8
\]

Thus the value that fills in the blank is **8**.

### Summary of Answers
1. Equivalent expressions: 1, 2, 3, 5
2. Equivalent expression for \(30(1/2x - 2) + 40(3/4y - 4)\): **15x + 30y - 220**
3. Value that fills in blank: **8**