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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

1 answer

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