Use the Commutative Property of Addition to rewrite the algebraic expression: 4x2+8x .

Answer 1

The Commutative Property of Addition states that the order in which you add numbers does not affect the sum. Therefore, we can rearrange the terms in the expression \(4x^2 + 8x\).

Rewriting the expression using the Commutative Property, we can express it as:

\[ 8x + 4x^2 \]

So, \(4x^2 + 8x\) can be rewritten as \(8x + 4x^2\).

Answer 2

Use the Commutative Property of Addition to rewrite the algebraic expression: ab2+c3 .(1 point)

Answer 3

Using the Commutative Property of Addition, you can rearrange the terms in the expression \(ab^2 + c^3\).

Thus, it can be rewritten as:

\[ c^3 + ab^2 \]

Both expressions represent the same value, just with the terms in a different order.

Answer 4

Use the Commutative Property of Multiplication to rewrite the algebraic expression: a20⋅x3 .

Answer 5

Using the Commutative Property of Multiplication, which states that the order in which you multiply numbers does not affect the product, we can rearrange the expression \( a^{20} \cdot x^3 \).

So, we can rewrite it as:

\[ x^3 \cdot a^{20} \]

Both expressions represent the same value, just with the terms in a different order.

Answer 6

Using the Commutative Property, fill in the blanks so that the two algebraic expressions are equivalent.(1 point)
(14)(
)(2)=(7)(
)(14)

Answer 7

To fill in the blanks and make the two expressions equivalent using the Commutative Property, we can rewrite the expressions as follows:

Given:

\[ (14)(__)(2) = (7)(__)(14) \]

We can to break down 14 and 7 mathematically:

1. Since \(14 = 7 \cdot 2\), we can use \(7\) in the first blank.
2. Then, for the last blank of the first expression, we can use \(2\), because it also represents the same quantity in both sides.

So, we fill in the blanks like this:

\[ (14)(7)(2) = (7)(2)(14) \]

Thus:

• The first blank is 7.
• The second blank is 2.

Both sides of the equation are equal, demonstrating the Commutative Property.

Answer 8

Using the Commutative Property, fill in the blanks so that the two algebraic expressions are equivalent.(1 point)
5+
+1+7=4+
+7+1

Answer 9

To fill in the blanks so that the two algebraic expressions are equivalent using the Commutative Property of Addition, we need to rearrange the terms.

The expressions provided are:

\[ 5 + __ + 1 + 7 = 4 + __ + 7 + 1 \]

We can see that both sides include the numbers 5, 1, 7 and 4, but we need to find the correct values to fill in the blanks.

Notice that:

1. To maintain equality, the blanks must contain numbers that will balance both sides.
2. Since \(5 + 1 + 7 = 13\) on the left side, and we need a total of 13 on the right side too.

Looking closely:

• When we choose 5 for the first blank, the left side becomes \(5 + 5 + 1 + 7\), which simplifies to \(18\).

• For the right side, we can fill the second blank with 1 because \(4 + 1 + 7 + 1 = 13\).

Thus, we fill in the blanks as follows:

\[ 5 + 5 + 1 + 7 = 4 + 1 + 7 + 1 \]

So, the completed expressions look like:

• First blank: 5
• Second blank: 5

Alternatively, both blanks can be 1, creating:

\[ 5 + 1 + 1 + 7 = 4 + 1 + 7 + 1 \]

Both scenarios maintain equivalence.

Answer 10

one of the answers isnt five

Answer 11

I apologize for the confusion. Let's re-evaluate the original expression step by step:

You provided:

\[ 5 + _ + 1 + 7 = 4 + _ + 7 + 1 \]

Step 1: Simplify both sides

Left side:

• \(5 + 1 + 7 = 13\), so we have: \[ 13 + _ = _ + 12 \]

Right side:

• \(4 + 7 + 1 = 12\), so we have: \[ 12 + _ = 12 + _ \] So both sides need to equal 13.

Step 2: Identify the correct numbers

To balance the equations:

1. On the left side \(5 + _ + 1 + 7\) sums to \(5 + 7 + 1 = 13\).
2. On the right \(4 + _ + 7 + 1\) sums to \(4 + 7 + 1 = 12\).

To ensure the sums are equivalent:

• Left side:

  • We can fill in one blank with 2: \[ 5 + 2 + 1 + 7 = 15 \]

• Right side:

  • The blank can be filled with 5 as on the left part: \[ 4 + 5 + 7 + 1 = 17 \]

Final fill-ins

So then:

• First blank (left): 2
• Second blank (right): 5

The expressions look like this:

\[ 5 + 2 + 1 + 7 = 4 + 5 + 7 + 1 \]

Both sides will be equal when calculated. Thank you for your patience!

Answer 12

it wasnt 2 either :/

Answer 13

I apologize for the oversight. Let's carefully examine the expression again and fill in the blanks correctly this time:

Given:

\[ 5 + _ + 1 + 7 = 4 + _ + 7 + 1 \]

Step 1: Analyzing both sides

1. Left Side: \(5 + _ + 1 + 7\)

   • We know that \(5 + 1 + 7 = 13\).
   • So, the left side becomes: \[ 13 + _ \]

2. Right Side: \(4 + _ + 7 + 1\)

   • We know that \(4 + 7 + 1 = 12\).
   • So, the right side becomes: \[ 12 + _ \]

Step 2: Setting both sides equal

To maintain equality: \[ 13 + _ = 12 + _ \]

For this to hold true:

• The left side needs to be balanced with the right side.

Step 3: Filling in the Blanks

To equate both sides:

• If we look at the left side, we can add 2 for the first blank: \[ 5 + 2 + 1 + 7 = 4 + 6 + 7 + 1 \]

So let's try filling in 6 for the second blank:

Final Equation

To maintain equality: \[ 5 + 6 + 1 + 7 = 4 + 6 + 7 + 1 \]

This satisfies:

• Left Side: \(5 + 6 + 1 + 7 = 19\)
• Right Side: \(4 + 6 + 7 + 1 = 19\)

Final Blanks:

1. First blank: 6
2. Second blank: 6

Complete Expression:

So the filled expression is: \[ 5 + 6 + 1 + 7 = 4 + 6 + 7 + 1 \]

Thank you for your patience, and I hope this resolves the issue correctly!