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Consider the expression [3(42+32÷4−5)]. Which quotient must be found to simplify the expression?(1 point)

Responses

96÷4
96 divided by 4

144÷4
144 divided by 4

32÷4
32 divided by 4

48÷4

7 answers

To simplify the expression \(3(42 + 32 ÷ 4 - 5)\), we first need to focus on the operations inside the parentheses.

Let's break it down step by step:

  1. Start with \(32 ÷ 4\).
  2. Calculate \(32 ÷ 4 = 8\).
  3. Substitute this back into the expression: \(42 + 8 - 5\).

Now, let's perform the addition and subtraction:

  1. \(42 + 8 = 50\).
  2. \(50 - 5 = 45\).

Now, we have:

\[3(45)\].

Although the final multiplication is \(3 \times 45\), the quotient that must be found to simplify the expression initially is:

32 ÷ 4.

So the response is: 32 ÷ 4.

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

The Commutative Property of Addition states that the order in which numbers are added does not change the sum.

For the expression \(4x^2 + 8x\), you can rearrange the terms while maintaining their addition. Here are two possible ways to rewrite the expression using the Commutative Property:

  1. \(8x + 4x^2\)
  2. \(4x^2 + 8x\) (which is the original expression, demonstrating that the property keeps it the same)

Either rearrangement is acceptable because of the Commutative Property.

So, one way to rewrite the expression is: 8x + 4x².

Use the Commutative Property of Addition to rewrite the algebraic expression: ab2+c3
.

Using the Commutative Property of Addition, which states that the order of addition does not change the sum, you can rearrange the terms in the expression \(ab^2 + c^3\).

You can rewrite this expression as:

\(c^3 + ab^2\)

Both forms represent the same value, but the order of the terms has changed according to the property.

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

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

You can rewrite this expression as:

\(x^3 \cdot a^{20}\)

Both forms represent the same value; the order of multiplication has changed according to the property.