Mathematics, 14.12.2020 18:30, andreamarie2004amg

Name the property of real numbers illustrated by the equation (2 + x) + 3 = 2 + (x + 3). Identity Property

Distributive Property

Associative Property

Commutative Property

Answers: 2

Show answers

Answers

answered: preachersgirl5

This equation illustrates the associative property of the real number field, $(\mathbb{R},\, +,\, \cdot)$ .

Step-by-step explanation:

All four choices here are indeed properties of the field of real numbers, $(\mathbb{R},\, +,\, \cdot)$ . However, the equation (2 + x) + 3 = 2 + (x + 3) makes use of only the associative property.

Identity Property

By identity property of fields, the real number field $(\mathbb{R},\, +,\, \cdot)$ should contain an identity element $e \in \mathbb{R}$ , such that for any element of that field $a \in \mathbb{R}$ :

a + e = a .

In particular, the identity element of the real number field $(\mathbb{R},\, +,\, \cdot)$ is the real number . The identity property (of addition) would then read:

a + 0 = a for any $a \in \mathbb{R}$ .

Distributive Property

By the distributive property of fields, for any three elements ( $a,\, b,\, c \in \mathbb{R}$ ) of the real number field $(\mathbb{R},\, +,\, \cdot)$ :

$a\cdot (b + c) = a \cdot b + a \cdot c$ .

$(a + b) \cdot c = a \cdot c + b \cdot c$ .

Note that this property features both addition and multiplication in the same equation. However, the equation in the question includes only addition. Therefore, this property would not apply here.

Associative Property

By the associative property of fields, for any three elements ( $a,\, b,\, c \in \mathbb{R}$ ) of the real number field $(\mathbb{R},\, +,\, \cdot)$ :

a + (b + c) = (a + b) + c .

$a \cdot (b \cdot c) = (a \cdot b) \cdot c$ .

In particular, the equation (2+ x) + 3 = 2 + (x + 3) (where $x \in \mathbb{R}$ ) illustrates the associative property of addition of the real number field.

Note that even though the location of the parentheses have changed, the elements are still in the same place (with , , and in the same order on both sides of the two equations.)

Commutative Property

By the commutative property of fields, for any two elements ( $a,\, b\in \mathbb{R}$ ) of the real number field $(\mathbb{R},\, +,\, \cdot)$ :

a + b = b + a .

$a \cdot b = b \cdot a$ .

The commutative property of fields allow the elements in the additions and in multiplications to be rearranged. (In contrast, the associative property allows for only the rearrangement of the parentheses.)

That doesn't apply to (2+ x) + 3 = 2 + (x + 3) because the numbers and symbols appear in the same order on both sides of the equation.

answered: Guest

(2,20) means that the 2 is 2 hours and 20 is 20$. so there both 20$ for 2 hours only the same price. like it says. so, the dunk tank and the bounce house are the same price (20$) for the same amount of time (2 hours).

hope i

answered: Guest

The answe maybbe