JY CHEN - Ask Anything, Learn Everything. Logo

In Mathematics / College | 2025-07-07

Choose the property of real numbers that justifies the equation.





Asked by erieben113

Answer (1)

Multiplication property of zero: 0 o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak c d o t 2 = 0 .
Associative property of multiplication: ( 3 o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak c d o t 7 ) o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak c d o t a = 3 o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak c d o t ( 7 o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak c d o t a ) .
Associative property of addition: ( 9 + n ) + 8 = 9 + ( n + 8 ) .
Additive identity property: 0 + 4 = 4 .

Explanation

Analyzing the Equations We are given four equations and asked to identify the property of real numbers that justifies each equation. Let's analyze each equation separately.

Multiplication Property of Zero

0 o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak c d o t 2 = 0 : This equation demonstrates the multiplication property of zero, which states that any real number multiplied by zero equals zero.

Associative Property of Multiplication

( 3 o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak c d o t 7 ) o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak c d o t a = 3 o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak c d o t ( 7 o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak c d o t a ) : This equation illustrates the associative property of multiplication. The associative property states that the grouping of factors does not affect the product. In other words, for any real numbers x , y , and z , ( x o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak c d o t y ) o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak c d o t z = x o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak c d o t ( yo b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak c d o t z ) .

Associative Property of Addition

( 9 + n ) + 8 = 9 + ( n + 8 ) : This equation demonstrates the associative property of addition. Similar to multiplication, the associative property of addition states that the grouping of addends does not affect the sum. For any real numbers x , y , and z , ( x + y ) + z = x + ( y + z ) .

Additive Identity Property

0 + 4 = 4 : This equation illustrates the additive identity property. The additive identity property states that the sum of any real number and zero is the original number. Zero is called the additive identity.

Final Answer In summary:



0 o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak c d o t 2 = 0 is justified by the multiplication property of zero.
( 3 o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak c d o t 7 ) o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak c d o t a = 3 o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak c d o t ( 7 o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak o b re ak c d o t a ) is justified by the associative property of multiplication.
( 9 + n ) + 8 = 9 + ( n + 8 ) is justified by the associative property of addition.
0 + 4 = 4 is justified by the additive identity property.

Examples
Understanding the properties of real numbers is crucial in various real-life scenarios. For instance, the associative property helps in organizing tasks efficiently. Imagine you have a series of errands to run: picking up groceries, going to the post office, and then visiting the dry cleaner. The associative property tells us that the order in which you group these tasks doesn't change the total time spent, as long as you complete all the errands. Similarly, the identity property is useful in balancing budgets, where adding zero to your expenses or income doesn't change your financial status. These properties, though abstract, provide a foundation for problem-solving in everyday situations.

Answered by GinnyAnswer | 2025-07-07

Related Questions in Mathematics

[Free] Select the correct answer. Which equation is equivalent to the given equation? [tex]$x^2-6 x=8$[/tex] A. [tex]$(x-6)^2=44$[/tex] B. [tex]$(x-3)^2=17$[/tex] C. [tex]$(x-6)^2=20$[/tex] D. [tex]$(x-3)^2=14$[/tex]

[Free] Which phrase best describes the translation from the graph [tex]y=6 x^2[/tex] to the graph of [tex]y=6(x+1)^2[/tex]? A. 6 units left B. 6 units right C. 1 unit left D. 1 unit right

[Free] What expression is equivalent to [tex]$\left(5 z^2+3 z+2\right)^2$[/tex] ? A. [tex]$5 z^4+3 z^2+4$[/tex] B. [tex]$5 z^4+9 z^2+4$[/tex] C. [tex]$25 z^4+30 z^3+19 z^2+12 z+4$[/tex] D. [tex]$25 z^4+30 z^3+29 z^2+12 z+4$[/tex]

[Free] The graph of [tex]y=\frac{5}{4} x+1[/tex] is shown below. The coordinate ([tex]0, y[/tex]) is a solution of the equation. Given the [tex]x[/tex]-value of 0, what is the value of the [tex]y[/tex]-coordinate for the coordinate ([tex]0, y[/tex])? [tex]y=[/tex] [blank]

[Free] If [tex]f(-2)=0[/tex], what are all the factors of the function [tex]f(x)=x^3-2 x^2-68 x-120[/tex]? Use the Remainder Theorem. A. [tex](x+2)(x+60)[/tex] B. [tex](x-2)(x-60)[/tex] C. [tex](x-10)(x+2)(x+6)[/tex] D. [tex](x+10)(x-2)(x-6)[/tex]