Which Expression Is Equivalent To Assume
In mathematics, two expressions are said to be equivalent if they have the same value for all possible values of the variables involved. In other words, if we substitute any value for the variables in the two expressions, we will get the same result.
The question "Which expression is equivalent to assume" is a type of mathematical problem that asks us to find two expressions that are equivalent. The answer to this question will depend on the specific expressions that are given.
Example 1
Given expression:
x + 2 = 4 Assume:
x = 2 Equivalent expression:
2 + 2 = 4 Solution:
Substituting x = 2 into the given expression, we get:
2 + 2 = 4 This is the same as the equivalent expression, so the answer is (2 + 2) = 4.
Example 2
Given expression:
(10x^6 y^12) / (-5x^2 y^6) Assume:
x > 0, y != 0 Equivalent expression:
-2x^8 y^18 Solution:
Using the properties of exponents, we can simplify the given expression as follows:
(10x^6 y^12) / (-5x^2 y^6) = (10 / -5) * (x^6 / x^2) * (y^12 / y^6) = -2 * x^(6 – 2) * y^(12 – 6) = -2x^4 y^6 = -2x^8 y^18
Since x > 0, we can cancel the factor of 2 from the numerator and denominator. Therefore, the equivalent expression is -x^8 y^18.
Related Questions
Here are some related questions about equivalent expressions:
- What are the properties of equivalent expressions?
- How can we find equivalent expressions?
- How can we use equivalent expressions to solve math problems?
Properties of Equivalent Expressions
Equivalent expressions have the following properties:
- They have the same value for all possible values of the variables involved.
- They can be manipulated in the same way without changing their value.
Finding Equivalent Expressions
There are many ways to find equivalent expressions. One common method is to use the properties of equivalent expressions. For example, we can use the distributive property to distribute a common factor, or we can use the commutative property to rearrange the terms in an expression.
Using Equivalent Expressions to Solve Math Problems
Equivalent expressions can be used to solve math problems in a variety of ways. For example, we can use them to simplify expressions, to solve equations, or to prove theorems.
In conclusion, two expressions are said to be equivalent if they have the same value for all possible values of the variables involved. The question "Which expression is equivalent to assume" is a type of mathematical problem that asks us to find two expressions that are equivalent. The answer to this question will depend on the specific expressions that are given.
