Answer:
Explanation:
Identifying like terms and simplifying expressions:
For the first expression: 8y + 2x + 11 + x - 3y
Like terms are terms that have the same variable(s) raised to the same exponent(s). In this expression, the like terms are 8y and -3y because both have the variable y raised to the power 1. Similarly, the terms 2x and x are also like terms as they both have the variable x raised to the power 1.
Simplifying the expression by combining like terms:
Combine the coefficients of like terms: 8y - 3y = 5y
Combine the coefficients of like terms: 2x + x = 3x
The simplified expression is: 5y + 3x + 11
For the second expression: 4x - y + 6x - 3 - 2y
Like terms are 4x and 6x as they both have the variable x raised to the power 1. Also, -y and -2y are like terms as they both have the variable y raised to the power 1.
Simplifying the expression by combining like terms:
Combine the coefficients of like terms: 4x + 6x = 10x
Combine the coefficients of like terms: -y - 2y = -3y
The simplified expression is: 10x - 3y - 3
Evaluating the expression: 4x^2 + 15y, when x = 3 and y = 2
Simply substitute the values of x and y into the expression:
4(3)^2 + 15(2) = 4(9) + 30 = 36 + 30 = 66
So, when x = 3 and y = 2, the expression 4x^2 + 15y evaluates to 66.
Solving A = 12s^2, where s = 14
Simply substitute the value of s into the expression:
A = 12(14)^2 = 12(196) = 2352
So, when s = 14, the value of A is 2352.
Writing an equivalent expression using the distributive property and simplifying by combining like terms:
Given expression: 4(2x + y) + 3x
Using the distributive property, we multiply the constant 4 by each term inside the parentheses:
4(2x) + 4(y) + 3x
Now, combine the like terms:
8x + 4y + 3x
Combine the coefficients of like terms: 8x + 3x = 11x
The equivalent expression after using the distributive property and simplifying is: 11x + 4y
To prove that the three expressions are equivalent, we can evaluate each expression for various values of x and y and check if they yield the same result. For example:
Let's take x = 5 and y = 2:
Expression 1: 5y + 3x + 11 = 5(2) + 3(5) + 11 = 10 + 15 + 11 = 36
Expression 2: 10x - 3y - 3 = 10(5) - 3(2) - 3 = 50 - 6 - 3 = 41
Expression 3: 11x + 4y = 11(5) + 4(2) = 55 + 8 = 63
As we can see, the three expressions yield different results for these particular values of x and y, indicating that they are not equivalent. Therefore, there may be a mistake or misunderstanding in the previous steps. To find the correct equivalent expression, we need to reevaluate the simplification and check for errors.