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The expression given, 64x + 24x = 30, demonstrates the Commutative Property of Addition. The Commutative Property states that the order in which two numbers are added does not change the sum. In this case, although the terms are organized as ’64x’ and ’24x’, they can be rearranged without affecting the result: For instance, we … Read more

An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant. To determine if the given sequence 7, 11, 15, 19 is arithmetic, we need to check the differences between its consecutive terms. Let’s break it down: First term: 7 Second term: 11 Third term: 15 Fourth … Read more

Solving the Linear Equations We have the following system of linear equations: Equation 1: 2x + y = 5 Equation 2: 3x + 2y = 4 Step 1: Solve Equation 1 for y From Equation 1, we can express y in terms of x: y = 5 – 2x Step 2: Substitute for y in … Read more

To determine the measure of angle BCD, we first need to understand the context in which angle BCD is situated. Angles can be found in various geometric shapes or configurations, such as triangles, quadrilaterals, or even in the context of intersecting lines. Here’s a detailed explanation of how to find angle BCD: Identify the Key … Read more

To determine the length of a rectangle when the perimeter and the width are known, we can use the formula for the perimeter of a rectangle, which is given by: Perimeter (P) = 2 * (Length (l) + Width (w)) In this case, we already know the perimeter and the width: Perimeter (P) = 34 … Read more

Solving the System of Equations To solve the system of equations 2x + y = 3 and x + 2y = 1, we can use the method of substitution or elimination. Here, we’ll use the elimination method for clarity. Step 1: Align the equations First, we write the equations one under the other: 2x + … Read more

To solve the quadratic equation x² + 8x + 3 = 0 using the completing the square method, follow these steps: Start with the original equation: x² + 8x + 3 = 0 Isolate the constant: x² + 8x = -3 Complete the square: To complete the square, we need to add and subtract the … Read more

The domain of a function refers to the set of all possible input values (x-values) that the function can accept. In the case of the function f(x) = 5x + 7, we are dealing with a linear function, which is one of the simplest forms of function in mathematics. For linear functions, there are no … Read more

To determine the type of polygon with an interior angle measuring 108 degrees, we can use the formula for calculating the interior angle of a regular polygon. The formula for the interior angle of a regular polygon with n sides is: Interior Angle = (n – 2) * 180° / n To solve for n, … Read more