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To find the next number in the sequence 8, 6, 9, 5, 10, 4, 11, we need to examine the pattern exhibited by the numbers given. First, let’s look at the odd and even indexed positions separately. The sequence can be split into two parts: Odd-indexed numbers: 8 (1st), 9 (3rd), 10 (5th), 11 (7th) … Read more

The sequence you’ve provided is comprised of the first four square numbers. Let’s break it down: The first term is 1

In the context of polynomials, a prime polynomial (or irreducible polynomial) is defined as a polynomial that cannot be factored into the product of two non-constant polynomials over the given field. In simpler terms, if you have a polynomial and you cannot break it down into simpler polynomial factors, then it is considered prime. To … Read more

To determine the value of x in the context of a parallelogram ABCD that is also a rhombus, we must first understand the properties of these shapes. A parallelogram is defined as a quadrilateral in which opposite sides are parallel and equal in length. The opposite angles are also equal. A rhombus is a special … Read more

In many contexts, particularly in mathematics and literature, letters are often utilized as substitutes for numerals. For instance, in mathematical equations, variables such as x and y represent unknown values, which can be numeric. This method allows for the representation of generality and abstraction, making complex concepts easier to handle. Moreover, the use of letters … Read more

To solve the equation x + 8 + 3x = x + 6, let’s first simplify it step by step. 1. **Combine like terms:** On the left side of the equation, we can combine the terms involving x. x + 3x simplifies to 4x. This gives us: 4x + 8 = x + 6 2. … Read more

Calculating the Percentage Change To find the percentage change when a value is increased from 40 to 56, you can follow these steps: First, determine the difference between the new value and the original value. In this case, you subtract the original value (40) from the new value (56): Difference = New Value – Original … Read more

To solve the quadratic equation x² + 14x + 24 = 0 by completing the square, we will follow these steps: Move the constant term to the other side: Start by rewriting the equation: x² + 14x = -24 Complete the square: To complete the square, we need to take the coefficient of x (which … Read more

To understand how many millions make up a billion, we first need to define the numbers clearly: A million is represented as 1,000,000 (one thousand thousand), while a billion is 1,000,000,000 (one thousand million). Now, if we break it down: 1 billion = 1,000 million Therefore, it takes a total of 1,000 millions to equal … Read more

The perimeter of a parallelogram can be calculated using the formula: Perimeter = 2 × (Length + Width) In the case of parallelogram WXYZ, to determine the perimeter, we need to identify the lengths of its sides. Let’s represent the length of side WX as ‘a’ and the length of side XY as ‘b’. Assuming … Read more