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To rewrite the expression 4×12 + 5×6 + 14 = 0 as a quadratic equation, we need to use a substitution that simplifies the terms. Let’s introduce a new variable, say y, where we define it as: y = x6 With this substitution, we can express: x12 = (x6)2 = y2 x6 = y Now … Read more

Understanding the Equation The equation given is 0x² + 6 = 0. Let’s break it down: In this equation, 0x² signifies that the coefficient of x² is zero. This means that the term involving x does not contribute to the equation. Thus, the equation simplifies to 6 = 0, which is clearly incorrect. Analyzing the … Read more

Solving the Equation √(2x + 1) = 3 To solve the equation √(2x + 1) = 3, follow these steps: Square both sides: Squaring both sides of the equation removes the square root: (√(2x + 1))² = 3² This simplifies to: 2x + 1 = 9 Solve for x: Next, isolate x by first subtracting … Read more

To determine the measure of angle WZY, we first need to clarify what the values given (545, 71, 1255, 180) represent. In geometrical contexts, angles are typically measured in degrees, and the sum of the angles in any triangle is always 180 degrees. Let’s assume the numbers provided relate to angles in a geometric configuration. … Read more

Understanding the Sequence Let’s break down the sequence: 4, 8, 12, 20, 52. At first glance, the pattern isn’t immediately obvious, so we need to investigate the relationships between the numbers. Identifying the Pattern We can look at the differences between consecutive numbers: 8 – 4 = 4 12 – 8 = 4 20 – … Read more

The discriminant is an important concept in the context of quadratic equations, as it provides valuable information about the nature of the roots of the equation. For a standard quadratic equation in the form: ax2 + bx + c = 0 the discriminant (denoted as D) is given by the formula: D = b2 – … Read more

To calculate the expression 1 i 1 i, first, it’s important to clarify what this expression means. It seems as though there is a misunderstanding or a typographical error. Typically, in mathematics, we deal with numbers and operators (like addition or multiplication). However, the presence of “i” suggests that we might be looking at imaginary … Read more

The sequence you’ve provided is: 2, 9, 28, 65, 126. To find the explicit formula for this sequence, let’s first examine the terms more closely and look for patterns. The first few terms can be expressed as follows where n starts from 1: 1st term: 2 2nd term: 9 3rd term: 28 4th term: 65 … Read more

To find the solution to the system of equations, we need to set the two equations equal to each other since both equal y: 1. The first equation is: y = 4x + 10 2. The second equation is: y = 2x + 6 Setting them equal: 4x + 10 = 2x + 6 Now, … Read more