To find the value of the discriminant for the quadratic equation 3x² + 2x, we first need to identify the coefficients in the standard form of a quadratic equation, which is generally expressed as ax² + bx + c = 0. Here, we can rewrite the equation: 3x² + 2x = 0 can be interpreted … Read more
To understand how many cubic feet are in one unit of sand, we first need to clarify what ‘unit of sand’ means, as this terminology can vary based on context and location. Often, one unit of sand can refer to a cubic yard, especially in construction and landscaping. If we take a cubic yard as … Read more
The least common multiple (LCM) of two numbers is the smallest multiple that is evenly divisible by both numbers. To find the LCM of the denominators 16 and 58, we can use the following steps: Prime Factorization: First, we will find the prime factorization of both numbers. For 16: 16 = 2 × 2 × … Read more
Understanding Set Equality To say that two sets are equal, we must verify that they contain exactly the same elements. In mathematical terms, if A and B are two sets, they are considered equal, written as A = B, if every element of A is also an element of B, and vice versa. Key Points … Read more
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