To determine the factors of 729 when expressed as x3, we first need to understand what 729 represents in terms of its prime factorization. 729 can be expressed mathematically as: 729 = 9 x 81 = 9 x 9 x 9 = 93 To break it down further: 9 can be represented as 32. So … Read more
Solving for x in the equation 3/4 * x = 5/8 + 4x To solve the equation 3/4 * x = 5/8 + 4x, we’ll go through the steps carefully: Isolate the variable x: First, we want to get all terms involving x on one side of the equation. To do this, we can subtract … Read more
The sequence you’ve provided is 4, 12, 6, 9, 8, 6. To find the next number in this series, let’s first analyze the pattern: The first number is 4. The second number, 12, is 4 multiplied by 3 (4 x 3 = 12). The third number, 6, can be seen as 12 divided by 2 … Read more
To determine which equations have both x = 5 and x = -5 as solutions, we need to consider the characteristics of the equations that yield these values. A polynomial equation can have multiple roots, and if we want both x = 5 and x = -5 to be solutions, we can formulate an equation … Read more
To solve this problem, we start with the understanding that in a right triangle, the two non-right angles are complementary. This means that angle L and angle M add up to 90 degrees: L + M = 90° Given that: sin L = 1920 Now, the sine function gives us the ratio of the length … Read more
Finding the Completely Factored Form of the Polynomial To factor the polynomial 6x³ + 13x² + 4x – 15, we can follow a systematic approach that involves several steps: Step 1: Use the Rational Root Theorem The Rational Root Theorem suggests that any rational solution (root) of the polynomial equation can be expressed as a … Read more
The equation a = pr²π is an expression that combines several important mathematical constants and variables, usually in the context of geometry or physics. Here’s a detailed breakdown of each component of the equation: a: This variable typically represents the area in geometric contexts. The specific area calculated could vary based on the context of … Read more
Point symmetry about the origin means that for every point (x, y) in a set, there is a corresponding point (-x, -y) also in the set. In simpler terms, you can visualize this as if you have a point on one side of the origin, you should have an identical point on the opposite side … Read more
To find the equation of a hyperbola when you have been given the center, focus, and vertex, you’ll follow a series of steps that relate these elements to the general form of a hyperbola’s equation. Here’s how: Step 1: Identify the Components A hyperbola can be characterized by its center, foci (plural of focus), vertices, … Read more