The coordinates of the vertex of the parabola represented by the equation y = x² + 2x – 3 can be determined by using the vertex formula for a quadratic function. A quadratic function can be expressed in the standard form as y = ax² + bx + c, where a, b, and c are … Read more
Finding the nth term of a sequence without a constant difference can be a bit challenging, but with the right approach, you can derive a formula to describe the sequence. There are a few steps you can follow: Identify the Pattern: Start by writing out the terms of the sequence clearly. Look for patterns such … Read more
To find the number of sides of a regular polygon based on its interior angle, we can use the formula for the measures of the interior angles of a polygon: Interior Angle = (n – 2) × 180° / n Where n is the number of sides of the polygon. In your case, you mentioned … Read more
To find the next three terms in the sequence 3, 12, 21, we first need to identify the pattern that the numbers follow. Let’s look at the differences between the terms: The difference between 12 and 3 is: 12 – 3 = 9 The difference between 21 and 12 is: 21 – 12 = 9 … Read more
In a unit circle, which has a radius of 1, every central angle (measured in radians) corresponds directly to the length of the arc that it subtends. To understand this relationship, we first have to look at how radians are defined. A radian is a measure of an angle based on the radius of the … Read more
To determine which expressions can be equal to zero for some value of x, we need to analyze specific types of mathematical expressions and their properties. Expressions can generally be categorized into linear expressions, quadratic equations, polynomial expressions, and other forms. Let’s look at a few examples: Linear Expressions: An expression like ax + b … Read more
To determine which number is greater, we can simply compare the two numbers: 16 and 23. By observing their values, it is straightforward to conclude that: 23 is greater than 16. In numerical terms, 16 is less than 23, which can also be represented in mathematical notation as: 16 < 23 This comparison indicates that ... Read more
To solve for the value of x in the equation where f(x) equals g(x), we start with the given functions: f(x) = 3x + 4 g(x) = 2 We want to find the value of x for which: f(x) = g(x) Substituting the functions into the equation gives us: 3x + 4 = 2 Next, … Read more
A vertical line is defined as a line that runs up and down on the Cartesian plane, and it does not have a defined slope (since it would be undefined, due to division by zero). The equation of a vertical line can be represented in the form of x = a, where a is the … Read more
When measuring the mass of your dog, the most suitable unit is typically kilograms (kg). This is a standard metric unit of mass and is widely used around the world, making it a practical choice for pet owners and veterinarians alike. For smaller breeds, grams (g) may also be relevant, especially in detailed weight tracking, … Read more