devyy

To find the coordinates of the vertex for the quadratic function f(x) = x² + 4x – 10, we can use the vertex formula. For a quadratic function of the form f(x) = ax² + bx + c, the x-coordinate of the vertex can be calculated using: x = -b / (2a) In our case, … Read more

When a quantity p varies jointly with two other variables, say r and s, it means that p can be expressed as a product of r and s, multiplied by a constant of variation, denoted as k. The mathematical relationship is represented as: p = k imes r imes s Here, the constant of variation … Read more

To determine whether the function f(x) = x3 + 5x + 1 is an even function, we need to apply the definition of an even function. An even function is one that satisfies the condition f(-x) = f(x) for all values of x in its domain. In simpler terms, this means that when we plug … Read more

The perimeter of a square is calculated by adding together the lengths of all four sides. Since a square has equal sides, you can also find the perimeter with a simple formula: Perimeter (P) = 4 × side length In this case, since each side of the square measures 6 inches, you can substitute that … Read more

Understanding the Relation: Graphing Points and Finding Domain and Range To graph the relation defined by the points (1, 12), (12, 132), and (0, 32), you can follow these steps: 1. Plotting the Points Begin by setting up your Cartesian coordinate system (x-y plane). Each point you have corresponds to an (x, y) coordinate: (1, … Read more

To find the value of f(g(4)), we need to break this problem down into two steps: first, we need to evaluate g(4), and second, we will use that result to evaluate f. Step 1: Calculate g(4) Given the function g(x) = 2x + 5, we substitute 4 for x: g(4) = 2(4) + 5 = … Read more

To find the volume of a box (also known as a rectangular prism), you can use the formula: Volume = Length × Width × Height In this case, the dimensions of the box are: Length = 10 cm Width = 82 cm Height = 35 cm Now, let’s substitute these values into the formula: Volume … Read more

To convert the quadratic function f(x) = 3x² + 6x + 9 into vertex form, which is expressed as f(x) = a(x – h)² + k, where (h, k) is the vertex of the parabola, follow these steps: Factor out the coefficient of x²: In this case, the coefficient is 3. We factor this out … Read more

To calculate the sum of an infinite geometric series, we first need to determine whether the series converges. An infinite geometric series converges if the absolute value of the common ratio, r, is less than 1 (|r| < 1). If it converges, the sum can be calculated using the formula: S = a / (1 ... Read more