To find the solutions to the quadratic equation 4x² + 3x – 24 = 0, we can use the quadratic formula: x = (-b ± √(b² – 4ac)) / (2a) Here, the coefficients are: a = 4 b = 3 c = -24 Now, we need to calculate the discriminant, which is the part under … Read more
To find the area of a regular hexagon when you know the length of the apothem, you can use the following formula: Area = (Perimeter x Apothem) / 2 First, let’s break it down: Find the side length: A regular hexagon can be divided into 6 equilateral triangles. The relationship between the apothem (a) and … Read more
To solve the inequality 3q + 11 < 8q + 99, we can follow these steps: Rearranging the inequality: First, we will move all the terms involving q to one side and the constant terms to the other side. We can do this by subtracting 3q from both sides: 3q + 11 – 3q < … Read more
To determine the number of edges in a polyhedron, we can use Euler’s formula, which relates the number of faces (F), vertices (V), and edges (E) in a convex polyhedron. The formula states: F + V – E = 2 In this case, we know: F (faces) = 5 V (vertices) = 5 Now, we … Read more
If you divide an inheritance of $4,560,000 among 22 heirs, each heir will receive a share calculated by simply dividing the total inheritance by the number of heirs. This can be done using the following calculation: Amount per heir = Total inheritance ÷ Number of heirs Amount per heir = $4,560,000 ÷ 22 Carrying out … Read more
The length of a circle, commonly known as its circumference, can be calculated using the formula: C = 2 × π × r In this formula: C represents the circumference. π (pi) is a mathematical constant approximately equal to 3.14159. r is the radius of the circle. To find the circumference of a circle and … Read more
To find the zeros of the quadratic function f(x) = 2x² + 10x + 3, we need to determine the values of x for which f(x) = 0. The zeros can be found using the quadratic formula: x = (-b ± √(b² – 4ac)) / 2a In our case, the coefficients are: a = 2 … Read more
To solve the inequality 42x + 15 > 3x, the first step is to isolate the variable on one side of the inequality. This can be done by getting all the terms containing x on one side and the constant terms on the other side. First, subtract 3x from both sides: 42x + 15 – … Read more
A factor tree is a visual representation that shows how a particular number can be expressed as a product of its prime factors. For the number 60, we can generate two distinct factor trees. Factor Tree 1 1. Start with the number 60 at the top. 2. The first step is to divide 60 by … Read more
To find the zeros of the function f(x) = x² + 2x + 3, we need to determine the values of x that make the equation equal to zero. In mathematical terms, we set the function equal to zero: x² + 2x + 3 = 0 This is a quadratic equation, and we can find … Read more