The graph of the equation y = mx, where m is greater than 0, represents a straight line through the origin (0, 0) of the Cartesian plane. This line has a positive slope, which means that as the value of x increases, the value of y also increases. To understand this better, let’s break down … Read more
Calculating the Dimensions and Cost of the Storage Container To determine the dimensions of the rectangular storage container with an open top, we need to use the given conditions: The volume of the container is 10 m³. The length of the base is twice the width. The material cost for the base is $15 per … Read more
To find the value of the expression 3 + 3i + 2 + 3i, we first need to combine like terms. The expression consists of both real and imaginary parts. 1. Start by identifying and separating the real numbers from the imaginary numbers: Real numbers: 3 and 2 Imaginary numbers: 3i and 3i 2. Next, … Read more
To rewrite the expression y = 4×2 + 2x + 7 in the form y = a(x – h)2 + k, we need to complete the square. This process allows us to express the quadratic in vertex form, which makes it easier to analyze its properties. The first step in this process is to factor … Read more
The sequence you provided is 2, 6, 18, 54. To determine the common ratio, we need to look at how each term relates to the one before it. The common ratio (r) of a geometric sequence is found by dividing any term by the preceding term. Let’s calculate it: For the first two terms: r … Read more
To find the radius of a sphere using its circumference, you can apply a simple mathematical formula. The circumference (C) of a sphere is related to its radius (r) through the formula: C = 2πr Where: C is the circumference of the sphere. r is the radius of the sphere. π (Pi) is approximately 3.14159. … Read more
A polyhedron with twelve flat faces is known as a dodecahedron. The term ‘dodecahedron’ is derived from the Greek words ‘dodeka’, meaning twelve, and ‘hedron’, which refers to faces or surfaces. This geometric shape is part of the family of Platonic solids, which are convex polyhedra with identical faces of regular polygons. In the case … Read more
The probability of rolling a sum of 6 with two dice can be calculated by determining the total possible outcomes and the favorable outcomes that result in that sum. When rolling two dice, each die has 6 faces, leading to a total of 36 possible outcomes (6 faces on die one multiplied by 6 faces … Read more
To find the surface area of a square pyramid, you can use a straightforward formula that combines both the area of the base and the area of the triangular faces. The formula for the surface area (SA) of a square pyramid is: SA = b² + 2 * (b * l / 2) where: b … Read more
When delving into the world of mathematics, it’s essential to understand the fundamental differences between an equation and an expression. Here’s a comprehensive breakdown: What is an Expression? An expression is a mathematical phrase that combines numbers, variables, and operators (such as +, −, ×, ÷) but does not contain an equality sign. Expressions can … Read more