Finding the Inverse of the Function To find the inverse of the given function y = 3x + 9, we will follow a step-by-step process. The inverse function essentially swaps the roles of x and y. Step 1: Replace y with x Start by rewriting the equation as: x = 3y + 9 Step 2: … Read more
To determine which lengths can form the sides of a triangle, we can refer to the Triangle Inequality Theorem. This theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side. Below are three lengths that can create a triangle: Length … Read more
Understanding the Equation To identify which solution of the equation 1x + 1 + 2 + 2x + 2 = 0 is extraneous, we first need to simplify and solve the equation. Simplifying the Equation We can rearrange the terms: 1x + 2x + 1 + 2 = 0 This simplifies to 3x + 3 … Read more
To determine if a triangle with sides of lengths 10, 24, and 26 is a right triangle, we can use the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the … Read more
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