To calculate the perimeter of a polygon, you need to add together the lengths of all its sides. Here’s a step-by-step guide: Identify the sides: Look at the polygon in the diagram and note down the lengths of each side. If the sides are not marked, you might need to measure them or use the … Read more
In mathematics, particularly in algebra, functions that exhibit symmetry have a specific line, known as the axis of symmetry, that divides the function into two identical halves. For functions with an axis of symmetry at x = 2, we can look at various types, but primarily, we are concerned with those functions where this line … Read more
To find the derivative of y with respect to x using implicit differentiation for the equation: x^2 + 4xy + y^2 = 4 we first need to differentiate both sides of the equation with respect to x. Remember that any term containing y will require the application of the chain rule since y is a … Read more
To solve the problem of dividing 1400 into three parts based on the given conditions, we can start by defining our three parts. Let’s denote the three parts as: First part: x Second part: y Third part: z According to the problem: The first part (x) is equal to 23 times the second part (y): … Read more
An even function is one that satisfies the condition f(-x) = f(x) for all values of x within its domain. This means that the function’s graph is symmetric with respect to the y-axis. Let’s evaluate each of the given functions to determine if they are even: 1. For f(x) = x: To check if this … Read more
To find the value of x, we need to set up an equation based on the information given about the measure of arc QS. The measure of arc QS is expressed as: 4x + 18 In many cases, the measure of an arc can be equated to a specific value if that context is provided … Read more
To determine if y varies directly with x, we first need to understand the concept of direct variation. A variable y is said to vary directly with x if there is a constant k such that: y = kx In this case, the equation we are considering is: 5y = 5x + 10 To check … Read more
To graph the system of equations given by y = 2x + 3 and 2x + 4y = 8, we need to first understand the individual graphs of these equations. Step 1: Understand the First Equation The first equation, y = 2x + 3, is already in slope-intercept form, where: slope (m) = 2 y-intercept … Read more
When you roll two six-sided number cubes (commonly known as dice), each die can land on a number from 1 to 6. To find the possible products of the numbers rolled, you can multiply the outcomes from each die. To illustrate, here’s a breakdown of all possible products: Die 1 Die 2 Product 1 1 … Read more
To determine how many three-digit positive integers are odd and do not contain the digit 5, we can break this down step by step. A three-digit integer can be represented in the form ABC, where: A is the hundreds place digit (1-9), B is the tens place digit (0-9), C is the units (or ones) … Read more