devyy The present value (PV) of an amount of money is calculated using the following expression: PV = FV / (1 + r)^n Where: PV: Present Value – the current worth of a given amount of money in the future. FV: Future Value – the amount of money you expect to receive in the future. r: … Read more
To determine the x-intercept of the line given by the equation 6x + 2y = 18, we follow a straightforward process. The x-intercept is the point where the line crosses the x-axis, which occurs when the value of y is zero. Here are the steps to find the x-intercept: Set y = 0 in the … Read more
To determine how many cups of tomato are needed for a salsa batch of 105 cups, we first need to understand how the ingredients are proportioned according to the given ratio of 3:5:7 for green pepper, onion, and tomato. The total parts in the ratio can be calculated as follows: Green pepper: 3 parts Onion: … Read more
To find the point on the line y = 2x + 4 that is closest to the origin (0, 0), we can use the concept of distance between points in a Cartesian plane. The distance d from any point (x, y) to the origin is given by: d = √(x2 + y2) In our case, … Read more
The sum of the interior angles of any quadrilateral is 360 degrees. This can be understood through a simple geometric principle. To visualize this, think of a quadrilateral as a four-sided figure, which can be any shape with four edges and four vertices. One effective way to see why the interior angles add up to … Read more
To determine if the system of equations is independent, dependent, or inconsistent, we can analyze the equations algebraically without graphing. The two equations in the system are: Equation 1: 2x + y = 9 Equation 2: 3x + 4y = 8 We can start by expressing one variable in terms of the other using Equation … Read more
To find the largest area of a rectangle inscribed under the parabola given by the equation y = 12 – x² and with its base on the x-axis, we can follow these steps: First, we recognize that the rectangle has its base on the x-axis, and its upper corners will touch the parabola. Since the … Read more
Factoring the polynomial x³ + 11x² + 3x + 33 by grouping is a systematic approach that can simplify the process of determining its factors. Here’s a step-by-step guide on how to do it: Group the Terms: First, we will group the polynomial into two pairs. This can help us factor them separately. So, we … Read more
To solve this problem, we start with the concept of joint variation. The relationship can be expressed with the formula: x = k imes y imes z where k is the constant of variation. Step 1: Find the constant of variation (k) We know from the question that when x = 8, y = 4, … Read more
The probability of an event that is certain to occur is always 1, or 100%. In probability theory, probabilities range from 0 to 1, where 0 represents an impossible event, and 1 signifies an event that will definitely happen. To understand why certain events have a probability of 1, consider an example: the event of … Read more