What Does Polygon Mean in Maths?
A polygon is a two-dimensional geometric figure that consists of a finite number of straight line segments connected to form a closed shape. The line segments are called the sides or edges, and the points where two sides meet are called vertices. Polygons can be classified based on the number of sides they have. For […]
Factor Completely 5x² – 40
To factor the expression 5x² – 40 completely, we start by looking for common factors in the terms. The coefficients are 5 and -40, so the greatest common factor (GCF) is 5. We can factor out 5 from the expression: 5(x² – 8). Now, we need to factor the expression inside the parentheses. The expression […]
The average of 5 distinct scores has the same value as the median of the 5 scores. The sum of the 5 scores is 420. What is the sum of the 4 scores that are not the median?
To solve this problem, we begin with the information provided: The sum of the 5 distinct scores is 420. The average of these scores equals the median. First, we can find the average of the five scores. The average is calculated as the total sum divided by the number of scores: Average = Total Sum […]
What is the value of c such that x² + 14x + c is a perfect square trinomial?
To determine the value of c that makes the expression x² + 14x + c a perfect square trinomial, we need to understand the structure of perfect square trinomials. A perfect square trinomial takes the form (a + b)², which expands to a² + 2ab + b². In our case, we can compare this with […]
A man 6 feet tall walks at a rate of 5 feet per second away from a light that is 15 feet above the ground. How does the distance from the light affect the length of his shadow?
To understand how the shadow’s length changes as the man walks away from the light, we can use similar triangles. The man is 6 feet tall, and the light is 15 feet above the ground. As the man moves away from the light source, a triangle is formed between the top of the light, the […]
What is the equation of the function y = 2x translated 3 units to the left and 4 units up?
To find the new equation after translating the function, we need to follow two basic translation rules for functions. 1. **Translation to the Left**: When we translate a function horizontally to the left by ‘h’ units, we replace ‘x’ with ‘x + h’ in the equation. In this case, we are translating 3 units to […]
The area of a square garden is 200m². How long is the diagonal?
To find the length of the diagonal of a square garden, we first need to know the relationship between the area and the side length of the square. The area (A) of a square is given by the formula: A = side² In this case, the area is 200 m². We can calculate the length […]
What is the general form of the equation for the given circle centered at (0, 0)?
The general form of the equation of a circle centered at the origin (0, 0) is given by: x2 + y2 = r2 Here, r represents the radius of the circle. This equation indicates that for any point (x, y) lying on the circle, the sum of the squares of its x-coordinate and y-coordinate is […]
What is the mean of a random discrete variable?
The mean of a random discrete variable, often referred to as the expected value, is a fundamental concept in probability and statistics. It provides a measure of the central tendency of the variable, indicating where most of its values tend to cluster. To calculate the mean of a discrete random variable, you multiply each possible […]
How to Find the Angles of an Isosceles Triangle Given Three Sides
Finding the angles of an isosceles triangle when you know all three sides is a straightforward process that utilizes the Law of Cosines. An isosceles triangle has two sides that are equal, which makes calculating the angles a bit easier. Step 1: Identify the sides Let’s label the sides of the triangle as follows: let […]