devyy The equation of a line can often be expressed in standard form as Ax + By = C, where A, B, and C are integers, and A should be non-negative. Let’s analyze the equation you’ve given: 2x + 3y = 6. To clarify further, the standard form of the line can be derived and rearranged … Read more
Finding the Minimum and Maximum of a Quadratic Function A quadratic function is typically expressed in the standard form: f(x) = ax² + bx + c, where a, b, and c are constants. The shape of the graph of a quadratic function is a parabola. To find the minimum or maximum value of this function, … Read more
To write the number 11,110 in words, you would say “eleven thousand one hundred ten.” This breakdown helps clarify the number’s components: Eleven Thousand: The first part of the number, “eleven thousand,” indicates that there are 11,000. One Hundred: The second part, “one hundred,” tells you that there are an additional 100 added to the … Read more
To find the smallest of three consecutive numbers that sum up to 72, we first need to establish a mathematical representation of the problem. Let the three consecutive numbers be represented as: x: the first number x + 1: the second number x + 2: the third number Now, we can set up the equation … Read more
Vertical angles are formed when two lines intersect, creating pairs of opposite angles that are equal to each other. To determine whether angles 1 and 2 are vertical angles, we need to visualize or identify their positions relative to the intersecting lines. Imagine two lines crossing each other, forming four angles at the intersection. Typically, … Read more
To find 1/4 of an hour, we first need to understand how long one hour is. An hour is made up of 60 minutes. To find a quarter (1/4) of 60 minutes, we can use a simple calculation: Step 1: Divide 60 by 4. This gives us 15. Step 2: Therefore, 1/4 of an hour … Read more
To find the equation of a line given two points, let’s denote the points as (x1, y1) and (x2, y2). The steps to derive the line’s equation—commonly expressed in slope-intercept form (y = mx + b)—involve calculating the slope and then using one of the points to find the y-intercept (b). Here’s how you can … Read more
To find the equation of a line that passes through two points, we can use the slope-intercept form of the equation of a line, which is given by: y = mx + b Where: m is the slope of the line b is the y-intercept of the line First, we need to calculate the slope … Read more
The mean of a probability distribution, often referred to as the expected value, is a fundamental concept in statistics and probability theory that provides a measure of the central tendency of the distribution. In simpler terms, it can be thought of as the “average” outcome you can expect when you conduct an experiment that follows … Read more
Understanding Least Common Multiple (LCM) To find the least common multiple (LCM) of two numbers, we can follow different methods, including prime factorization, listing multiples, or using the greatest common divisor (GCD). In this case, we will find the LCM of 150 and 500 using the GCD approach for efficiency. Step 1: Prime Factorization Let’s … Read more