To determine what must be subtracted from 3 to get 9, we can set up a simple equation. Let’s denote the unknown number we need to subtract as x. The equation can be stated as: 3 – x = 9 To find x, we can rearrange the equation: – x = 9 – 3 – … Read more
To prove that triangles LNO and PNM intersect at point Q on segment LO, we must first analyze the given conditions thoroughly. 1. **Understanding Congruence**: We are given that segment LN is congruent to segment NP. This means that the lengths of these segments are equal, denoted as LN = NP. 2. **Defining the Triangles**: … Read more
To find the value of x when g(x) = 3x + 2 and g(x) = 6, we need to set up an equation based on the provided information. Start with the equation: g(x) = 6 Now, substitute the definition of g(x) into the equation: 3x + 2 = 6 Next, we can solve for x. … Read more
To find the slope-intercept form of a line that passes through two points, we start by identifying the points given: (3, 4) and (5, 16). The slope-intercept form of a line is represented as: y = mx + b where: m is the slope of the line. b is the y-intercept where the line crosses … Read more
Finding the Derivative of gx = 7x Using the Definition The derivative of a function provides insight into its rate of change at any point. To find the derivative of the function g(x) = 7x using the definition of the derivative, we can use the limit definition: f'(x) = lim (h -> 0) [(f(x + … Read more
A horizontal line is characterized by a constant y-value, which means that the y-coordinate does not change regardless of the x-coordinate. For a line to be horizontal, it can be expressed in the form: y = b where b is the constant y-value across all points on that line. In this case, we’re given the … Read more
To find all polar coordinates of the point P, given that its polar representation is (7, 3π), we start by understanding the polar coordinate system. In this system, a point is represented as (r, θ), where r is the distance from the origin, and θ is the angle measured from the positive x-axis. The point … Read more
To evaluate the summation of the expression 2n + 5 from n = 1 to n = 12, we follow these steps: Understanding the Summation Notation: The notation ∑ represents the sum of an expression evaluated at different values of n. In this case, we start at n = 1 and end at n = … Read more
The least common multiple (LCM) of a set of numbers is the smallest positive integer that is divisible by each of the numbers in that set. To find the LCM of the numbers from 1 to 10, we can follow a systematic approach. The numbers in this range are: 1, 2, 3, 4, 5, 6, … Read more