To write the equation of a line in point-slope form, we use the formula: y – y1 = m(x – x1) Here, (x1, y1) is a point on the line, and m is the slope. In your case, the point provided is (4, 4), meaning x1 = 4 and y1 = 4. The slope m … Read more
To solve the equation 9x = 27, we need to isolate the variable x. Here are the steps: Start with the original equation: 9x = 27. To isolate x, divide both sides of the equation by 9: x = 27 / 9 Now perform the division: x = 3 Therefore, the solution to the equation … Read more
The inequality 2x ≤ 10 can be solved step by step to understand what values of x satisfy the inequality. Step 1: Solving the Inequality To isolate x, divide both sides of the inequality by 2: x ≤ 5 This inequality means that x can take on any value that is less than or equal … Read more
In a circle, angles can be classified into various types based on their position and relation to the circle. In the case of angle LMN in circle A, we need to determine its measure based on its position relative to the circle and any relevant properties of circles and angles. First, if angle LMN is … Read more
To find the present ages of the father and son, let’s denote the current ages as follows: Father’s current age: F Son’s current age: S According to the problem: Two years ago, the father’s age was (F – 2) and the son’s age was (S – 2). At that time, the father was three times … Read more
The vertex of a quadratic function in the standard form, y = ax² + bx + c, can be determined using the vertex formula. For the given function y = 3x² + 2x + 1, we identify: a = 3 b = 2 c = 1 To find the x-coordinate of the vertex, we use … Read more
Finding the Equation of a Parallel Line To find the equation of a line that is parallel to a given line, you need to determine two key components: the slope of the given line and the point through which the new line passes. Step 1: Identify the Slope The provided line is given by the … Read more
The expression 18×5 + 6×4 + 12×3 + 6×2 can be tackled by factorization and simplification. Let’s break it down step by step: Identify the common factor: The common factor among the terms is 6×2. Factor out: By factoring out 6×2, we get: 6×2(3×3 + x2 + 2x + 1) Analyze the remaining polynomial: You … Read more
To find the equation of the line in slope-intercept form (which is y = mx + b, where m is the slope and b is the y-intercept), we first need to determine the slope (m) of the line that passes through the two given points: (3, 1) and (1, 5). The formula to calculate the … Read more