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
To find the number from which you can subtract half and end up with zero, we can set up a simple equation. Let’s call the unknown number X. According to the problem, when you subtract half of this number from itself, you should get zero. We can express this mathematically as: X – (1/2)X = … Read more
To determine the value of dy/dx when given the expression 3x^2y^2, we need to perform implicit differentiation, assuming there is a relationship between x and y. First, let’s set the expression equal to a constant, say C
To find the slope of the tangent line to the parabola given by the equation y = 8x – x2 at the point (1, 7), we need to perform the following steps: Step 1: Differentiate the Equation The first step is to calculate the derivative of the function with respect to x. The derivative will … Read more
Rewriting the Quadratic in Vertex Form To convert the quadratic function f(x) = x² + 6x + 4 into vertex form, we need to complete the square. The vertex form of a quadratic function is given by: f(x) = a(x – h)² + k where (h, k) is the vertex of the parabola. Steps to … Read more
To solve the equation 1 3 7x 1 1 4, we first need to clarify the format and structure of this expression. It seems there might be some confusion with the formatting. Let’s break it down step by step: If we interpret 1 3 7x 1 1 4 as a linear equation in the form … Read more
Understanding the Value of 1/10 To find the value of 1/10 in relation to the provided number 103162, we simply need to perform a calculation using division. Calculation: The fraction 1/10 represents one part of ten, which means it is equal to 0.1. Now, to find 1/10 of 103162, you need to multiply 103162 by … Read more