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
To determine the ranges of the functions f(x) = 45x and g(x) = 45x + 6, let’s analyze each function one by one. 1. Range of f(x) = 45x: This function is a linear function with a slope of 45. Linear functions are defined for all real numbers, which means the output can take any … Read more
To find out how many games the soccer team won, we need to calculate 65% of the total games played, which is 160. The formula to calculate the number of wins is: Number of Wins = Total Games Played × Win Percentage In this case: Number of Wins = 160 games × 0.65 Now, performing … Read more
To convert the expression x² + 10x into a perfect square trinomial, we need to find a specific value that, when added, completes the square. A perfect square trinomial takes the form (x + a)², which expands to x² + 2ax + a². In this case, we have: The coefficient of x is 10 In … Read more