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The standard form of the equation of an ellipse centered at the origin (0,0) depends on whether the major axis is horizontal or vertical. In our case, we have vertices at (6, 0) and (0, 4). The distance from the center to the vertices on the x-axis is 6, which indicates that the major axis … Read more

To find the derivative of the function f(x) = 5x^9 at x = 2, you’ll want to follow these steps: First, apply the power rule of differentiation. The power rule states that if you have a term of the form ax^n, the derivative is given by n * a * x^(n-1). In our case, f(x) … Read more

To find the image of point e after applying a dilation centered at the origin (0,0) with a scale factor of 6, we first need to know the coordinates of point e. Let’s assume that point e has coordinates (x, y). A dilation with a scale factor of k multiplies the coordinates of a point … Read more

In the linear equation y = mx + b, the variable b signifies the y-intercept. The equation expresses the relationship between the dependent variable y and the independent variable x. Here, m denotes the slope of the line, indicating how steeply the line ascends or descends. The y-intercept, represented by b, is the point where … Read more

To find the two numbers, let’s denote the two unknowns as x and y. We have the following two equations based on the problem: x + y = 40 (Equation 1: The sum of the two numbers is 40) x – y = 10 (Equation 2: The difference of the two numbers is 10) We … Read more

To solve for the two numbers based on the conditions given in the question, we can use a bit of algebra. Let’s denote the two numbers as x and y. We are provided with two key pieces of information: The sum of the two numbers: x + y = 19 The difference between the two … Read more

The smallest 6-digit number is 100000, while the greatest 4-digit number is 9999. To find the difference between these two numbers, we perform the following calculation: 100000 – 9999 = 90001 So, the difference between the smallest 6-digit number and the greatest 4-digit number is 90001.

To solve the problem of finding a number that, when multiplied by 8, results in a product of at least 25, we can set up the inequality: 8x ≥ 25 Here, x represents the unknown number we are trying to determine. To isolate x, we need to divide both sides of the inequality by 8: … Read more

To find the measure of angle YAC (denoted as yAC), we start by reviewing some important properties of circles and tangents. When a tangent line intersects a circle, it forms a right angle with the radius that connects the point of tangency to the center of the circle. In this scenario, we have: The circle … Read more

Solving equations with fractions and variables in the denominator can be a bit tricky, but with a systematic approach, you can tackle these problems confidently. Here’s a detailed step-by-step method to help you: Step 1: Identify the Equation Start by clearly identifying the equation you need to solve. For instance, you might have something like: … Read more