How can I find the standard form equation of a hyperbola that has vertices at (0, 4) and foci at (0, 5)?

To find the standard form equation of the hyperbola, we start by identifying the key components from the information provided: Vertices: The hyperbola has vertices at (0, 4). Since hyperbolas are defined by their vertices, we can derive the center and the orientation of the hyperbola from this information. Foci: The foci are located at … Read more

How can I convert a repeating decimal into a fraction?

Converting a repeating decimal to a fraction is a straightforward process that you can accomplish with a few simple steps. Let’s break down the method: Identify the repeating decimal: Suppose you have a repeating decimal, such as 0.666…, which can also be written as 0.ar{6}. Set up an equation: Let x equal the repeating decimal. … Read more

How do you determine the measure of angle d if angle a is 52x + 16, angle b is 72x + 20, angle c is 32x + 68, and angle d is 32x + 40?

Finding the Measure of Angle D To determine the measure of angle d, we need to set up an equation based on the information provided about the other angles. In a triangle, the sum of all interior angles is always 180 degrees. Therefore, we can express this relationship mathematically: Let: Angle A: 52x + 16 … Read more

What will be the new profit-sharing ratio and sacrificing ratio when partner C is admitted for a 1/4 share in a partnership between A and B, who initially share profits and losses in the ratio of 3:2?

When A and B, the existing partners, decide to admit C into their partnership, certain calculations need to be made to determine the new profit-sharing ratio and the sacrificing ratio. Here’s how we can approach this problem: 1. Initial Ratios: A and B share profits and losses in the ratio of 3:2. – Total parts … Read more