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To find the fraction that bears the same ratio to 17 as 37 does to 59, we can set up a proportion. Let the unknown fraction we want to find be represented as x. We write the proportion as follows: x / 17 = 37 / 59 Next, we can solve for x by cross-multiplying: … Read more

The circumcenter of a triangle is a vital point that holds significant geometrical and mathematical importance. It is defined as the point where the perpendicular bisectors of the sides of the triangle intersect. This unique point can serve various purposes in geometry, such as providing the center of the circumcircle—the circle that passes through all … Read more

The first step in rewriting the expression y = 6×2 + 18x + 14 in the form y = a(x – h)2 + k is to identify the value of a, which is the coefficient of x2. In this case, a = 6. Next, since we want to transform the quadratic expression into vertex form, … Read more

To find the slope of a function represented by a table of values, you can follow these steps: Identify the coordinates: Each row in the table represents a point on the Cartesian plane, typically in the form of (x, y). For example, if your table shows: (1, 2) (2, 3) (3, 5) Use the slope … Read more

Using Euler’s Formula to Find the Number of Faces Euler’s formula is a fundamental relation in geometry that connects the number of vertices (V), edges (E), and faces (F) of a convex polyhedron. The formula is expressed as: V – E + F = 2 In this case, we are given: Number of vertices (V) … Read more

To find how many multiples of 4 lie between 10 and 250, we need to identify the first and last multiples of 4 within this range. 1. **Finding the first multiple of 4 greater than or equal to 10:** The first multiple of 4 that is greater than or equal to 10 can be calculated … Read more

Determining if a year is a leap year involves applying a simple set of rules. Here’s how you can check: Check if the year is divisible by 4: If a year is evenly divisible by 4, it may be a leap year. For example, 2020 and 2024 are divisible by 4. Check if it is … Read more

Given the equation sin(8x) = 4, we first need to recognize that sine of any angle must lie within the range of -1 to 1 (inclusive). Given that 4 is outside this range, it indicates a misunderstanding in the formulation of the problem. Normally, sine values cannot exceed 1 in absolute terms. However, assuming you … Read more

To find the area of the shaded region in a rectangle, you need to follow a few simple steps. Here’s a detailed breakdown: Identify the Dimensions: First, you must determine the dimensions of the rectangle. Let’s assume the total length of the rectangle is L and the total width is W. Identify the Shaded Region: … Read more

To model the growth of a bacteria culture that starts with 500 bacteria and doubles in size every 3 hours, we use the concept of exponential growth. The general form of an exponential growth function can be described by the formula: N(t) = N0 * ekt Where: N(t) is the number of bacteria at time … Read more