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Quadrilaterals are intriguing shapes that play a significant role in both geometry and our everyday lives. A quadrilateral is defined as a polygon with exactly four sides, four vertices, and four angles. The beauty of quadrilaterals lies in their diversity, with several specific types that each have distinct properties. Below, we explore the various shapes … Read more

To determine how many different combinations of 4 students can be selected from a group of 12 students, we use the concept of combinations in combinatorics. Combinations are used when the order of selection does not matter. The formula for combinations is given by: C(n, r) = n! / (r! * (n – r)!) Where: … Read more

To find the function g given that gx = 3 and x = e, we first need to understand the relationship described by the equation. Here, we can express g as: g = 3/x Now, substituting x = e into the equation, we get: g(e) = 3/e At this point, we have determined that g … Read more

The given geometric sequence starts with the first term a = 2, and the common ratio r can be found by dividing the second term by the first term. Thus, the common ratio is: r = 10 / 2 = 5 Now that we have identified the first term and the common ratio, we can … Read more

Finding the area of a triangle typically involves using the height of the triangle. However, there are several alternative methods to calculate the area when the height is not readily available. Here are some of the most effective methods: 1. Using Heron’s Formula If you know the lengths of all three sides of the triangle … Read more

To solve for f(1), we start with the given equation: f(x) = 2f(x^4) + 18 We know from the problem statement that: f(1) = 2 Now, let’s plug in x = 1 into the function: f(1) = 2f(1^4) + 18 Since 1^4 = 1, we can simplify this to: f(1) = 2f(1) + 18 Now, … Read more

To determine the value of x for which the lines p and q are parallel, you must understand that two lines are parallel if their slopes are equal. In this case, the slopes are given as: m1 = 9x m3 = 117 Since the lines are parallel, we can set the slopes equal to each … Read more

The arc length formula is a valuable tool in mathematics used to calculate the length of an arc in a circle. The formula is given by: Arc Length (L) = r * θ where: L is the arc length. r is the radius of the circle. θ is the central angle in radians. In this … Read more

To find the area of a circle, we can use the formula: Area = π × r² where r is the radius of the circle. First, we need to determine the radius from the diameter. The radius is half of the diameter. In this case: Diameter = 14 meters So, Radius (r) = Diameter / … Read more

To analyze the sum of the square roots of 50 and 18, let’s break down the calculation step-by-step: Step 1: Calculate square roots First, we need to determine the square roots: Square root of 50: This can be simplified. The square root of 50 is the same as the square root of 25 times the … Read more