A regular polygon is a polygon with all sides and all angles equal. In the case of a regular polygon with 22 sides, also known as a 22-gon, we can determine the number of lines of symmetry by understanding a few basic properties of regular polygons. Each regular polygon has as many lines of symmetry … Read more
To find a quadratic equation equivalent to the expression x² + 5x + 6, we can utilize factorization. A quadratic equation is typically in the form of ax² + bx + c = 0, and in this case, we have: a = 1, b = 5, c = 6 We begin by looking for two … Read more
When we say that the limit as x approaches infinity is 8, we are indicating a particular behavior of a function as the input (x) grows very large, without bound. This concept is a fundamental part of calculus, specifically in understanding limits. To break this down further, let’s explore what it means: Limit: In mathematics, … Read more
To find the value of cos(15°), we can utilize the cosine subtraction identity, which is given by: cos(a – b) = cos(a)cos(b) + sin(a)sin(b) In this case, we can express 15° as the difference of two angles: 45° and 30°. So, we set: a = 45° b = 30° Now substituting into the cosine subtraction … Read more
To find the quotient of the expression 6×4 ÷ 15×3 ÷ 2×2 ÷ 10x ÷ 4 ÷ 3×2 ÷ 2, we need to follow a systematic approach. First, let’s simplify each term in the numerator and the denominator: Numerator: The numerator is simply 6×4. Denominator: The terms we have in the denominator are: 15×3, 2×2, … Read more
To factor the expression x3 + 7×2 + 5x + 35 using the grouping method, we can follow these steps: First, we should group the terms in pairs: (x3 + 7×2) + (5x + 35) Next, we factor out the greatest common factor (GCF) from each group: From the first group (x3 + 7×2), the … Read more
To express the amount “one lakh thirty thousand” in numerical form, you break it down into two parts: One lakh: In the Indian numbering system, ‘lakh’ refers to one hundred thousand (100,000). Thirty thousand: This is simply represented as 30,000. Now, when you combine these two values, you get: 100,000 (for one lakh) 30,000 (for … Read more
To calculate 60 percent of 90, you can follow a simple mathematical formula. Percentages are a way to express a number as a fraction of 100, so 60 percent can be written as 60/100 or simply 0.6 in decimal form. Here is how you can do the calculation: Convert the percentage to decimal: 60% = … Read more
To express the remainder as a fraction when dividing 64 by 30, we start by performing the division. When you divide 64 by 30, it goes 2 times (because 30 x 2 = 60), leaving a remainder. To find the remainder, you subtract: Remainder = 64 – 60 = 4 Now, we can express the … Read more
To solve the equation 3x + 5 = 35 – x + 8 + x – 5 + 2x + 10, we first need to simplify both sides of the equation. 1. **Simplify the right-hand side:** Combine like terms on the right side: Start with the constants: 35 + 8 – 5 + 10 = … Read more