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To factor the polynomial expression 15x³ + 5x² + 6x + 2 by grouping, we will follow a systematic approach. Here’s how we do it: First, let’s group the terms: (15x³ + 5x²) + (6x + 2) Next, we factor out the common factors from each group: From the first group (15x³ + 5x²), we … Read more

To find the solutions of the quadratic equation x² + 7x + 4, we can use the quadratic formula, which is given by: x = (-b ± √(b² – 4ac)) / (2a) In our equation, we identify the coefficients as follows: a = 1 (the coefficient of x²) b = 7 (the coefficient of x) … Read more

Angles that share a vertex but do not share a side are referred to as vertically opposite angles. To elaborate, when two lines intersect, they create two pairs of opposite angles. Each angle in one pair is opposite to the angle in the other pair, and they share a common vertex, but their sides do … Read more

To solve the equation 2×2 = 2, we can start by simplifying it. First, divide both sides of the equation by 2: x2 = 1 Next, to find the values of x, we take the square root of both sides: x = ±1 This means that the solutions to the equation are x = 1 … Read more

The set of all numbers, often referred to as the set of real numbers, includes both rational and irrational numbers. To understand this better, let’s delve into each category. Rational Numbers Rational numbers are numbers that can be expressed as the quotient or fraction of two integers, where the denominator is not zero. This means … Read more

To solve for c in the expression c = 5cos(35°) + 5sin(35°), we start by isolating c in the given equation. Reorganizing, we have: c = 5cos(35°) + 5sin(35°) Next, we can factor out the constant 5: c = 5(cos(35°) + sin(35°)) Now, we need to calculate cos(35°) and sin(35°). Using a calculator: cos(35°) ≈ … Read more

To determine how many thousands there are in 10 crores, we first need to understand the relationship between these two units of measurement. 1 crore is equivalent to 10 million, or 10,000,000. Thus, 10 crores can be calculated as follows: 10 crores = 10 x 1 crore = 10 x 10,000,000 = 100,000,000 (or 100 … Read more

Proving the Equation: sin(a + b) = sin(a)cos(b) + cos(a)sin(b) To prove the identity sin(a + b) = sin(a)cos(b) + cos(a)sin(b), we will use the unit circle and properties of sine and cosine functions. 1. Understanding the Unit Circle The unit circle is a circle with a radius of 1, centered at the origin (0,0) … Read more

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