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To solve the quadratic equation 2x² + 4x + 7 = 0 using the quadratic formula, we first need to identify the coefficients of the equation. The standard form of a quadratic equation is: ax² + bx + c = 0 For our equation: a = 2 b = 4 c = 7 Next, we … Read more

A leap year consists of 366 days, which is one day more than a standard year that has 365 days. The extra day is added to the month of February, making it 29 days long instead of the usual 28. The concept of a leap year was introduced to help synchronize the calendar year with … Read more

The dot product of two vectors is a crucial concept in linear algebra and can provide insights into the relationship between those vectors, including their relative direction. The mathematical definition of the dot product of two vectors, A and B, is given by: A · B = |A| |B| cos(θ) Here, |A| and |B| are … Read more

An isosceles triangle is a unique and visually striking geometric shape that features two sides of equal length, known as the legs, and one side that is different in length, referred to as the base. The angles opposite the equal sides are also equal, giving the isosceles triangle its characteristic symmetry. When you visualize an … Read more

The multiplicative inverse, also known as the reciprocal, of a number is a value that, when multiplied by the original number, results in 1. In simpler terms, it answers the question: “What do I need to multiply by 14 to get 1?” For the number 14, the multiplicative inverse is found by taking the fraction … Read more

To find the factors of the quadratic expression x² + 9x + 14, we can use the method of factoring by grouping or applying the quadratic formula. However, in this case, factoring by grouping is quite straightforward. First, we’ll look for two numbers that add up to the coefficient of x (which is 9) and … Read more

To find the solution to the equation 28x + 4 + 2x + 5 + x + x + x + 6 + x + 6, we first need to combine like terms. The terms that include x can be summed up, as well as the constant numbers. Let’s break this down: x terms: 28x … Read more

Solutions to the Quadratic Equation To find the solutions of the quadratic equation 3x² + 14x + 16 = 0, we can use the quadratic formula, which is given by: x = (-b ± √(b² – 4ac)) / (2a) In this equation, the coefficients are: a = 3 b = 14 c = 16 Now, … Read more

The area of a circle can be calculated using the formula: A = πr2, where A is the area, π (pi) is a mathematical constant approximately equal to 3.14159, and r is the radius of the circle. In this case, the radius (r) is given as 4. To find the area, we will substitute the … Read more