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To determine if the roots of the quadratic equation 5x² + 4x + 3 = 0 are real or non-real, we can use the discriminant (D). The discriminant is part of the quadratic formula used to find the roots of a quadratic equation: The general form of a quadratic equation is: ax² + bx + … Read more

Solving the Differential Equation The given differential equation is: xy² + x²y = 0 To solve this equation, we can start by factoring it: y(xy + x²) = 0 This equation gives us two factors that can be set to zero: Factor 1: y = 0 Factor 2: xy + x² = 0 Case 1: … Read more

The given sequence is 8, 5, 2, 1, 4. To find a formula that describes this sequence, we first need to analyze the relationship between the terms. 1. **Identifying the Sequence Pattern:** We can observe that the sequence does not follow a simple arithmetic or geometric pattern. By examining the differences between consecutive terms, we … Read more

To find the solutions for the equation 3x^2 + 22x = 0, we can start by factoring the equation. First, we notice that there is a common factor in both terms: 3x^2 + 22x = 0 We can factor out x from the equation: x(3x + 22) = 0 Now we have a product equal … Read more

To find the area of a triangle, you can use the following formula: Area = (base * height) / 2 In this case, the base of the triangle is 5 inches and the height is 12 inches. Plugging these values into the formula gives: Area = (5 * 12) / 2 Now, let’s do the … Read more

The binomial expansion of an expression of the form (a + b)n has a specific formula for determining the number of terms. This formula states that the number of terms in the expansion is given by n + 1, where n is the exponent. In your case, we are looking to expand (2x + 3)5. … Read more

To determine the equation of a vertical line that passes through a specific point, it is important to understand the properties of vertical lines in a coordinate plane. A vertical line has the same x-coordinate for every point on the line. Given the point (3, 5), we can see that the x-coordinate is 3. Therefore, … Read more

To determine the value of g(3), we first need to know the definition of the function g(x). Functions are often defined by an expression or formula that tells us how to calculate the output (the value of g(x)) based on the input (the value of x). For instance, if g(x) is defined as g(x) = … Read more

To solve the equation 2/5 + 3x/5 = (x + 5)/10, we can follow these steps: Eliminate the fractions: To make the equation easier to work with, we can eliminate the fractions by multiplying every term by 10, which is the least common multiple of the denominators (5 and 10). This gives us: 10 * … Read more

Finding the Center and Radius of the Circle To find the center and radius of the circle given the equation x² + 2x + y² + 4y = 20, we need to rewrite this equation in the standard form of a circle, which is: (x – h)² + (y – k)² = r² where (h, … Read more