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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

When the graph of a system of two linear equations has no solution, this indicates that the lines representing the equations are parallel. In more detail, parallel lines never intersect; thus, there is no point at which they meet. This lack of intersection implies that there are no values of the variables that satisfy both … Read more

The discriminant of a quadratic equation is a key component that helps determine the nature of the roots of the equation. For a standard quadratic equation of the form ax² + bx + c = 0, the discriminant can be calculated using the formula: D = b² – 4ac In your case, the quadratic equation … Read more

To derive the equation of a parabola from a given focus and directrix, we follow a geometric definition: a parabola is the set of all points (x, y) that are equidistant from the focus and the directrix. In this case, the focus is at the point (0, 4), and the directrix is given by the … Read more

To solve for the value of md, we first need to recognize that vertical angles are equal. This means that: mc = md According to the problem, we have: mc = 26x md = 2x + 10 Setting these two expressions equal to each other, we can write: 26x = 2x + 10 Now, let’s … Read more

To write an equation in point-slope form, you can use the formula: y – y1 = m(x – x1) Where: (x1, y1) is a point on the line (in this case, (8, 3)) m is the slope of the line (which is 8 here) Now, we can substitute the values into the formula: Point: (8, … Read more

The expression i0 + i1 + i2 + i3 + i4 involves the imaginary unit i, which is defined as the square root of -1. To evaluate this expression, we will calculate each power of i and then sum them up. Let’s break it down: i0 = 1 (Any number to the power of zero … Read more

The given expression appears to contain some formatting issues. However, if we interpret it as a standard quadratic equation, we can rewrite it more clearly. The standard form of a quadratic equation is typically stated as: ax² + bx + c = 0 In our case, it looks like you’re asking about the quadratic equation … Read more