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
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