devyy The parabola given by the equation y = x² + 7x + 18 can be analyzed based on its standard form. To determine the direction in which it opens, we first need to identify the leading coefficient of the quadratic term, which is the coefficient of x². In this equation, the coefficient of x² is … Read more
When a data line on a graph slopes down as it moves to the right, it generally indicates a negative correlation between the two variables being represented. In simpler terms, as one variable increases, the other variable decreases. This type of relationship is common in various fields such as economics, physics, and social sciences. For … Read more
To find the sample standard deviation (SD) from the given data, we can follow a straightforward process: Understand the terms: The mean (m) of your sample is 20. The variance (s2) is 9. The sample size (n) is 25. Find the sample standard deviation: The sample standard deviation (SD) is the square root of the … Read more
To find the absolute value of a complex number, we can use the formula: If z is a complex number of the form z = a + bi, where a is the real part and b is the imaginary part, then the absolute value (or modulus) of z, denoted as |z|, is given by: |z| … Read more
To find out how many ways we can select a committee of 4 members from a club with 12 members, we can use the concept of combinations in combinatorics. When selecting a group where the order of selection does not matter, we use the combination formula: C(n, r) = n! / (r! * (n – … Read more
To simplify the expression (1 / x²) ÷ (3 / x³), we can start by rewriting the division as multiplication by the reciprocal. This can be expressed as: 1 / x² * x³ / 3 Now, we can combine the fractions: 1 * x³ / (3 * x²) = x³ / (3x²) Next, we can … Read more
When considering the system formed by a quadratic equation and a linear equation, the number of intersection points can vary based on the specific equations involved. Here’s a detailed breakdown: 1. **Two Points of Intersection:** This scenario occurs when the quadratic curve opens either upwards or downwards, and the linear line intersects it in two … Read more
Understanding the Surface Area of a Rectangular Prism A rectangular prism, also known as a cuboid, is a three-dimensional shape that has six rectangular faces. To determine the total surface area of this geometric figure, you can follow a straightforward mathematical formula. The Formula The formula for calculating the surface area (SA) of a rectangular … Read more
To solve the problem of subtracting the polynomial 2y² + 3y + 5 from y³ + 6y² + 5y, we need to perform the following calculation: (y³ + 6y² + 5y) – (2y² + 3y + 5) Let’s break this down step-by-step: Align the polynomials: We will first write both polynomials in standard form, aligning … Read more
The function given is a quadratic function, typically represented as f(x) = ax^2 + bx + c. In this case, we have: a = 1 b = 0 c = 4 Finding the Vertex The vertex of a quadratic function can be determined using the formula for the x-coordinate of the vertex, x = -b … Read more