Finding the Vertex of the Quadratic Function The vertex of a quadratic function is a crucial point that represents either the maximum or minimum value of the function. In the case of the quadratic function, it can be expressed in the standard form as: f(x) = ax2 + bx + c In your question, however, … Read more
Determining whether a graph is symmetric with respect to the origin involves a straightforward examination of the function represented by the graph. A function exhibits origin symmetry if, for every point (x, y) on the graph, the point (-x, -y) is also on the graph. Here’s a step-by-step method to check for this symmetry: Identify … Read more
If A is related to B and B is related to C, we can infer that there is a transitive relationship between A and C. This means that the connection that A has with B does not just end there; it extends to C as well. To illustrate this, consider A, B, and C as … Read more
To calculate the slope of a line that passes through two points, you can use the formula: slope (m) = (y2 – y1) / (x2 – x1) In this case, the two points are (3, 4) and (4, 1). Here, we designate: (x1, y1) = (3, 4) (x2, y2) = (4, 1) Now, we can … Read more
The area of a rectangle can be determined using the formula: Area = Length × Width In this case, the width is 12 feet and the length is 10 feet. Plugging these values into the formula gives: Area = 10 feet × 12 feet Now, calculating that: Area = 120 square feet Therefore, the area … Read more
To complete the square for the expression x² + 5x – 7, we first focus on the quadratic and linear terms, which are x² and 5x. The goal is to transform this part of the expression into a perfect square trinomial. Here are the steps: Take the coefficient of the x term (which is 5), … Read more
When a balloon rises vertically above a level, straight road at a constant rate of 1 foot per second, several interesting dynamics are at play. Firstly, the balloon’s ascent is steady, meaning it maintains its speed without any sudden accelerations or decelerations. This steady motion can be described mathematically as a linear function of time. … Read more
Understanding Similar Triangles When we say that two triangles are similar, it means that their corresponding angles are equal, and the lengths of their corresponding sides are proportional. Let’s break this down step-by-step to find the value of x when we have two similar triangles. Step 1: Identify the Corresponding Parts Assuming we have two … Read more
To solve the equation sin(2x) * sin(x) = 0, we need to find the values of x that make either sin(2x) or sin(x) equal to zero. ### Step 1: Set Each Factor to Zero 1. sin(2x) = 0 The sine function equals zero at integer multiples of π: So, we set 2x = nπ, where … Read more
An irrational number is a type of real number that cannot be expressed as a fraction where both the numerator and the denominator are integers. In simpler terms, if you can’t write a number in the form of a/b where a and b are whole numbers (with b not being zero), then it’s irrational. To … Read more