To find the points of discontinuity for the rational function y = (8x^2 + 5x + 6), we need to analyze the function’s denominator. A rational function can be expressed in the form: y = f(x) = \frac{P(x)}{Q(x)}, where P(x) is the numerator and Q(x) is the denominator. The points of discontinuity occur when the … Read more
To find the measure of angle ABC when the arc AC measures 130 degrees, we can use the properties of tangents and arcs in a circle. When two tangent lines intersect a circle, the angle formed between the two tangents (in this case, angle ABC) is equal to half the measure of the intercepted arc. … Read more
To determine the number of zeros for the function f(x) = 2×14 + 14×6 + 27×3 + 13x + 12, we can analyze this polynomial by considering its degree and applying the Fundamental Theorem of Algebra. The degree of the polynomial is determined by the term with the highest exponent, which in this case is … Read more
To determine the slope of a line that passes through two points, you can use the slope formula, which is defined as: Slope (m) = (y2 – y1) / (x2 – x1) In this case, the two points given are: Point 1: (3, 5) with coordinates (x1, y1) Point 2: (4, 5) with coordinates (x2, … Read more
To find the points on the graph of the function f(x) = x² that are closest to the point (0, 4), we can follow these steps: Identify the Distance Formula: We will use the distance formula to calculate the distance between any point (x, f(x)) on the graph and the point (0, 4). The distance … Read more
The point-slope form of a linear equation is generally represented as: y – y1 = m(x – x1) Here, m is the slope of the line, while (x1, y1) is a point that the line passes through. In your case, the equation you provided is: y = 3x – 2 To convert this into a … Read more
The imaginary unit, denoted as i, is defined as the square root of -1. This means that i^2 equals -1. When i is raised to different powers, it results in a repeating pattern of values depending on whether the exponent is even or odd. Let’s break down what happens when i is raised to odd … Read more
To simplify the expression 6×2 + 3 + 5×3 + 4×3 + 2×2 + 16, we will first combine like terms. 1. Identify the like terms: The x3 terms: 5×3 + 4×3 The x2 terms: 6×2 + 2×2 Constant terms: 3 + 16 2. Combine the like terms: x3 terms: 5×3 + 4×3 = 9×3 … Read more
When rolling a pair of standard six-sided dice, we’re interested in the outcome of the first die specifically. Each die has six faces, numbered from 1 to 6. Among these numbers, the even numbers are 2, 4, and 6. Let’s break down the calculation of the probability: The total number of possible outcomes when rolling … Read more
In the parallelogram LMNO, we have the following segments defined: MP = 21 m LP = 3 m + y NP = 3y + 1 m OP = 2x + 1 m To understand the relationships between these segments, we need to use the properties of a parallelogram. Properties of Parallelograms In any parallelogram: Opposite … Read more