devyy To find the equation of a line given a point and a slope, you can use the point-slope form of a linear equation. The point-slope form is expressed as: y – y1 = m(x – x1) Where: (x1, y1) is a point on the line (in this case, (7, 2)), m is the slope of … Read more
To find the expression equivalent to pq(x), we first need to interpret the given definitions of p and q. We have: p: px = x^2 + 1 q: qx = 5x + 1 Now, let’s compute the product pq(x): Substituting the expressions for p and q into the product gives: pq(x) = (x^2 + 1)(5x … Read more
To find the value of x when you are given that two rectangles are similar, you first need to understanding the properties of similar figures. When two shapes are similar, their corresponding sides are in proportion. Let’s say we have two rectangles: Rectangle A and Rectangle B. If the sides of Rectangle A are known, … Read more
The average rate of change of a function g(x) between two points a and b is calculated using the formula: Average Rate of Change = (g(b) – g(a)) / (b – a) In this case, we are given: a = 4 b = 7 Average Rate of Change = 5/6 According to the formula, we … Read more
To determine which equation has an axis of symmetry at x = 0, we need to consider the properties of various equations, primarily focusing on quadratic equations. The standard form of a quadratic equation is: y = ax² + bx + c In this case, the axis of symmetry can be found using the formula: … Read more
Creating the Equation of a Line The slope-intercept form of a line is expressed as: y = mx + b m = slope of the line b = y-intercept of the line Given: The point (6, 1) The slope m = 4 We can substitute the given slope and the coordinates of the point into … Read more
Calculating the Length of an Arc The length of an arc in a circle can be calculated using the formula: Arc Length (L) = (θ/360) × (2 × π × r) Where: θ = the central angle in degrees r = the radius of the circle π (Pi) ≈ 3.14159 In this case, the radius … Read more
Understanding Perfect Squares A perfect square is a number that can be expressed as the square of an integer. In other words, if you take a whole number (also known as a non-negative integer) and multiply it by itself, the result is a perfect square. Examples of Perfect Squares 1 is a perfect square because … Read more
To find the other factor when one of the factors of the polynomial x² + 20 is x + 5, we can use polynomial division or factorization methods. We begin by recognizing that the expression x² + 20 is a quadratic polynomial. We can express it in the form: (x + 5)(x + b) = … Read more
The function f(x) = 3×4 + 1 represents a polynomial curve where the highest degree term is x raised to the power of 4. Here are some key characteristics and steps to understand its graph: 1. Basic Formula The polynomial function consists of a leading coefficient of 3 and a constant term of 1. This … Read more