devyy To determine which equation has a graph that is a parabola with a vertex at the point (5, 3), we can use the vertex form of a quadratic equation. The vertex form is expressed as: y = a(x – h)² + k In this equation: (h, k) are the coordinates of the vertex. a determines … Read more
To find the Highest Common Factor (HCF) and the Least Common Multiple (LCM) of the numbers 120 and 90, we can follow a systematic approach. Finding the HCF The HCF is the largest number that divides both numbers without leaving a remainder. One method to find the HCF is through prime factorization. Step 1: Prime … Read more
To determine whether the line represented by the equation y = 4x + 5 crosses the vertical axis at y = 5, we need to understand what it means for a line to intersect the vertical axis, also known as the y-axis. The y-axis is the vertical line where x = 0. When a line … Read more
Dividing Polynomials: A Step-by-Step Guide To divide the polynomial x4 + 9×2 – 9 by x2 + 3x, we can use polynomial long division. Here’s how to perform the division: Step 1: Set Up the Division Write the dividend (the polynomial you are dividing) and the divisor (the polynomial you are dividing by) in a … Read more
To determine the fraction of a day that you spend sleeping, we first need to understand how many hours there are in a full day. A standard day consists of 24 hours. If you sleep for 8 hours each day, you can express this as a fraction of the total hours in a day: Fraction … Read more
The area of a trapezoid can be calculated using a simple formula that takes into account the lengths of its two parallel sides and its height. The formula is as follows: Area = 0.5 × (b₁ + b₂) × h In this formula: b₁ = Length of the first (longer) parallel side b₂ = Length … Read more
To find the points on the curve where the tangent is horizontal, we need to start by analyzing the derivative of the function. A horizontal tangent occurs when the derivative of the function is equal to zero. Assuming the function is given as: y = 2x^3 + 3x^2 + 12x^2 First, let’s simplify this equation: … Read more
To determine which equation matches the provided data from the table, let’s break it down step by step. The table consists of various relationships between the variables y and x. The given statements are: y = x y = 3 y = 4x y = x + 3 To analyze these equations: 1. y = … Read more
Understanding Graph Conversion to Pie Charts When considering which types of graphs can be effectively converted into a pie chart, it’s important to understand the data each graph typically represents. A pie chart visually displays the proportions of a whole, making it ideal for categorical data that represents parts of a single entity. Let’s evaluate … Read more
To determine the symmetry of the graph given by the polar equation r = 5 cos(3θ), we can analyze it based on the definitions of symmetry in polar coordinates. 1. Symmetry about the x-axis: A graph is symmetric about the x-axis if replacing θ with -θ yields the same result for r. Let’s test this: … Read more