To determine the slope of a line that is perpendicular to another line, we first need to understand the slope of the line described by the equation y = 2x + 5. The equation is in the slope-intercept form, which is y = mx + b, where m represents the slope and b is the … Read more
To divide 33 photos into two groups with a ratio of 4:7, first, sum the parts of the ratio. In this case, 4 (for the first group) + 7 (for the second group) equals 11 parts in total. Next, calculate the value of one part by dividing the total number of photos (33) by the … Read more
To determine the completely factored form of the expression 8×2 + 50, we will first look for the greatest common factor (GCF) of the terms in the expression. The coefficients are 8 and 50, and their GCF is 2. Now, let’s factor out the GCF: 8×2 + 50 = 2(4×2 + 25) Next, we see … Read more
Finding the radius of a circle on a graph is a straightforward process, especially if you have the equation of the circle or you can identify key points on the graph. Here’s a step-by-step guide: Method 1: Using the Circle’s Equation If you know the equation of the circle, which is generally written in the … Read more
To prove that the mnth term of an arithmetic progression (AP) is zero under the given conditions, we start by recalling the formula for the nth term of an AP. Let the first term of the AP be denoted as a, and the common difference be denoted as d. The nth term of the AP … Read more
When you take a cross-section of a square pyramid parallel to its base, the resulting shape is a smaller square. This is due to the uniform tapering of the sides of the pyramid towards the apex, which maintains the square shape at various heights. The size of the square decreases as you move up from … Read more
Understanding the Table of Binomial Multiplication When we multiply two binomials, we often use the distributive property, which is also known as the FOIL method (First, Outer, Inner, Last). The resulting table helps in visualizing how each term interacts with others. For example, consider two binomials: (x + 3) (x + a) If we were … Read more
To find the other factor of the polynomial 3x² + 10x + 8, given that one factor is 3x + 4, we can use polynomial long division. 1. **Set up the division**: We will divide 3x² + 10x + 8 by 3x + 4. 2. **Divide the leading terms**: Take the leading term of the … Read more
Identifying Similar Polygons When we talk about similar polygons, we are referring to shapes that have the same form but may vary in size. This means that their corresponding angles are equal, and the lengths of their corresponding sides are proportional. Key Characteristics of Similar Polygons Equal corresponding angles: All the angles in one polygon … Read more
To find the number of sides (n) in a polygon when given the sum of its angle measures, we can use the following formula: Sum of interior angles = (n – 2) × 180 In this case, we’re told that the sum of the angle measures is 2880 degrees. So we can set up the … Read more