devyy To find the factors of the quadratic expression m² + 14m + 48, we need to factor it into the form (m + p)(m + q), where p and q are such that: p + q = 14 (the coefficient of m) p * q = 48 (the constant term) Next, we need to identify … Read more
Adding and subtracting integers can be accomplished easily without a number line by using mental math strategies, understanding the rules of signs, and employing visual aids or manipulatives. Here’s a breakdown of some effective methods: Addition of Integers 1. **Same Signs**: When adding two integers with the same sign, simply add their absolute values and … Read more
A three-dimensional shape, often referred to as a 3D shape, is a form that has depth, width, and height, distinguishing it from two-dimensional shapes that have only length and width. These shapes occupy space and can be found all around us, from everyday objects to complex architectural designs. In geometry, three-dimensional shapes can be classified … Read more
To factor the expression 3x² x 7 completely, we begin by identifying the components of the expression. This expression consists of two factors: 3x² and 7. 1. **Identify the individual factors**: The first part of our expression, 3x², can be thought of as having its own factors: 3: This is a prime number, and it … Read more
To determine whether the numbers 24, 32, and 40 can form a right triangle, we can apply the Pythagorean theorem. The Pythagorean theorem states that for a right triangle with sides of lengths a, b, and hypotenuse c, the following equation holds: a² + b² = c² In our case, we need to identify the … Read more
Finding the Area of a Rhombus with One Diagonal and Perimeter The area of a rhombus can be determined easily if you have one diagonal and the perimeter. Let’s break down the steps. Understanding the Properties of a Rhombus A rhombus is a type of polygon that is a quadrilateral (four sides) with all sides … Read more
When discussing numerical comparisons, the terms rate and ratio often come up, and while they may sound similar, they serve different purposes in mathematics and data analysis. A ratio is a quantitative relationship between two numbers, showing how many times one value contains or is contained within the other. For instance, in a classroom with … Read more
To find the value of p in the linear equation 24p + 12 = 18p + 10 + 2p + 6, we first need to simplify the equation. Step 1: Combine like terms on the right side of the equation. 18p + 2p + 10 + 6 = 20p + 16 Now we can rewrite … Read more
To find the standard form of the equation of a line given two points, you can follow these steps: Identify the Points: We have the points (0, 5) and (4, 0). Calculate the Slope: The slope (m) of a line through two points (x1, y1) and (x2, y2) can be calculated using the formula: m … Read more
The polynomial in question is y² + 3y + 12. Let’s break down its key characteristics: Degree: The degree of this polynomial is 2 because the highest exponent of the variable y is 2. Leading Coefficient: The leading coefficient (the coefficient of the term with the highest degree) is 1, which means that the polynomial … Read more