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
To simplify the expression a²a³, you can use the property of exponents that states when you multiply two numbers with the same base, you add their exponents. In this case, both terms have the same base, which is a. The exponents are 2 and 3. According to the property: am an = am+n Now, applying … Read more
The factors of 16 are the numbers that can be multiplied together in pairs to yield the product of 16. To find these factors, we can start by identifying the numbers that divide 16 evenly without leaving a remainder. Let’s break it down: 1 x 16 = 16 2 x 8 = 16 4 x … Read more
To find the solution to the equation 9w + 4 + 7w + 53w – 2 = 0, we first need to combine like terms. Here’s how we can solve it step by step: Combine like terms: Look for terms that contain the variable w and constants separately. The w terms are: 9w, 7w, and … Read more