Solving linear equations in two variables can be approached through several methods, each with its unique techniques and applications. Here are some of the most commonly used methods: 1. Graphical Method The graphical method involves plotting the equations on a coordinate plane. Each equation represents a line, and the solution to the system of equations … Read more
To solve the equation log4(y) = 9 log4(3) log4(81), we will follow these steps: First, simplify log4(81). Since 81 = 34, we can rewrite it as: log4(81) = log4(34) = 4 * log4(3) Now, substituting this back into our equation gives: log4(y) = 9 * log4(3) * (4 * log4(3)) This simplifies to: log4(y) = … Read more
To solve the system of equations where y = 25×3 and y = x2, we first need to set the two expressions for y equal to each other: 25×3 = x2 Next, we can rearrange this equation by moving all terms to one side: 25×3 – x2 = 0 Now, we can factor out the … Read more
To find the result of multiplying the functions f(x) = 4x + 5 and g(x) = 6x + 3, you will perform the operation f(x) imes g(x). Here is the detailed step-by-step process: First, write down the functions: f(x) = 4x + 5 g(x) = 6x + 3 Next, set up the multiplication: f(x) * … Read more
Calculating 30 with Reusable Numbers If you’re looking to reach the total of 30 using the numbers 1, 3, 5, 7, 9, 11, 13, and 15, and you’re allowed to repeat these numbers, you can approach this problem through various combinations. Understanding the Options The exciting part of this challenge is the flexibility you have … Read more
To find the distance driven, we can use the formula: Distance = Speed × Time In this case, the speed is 60 miles per hour (mph) and the time is 3.5 hours. Now, let’s plug in the values: Distance = 60 mph × 3.5 hours Distance = 210 miles So, if you drive at 60 … Read more
Synthetic division is a simplified form of polynomial long division, and it can be particularly useful for evaluating polynomials at specific points. To find p(2) for the polynomial p(x) = x4 + 9×3 + 9×2, we will perform synthetic division using 2 as the divisor. First, we need to set up our synthetic division: Write … Read more
The sequence you’ve provided is a geometric sequence where each term is obtained by multiplying the previous term by a constant factor. Let’s break it down: The first few terms are: 1st term: 4 2nd term: 8 3rd term: 16 4th term: 32 Looking closely, we can see that: 8 = 4 × 2 16 … Read more
To factor the expression 4x² – 25x + 6 + 4x + 6 + 4x + 6x + 1 + 2x + 32x + 2 + 2x + 62x + 1 completely, we first need to simplify it by combining like terms. Start by collecting all terms: 4x² – 25x + 4x + 6 + … Read more
Understanding the Reflection of Trapezoid PQRS Across Line WY In geometry, reflecting a shape across a line means flipping the shape over that line, while maintaining its size and shape. Trapezoid PQRS undergoes this transformation when reflected across line WY. Analyzing Trapezoid PQRS Let’s assume that trapezoid PQRS is located at specific coordinates in a … Read more