devyy To solve the system of equations 2x + 3y = 40 and 2x + 2y = 20, we can use either the substitution method or the elimination method. Here, we’ll use the elimination method for clarity. First, we can align the two equations for clarity: Equation 1: 2x + 3y = 40 Equation 2: 2x … Read more
The given arithmetic sequence is defined by the formula a_n = 4n + 1, where n represents the term number in the sequence. In an arithmetic sequence, the variable n typically represents a positive integer, as it denotes the position of the term within the sequence. Therefore, the most common interpretation of the domain for … Read more
To determine the center of the circle represented by the equation x² + y² – 12x – 2y + 12 = 0, we first need to rewrite this equation in the standard form of a circle equation: The standard form of a circle’s equation is given as: (x – h)² + (y – k)² = … Read more
In a parallelogram, opposite sides are equal and opposite angles are also equal. If we need to determine the value of ‘r’ in parallelogram CDEF, we usually look for properties relating the sides or angles, or we may have equations set based on the dimensions given. For example, if sides CD and EF are known … Read more
To find the 30th and 90th percentiles of a dataset, you first need to understand the concept of percentiles. Percentiles are values below which a certain percentage of the data falls. For example, the 30th percentile is the value below which 30% of the observations fall. Here’s how to calculate the 30th and 90th percentiles … Read more
To find the new equation of the graph of the function y = x³ after it has been shifted, we need to take into account the transformations described. 1. **Horizontal Shift**: Shifting the graph horizontally to the left by 4 units means adding 4 to the x-coordinates. This transforms the original function as follows: y … Read more
To approximate the value of y in the equation 2^(2y) = 5 using the graph of f(x) = log2(x), we can follow these steps: Rewrite the equation in logarithmic form: The equation can be rewritten using logarithms for easier manipulation. Since we are dealing with base 2, take the logarithm (base 2) of both sides: … Read more
To find the equation of a line given a slope and a point, you can use the point-slope form of the equation of a line, which is expressed as: y – y1 = m(x – x1) In this equation: m is the slope of the line. (x1, y1) is the point through which the line … Read more
The perimeter of a parallelogram is calculated by the formula: Perimeter = 2(AB + AD) In this case, we are given that the perimeter is 46 inches. Therefore, we can set up the equation: 2(AB + AD) = 46 To simplify, we divide both sides by 2: AB + AD = 23 Next, we need … Read more
To find the two numbers from the given information, we can use the relationship between the highest common factor (HCF), least common multiple (LCM), and the numbers themselves. We have: The highest common factor (HCF) of the two numbers is 23. The least common multiple (LCM) includes two factors: 13 and 14. Firstly, we need … Read more