To solve the algebraic expressions 3x + 4 – 2 and 2x + 11 – 1, we will simplify each expression step by step. 1. Simplifying the first expression: Start with the expression: 3x + 4 – 2 Next, combine the constant terms (4 and -2): 3x + (4 – 2) = 3x + 2 … Read more
To find the derivative of the function f(t) = 7t using the formal definition of a derivative, we start with the definition itself: The derivative of a function f(t) at a point t is defined as: D = lim (h → 0) [f(t + h) – f(t)] / h Now, let’s apply this definition step … Read more
True. The mean, often referred to as the average, is calculated by summing all the values in a dataset and dividing that sum by the number of values. This means that every number in the dataset contributes to the final calculation of the mean. When an extreme value, known as an outlier, is present in … Read more
To solve the problem of how many kilograms of tea worth 300 rupees per kilogram should be mixed with 10 kilograms of tea worth 240 rupees per kilogram to achieve a mixture costing 260 rupees per kilogram, we can apply the concept of weighted averages. Let’s denote: x: the number of kilograms of tea at … Read more
To find the solution to the system of linear equations: Equation 1: 2x + y = 1 Equation 2: 3x + y = 6 We can solve this system using the substitution or elimination method. Here, we’ll use the elimination method: Step 1: Align the equations Let’s write both equations clearly: 1) 2x + y … Read more
To find out the number when 32 percent of it is equal to 64, you can use a simple mathematical formula. Let’s denote the unknown number as X. First, we understand that 32 percent can be expressed as a decimal, which is 0.32. Therefore, we can set up the equation: 0.32 * X = 64 … Read more
The factors of a number are the integers that can be multiplied together to produce that number. Let’s break down the factors of 18, 19, and 200 individually: Factors of 18 18 is an even number and can be divided by the following integers: 1 2 3 6 9 18 So, the complete list of … Read more
The equation y = x + 1 represents a linear function, where for every value of x, there is a corresponding value of y. To find the solutions to this equation, we can rearrange it based on specific values of x. Let’s explore how to find solutions: When x = 0: Substitute x with 0: … Read more
The rate of change of an exponential function, especially in the context of compounding interest, can be determined by examining the function itself. In this case, we can consider a general form of a compound interest function, which can be represented as: A(t) = A_0 e^{rt} Where: A(t): The amount of money accumulated after time … Read more
The inverse of the logarithmic function is the exponential function. For the logarithmic function f(x) = log9(x), the base of the log is 9. To find the inverse, we can set up the relationship: Let y = log9(x). This implies that: 9y = x Now, to express the inverse function, we will switch the roles … Read more