devyy To find the area of an isosceles trapezoid with bases of lengths 4 and 10, and a base angle of 45 degrees, we can break the problem down into steps. First, we need to understand the geometry of the trapezoid. An isosceles trapezoid has two parallel sides (the bases) and the non-parallel sides (the legs) … Read more
The average age of everyone in the class is a prime example of descriptive statistics. Descriptive statistics are used to summarize and organize data in a meaningful way. They provide a quick overview of the data set’s characteristics without making predictions or inferences about a larger population. In this case, the average age gives us … Read more
To determine whether a specific group of numbers consists entirely of prime numbers, we first need to know what a prime number is. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. In simpler terms, it can only be divided evenly by 1 and … Read more
To find the product of the numbers 5, 22, 2, 13, and another 5, we simply multiply them together. First, we can simplify this process by grouping the numbers. Let’s start by multiplying 5 and 22: 5 x 22 = 110 Next, we take this result and multiply it by 2: 110 x 2 = … Read more
To find the point on the parabola y = x² that is closest to the point (3, 0), we’ll need to minimize the distance between a point on the parabola and the point (3, 0). The distance D between a point (x, y) on the parabola and the point (3, 0) is given by the … Read more
To solve the system of equations 7x + 5y = 19 and 7x + 2y = 16, one of the simplest methods you can use is the elimination method. This method allows us to eliminate one variable, making it easier to solve for the other. Here are the steps to apply the elimination method: Write … Read more
To calculate the population of the city after 3 years, we start with the initial population and then account for the annual increase over the specified period. The initial population of the city is 20,000. Each year, the population increases by 5 people. Therefore, over 3 years, the total increase can be calculated as follows: … Read more
Solving the System of Equations Algebraically To solve the system of equations: Equation 1: 5x + 2y = 10 Equation 2: 3x + 2y = 6 We will use the elimination method to find the values of x and y. Step 1: Align the Equations We start with both equations: 5x + 2y = 10 … Read more
To find the diagonal of a square, you can use the Pythagorean theorem. The formula for the diagonal (d) of a square with side length (s) is given by: d = s × √2 In this case, you are given that each side of the square is 3√2. Plugging this value into the formula gives: … Read more
Finding the Composition of Functions To find the composition of two functions, we denote it as (f ∘ g)(x), which means we will substitute g(x) into f(x). Step 1: Identify the Functions We have the following two functions: f(x) = 3x² + 2 g(x) = 5x² + 1 Step 2: Substitute g(x) into f(x) We … Read more