To find the area of a regular hexagon, you can use the formula: Area = (Perimeter × Apothem) / 2 First, we need to calculate the perimeter of the hexagon. A regular hexagon has six equal sides, so the perimeter (P) can be calculated as: P = 6 × Side length Given that the side … Read more
To find the median of an even set of numbers, you can follow these simple steps: Step 1: Organize the Numbers Start by arranging your numbers in ascending order. This is crucial because the median is determined based on the positional value of the numbers in a sorted list. Step 2: Identify the Total Count … Read more
To determine if a number is a multiple of 8, you can follow a simple method: check if the number can be divided by 8 without any remainder. Here’s how you can do it: Take the number in question. Divide that number by 8. If the result is a whole number (meaning the division yields … Read more
To find the probability of rolling an odd number or a number less than 4 on a single die, we need to first understand the total possible outcomes and the favorable outcomes for the criteria specified. A standard die has six faces, numbered from 1 to 6. Let’s break down the two situations: Odd Numbers: … Read more
To solve for the variable x in the equation 2x + 3 = 7, follow these steps: Subtract 3 from both sides: This will help isolate the term with the variable. Therefore, we rewrite the equation: 2x + 3 – 3 = 7 – 3 This simplifies to: 2x = 4 Divide both sides by … Read more
To simplify the expression (x2/5)5/6, we can use the rules of exponents, particularly the power of a power rule. This rule states that when you raise a power to another power, you multiply the exponents. Therefore: First, we identify the exponents: the base is x, and we have two exponents: 2/5 and 5/6. Next, we … Read more
In a geometric sequence, each term is found by multiplying the previous term by a constant factor known as the common ratio (r). In this case, you have: First term (a1): 30 Common ratio (r): 12 The formula for the n-th term of a geometric sequence can be represented as: an = a1 × r(n-1) … Read more
To find the x and y intercepts of the equation y = x + 8, we follow these steps: Finding the Y-Intercept: The y-intercept occurs when x = 0. To find the y-intercept, substitute x = 0 into the equation: y = 0 + 8 y = 8 Therefore, the y-intercept is (0, 8). This … Read more
The expression tan(9°) * tan(27°) * tan(63°) * tan(81°) can be evaluated using the properties of the tangent function and its symmetrical properties in trigonometry. First, it’s essential to note that: tan(81°) is the same as cot(9°), because tan(90° – x) = cot(x). tan(27°) is the same as cot(63°), for the same reason. This gives … Read more
To solve the problem of finding two positive numbers whose product is 100 and whose sum is minimized, we can approach it using algebraic methods. Let’s denote the two numbers as x and y. From the problem, we know: Product: x * y = 100 We want to minimize the sum: S = x + … Read more