To determine which exponential function goes through the points (1, 6) and (2, 12), we start by considering the general form of an exponential function: f(x) = a * b^x Here, a is the initial value when x = 0, and b is the base of the exponential growth. Since we have two points, we … Read more
To find the composition of two functions, such as p(q(x)), you need to substitute q(x) into the function p(x). Here, p(x) is defined as p(x) = 2x + 4 and q(x) is defined as q(x) = x + 3. 1. Start by calculating q(x): q(x) = x + 3. 2. Now substitute q(x) into p(x): … Read more
The total volume of water in the world’s oceans is approximately 1.332 billion cubic kilometers (or 1,332,000,000 cubic kilometers). This immense volume accounts for about 97% of the Earth’s water supply, with the remaining 3% found in glaciers, ice caps, groundwater, and freshwater lakes and rivers. To put this figure into perspective, consider that a … Read more
The circumference of a circle is directly related to its radius through the formula: C = 2πr Here, C represents the circumference, r is the radius, and π (pi) is a constant approximately equal to 3.14159. To find the area of the circle, we can follow these steps: Find the Radius: Given that the circumference … Read more
Triangular numbers are a special sequence of numbers that can be represented in the shape of an equilateral triangle. They are formed by the arrangement of objects in a triangular pattern, where each subsequent row of objects has one more item than the previous row. To understand triangular numbers better, let’s look at how they … Read more
To find the value of x such that sin(x) = cos(19) within the interval 0 ≤ x ≤ 90, we can use the trigonometric identity that states: sin(x) = cos(90 – x) Given this identity, we can rewrite the equation: sin(x) = cos(19) => cos(90 – x) = cos(19) From the equation cos(A) = cos(B), … Read more
To determine a possible value of x such that the expression simplifies to 12, we first need to understand the expression itself. Let’s say we have an expression in the form of an equation, for example: ax + b = 12 Here, a and b represent constants. The goal is to isolate x. To do … Read more
The sum of the angle measures of any polygon can be found using the formula: Sum of interior angles = (n – 2) × 180° where n is the number of sides of the polygon. For an octagon, which has 8 sides, we can substitute 8 for n in the formula: Sum of interior angles … Read more
To find the value of x in the equation 42x – 12 = 0, follow these steps: Add 12 to both sides of the equation: This gives: 42x – 12 + 12 = 0 + 12 So the equation simplifies to: 42x = 12 Divide both sides by 42: This allows us to isolate x: … Read more