devyy

To determine what number can be added to p to yield a rational number, we must first understand what a rational number is. A rational number is any number that can be expressed as the quotient or fraction m/n, where m is an integer and n is a non-zero integer. If p is already a … Read more

To find the remainder when the polynomial 4×3 + 20x + 50 is divided by x3, we can use the polynomial remainder theorem. According to this theorem, the remainder of a polynomial division can be found by evaluating the polynomial at specific values. However, since we are dividing by x3, the remainder will have a … Read more

To factor the polynomial x² + 12x + 36, we can recognize that it takes the form of a trinomial. A trinomial can often be factored using various methods, but in this case, we can employ the method of perfect square trinomials. A perfect square trinomial has the general form (a + b)² = a² … Read more

A geometric sequence is a series of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio. In this case: First term (a): 4 Common ratio (r): 5 To find the first three terms of the geometric sequence, we can use the … Read more

To find fg, we need to substitute the function g(x) into f(x). Here, we have: f(x) = x² + 16 g(x) = x + 4 Now we will compute f(g(x)): f(g(x)) = f(x + 4) = (x + 4)² + 16 Next, we expand the expression: (x + 4)² = x² + 8x + 16 … Read more

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