Identify the values that create ordered pairs that are solutions to the equation 3x + 5y = 205y + x^2
To find the ordered pairs (x, y) that are solutions to the equation 3x + 5y = 205y + x^2, we first need to rearrange the equation into a standard form. Starting from: 3x + 5y = 205y + x2 we can move all terms to one side: x2 – 3x + 200y […]
How do you solve the system of equations y = x + 2 and y = 2x + 7?
To solve the system of equations, we start with the two equations: 1. y = x + 2 2. y = 2x + 7 Since both equations are equal to y, we can set them equal to each other: x + 2 = 2x + 7 Now, we will solve for x. First, we can […]
A falling stone takes 0.33 s to travel past a window 22m tall. From what height above the top of the window did the stone fall?
To find the height from which the stone fell, we can use the equations of motion under gravity. Given that the stone takes 0.33 seconds to pass a window that is 22 meters tall, we can first calculate its speed as it passes the window. Using the formula for distance traveled under constant acceleration (in […]
Find the Lateral and Total Surface Area of the Following Pyramids
To find the lateral and total surface area of a pyramid, we first need to understand the basic formulas involved. Lateral Surface Area The lateral surface area (LSA) of a pyramid is the sum of the areas of its triangular faces. The formula for the lateral surface area of a pyramid can be expressed as: […]
If fx = sin x and gx = cos x, then find gofx and fogx?
To find gofx and fogx, we start by understanding what these notations mean. Here, gofx means we need to substitute fx into g, and fogx means we substitute gx into f. First, let’s find gofx: Given that fx = sin x, we need to find g(sin x). Since g(x) = cos x, we replace x […]
Prove that ddx csc x csc x cot x
To prove that the derivative of the expression csc(x) imes csc(x) imes cot(x) can be derived, we will use the product rule and the chain rule from calculus. The expression can be simplified as follows: y = csc(x) imes csc(x) imes cot(x) = csc^2(x) imes cot(x) Now, to find ddx y, we will apply the […]
Given the arithmetic sequence an = 2 + 5n – 1, what is the domain for n?
To determine the domain for n in the arithmetic sequence defined by an = 2 + 5n – 1, we first need to simplify the expression. Simplifying the equation gives us: an = 1 + 5n This sequence is defined for all real numbers since n can take on any real value without any restrictions. […]
The quadratic equation 2x² + 4x + 12 = 0 has?
The quadratic equation 2x² + 4x + 12 = 0 has no real solutions. To understand why, we can use the quadratic formula, which is given by: x = (-b ± √(b² – 4ac)) / 2a Here, a = 2, b = 4, and c = 12. We first need to calculate the discriminant, which […]
If a Trap is an Isosceles Trapezoid, What is the Value of x?
In an isosceles trapezoid, the two non-parallel sides are of equal length, and the base angles are also equal. This unique property of isosceles trapezoids can help us determine the value of x. To find x, we typically set up an equation based on the angles or the lengths of the sides. If we have […]
How to Calculate the Volume of a Figure Given Different Measurements?
To calculate the volume of a figure, you need to know the formula that corresponds to the shape of the object in question. If you only have the values 15 cm³, 33 cm³, 45 cm³, and 54 cm³, these numbers appear to represent the volumes rather than measurements to calculate a volume from. If you’re […]