How to Find the Equation of a Hyperbola Given the Center, Focus, and Vertex
To find the equation of a hyperbola when you have the center, focus, and vertex, you can follow these steps: Identify the Center: Let’s denote the center of the hyperbola as (h, k). Determine the Orientation: Hyperbolas can open either horizontally or vertically. If the vertices and foci are aligned horizontally, the standard form of […]
What is the value of x when 10x + 2 = 5x + 8?
To find the value of x in the equation 10x + 2 = 5x + 8, we will start by rearranging the terms to isolate x. First, we can subtract 5x from both sides: 10x – 5x + 2 = 8 This simplifies to: 5x + 2 = 8 Next, we can subtract 2 from […]
Which trig expression is equal to sin 72°?
The expression that is equal to sin 72° is sin(90° – 18°), which can also be expressed as cos(18°). This is derived from the co-function identity of sine and cosine. To understand this, we can use the complementary angle property of trigonometric functions. According to this property, the sine of an angle is equal to […]
1 cusec is equal to how many litres?
1 cubic foot per second (cusec) is equivalent to approximately 28.3168 litres per second. This conversion is based on the fact that 1 cubic foot equals about 28.3168 litres. To break this down further: a cusec measures the flow rate of water in cubic feet per second. Since we convert cubic feet to litres by […]
What are the solutions to m2 – 9 = 0?
To find the solutions for the equation m2 – 9 = 0, we can start by factoring it. This equation can be factored as: (m – 3)(m + 3) = 0 Setting each factor equal to zero gives us two possible solutions: m – 3 = 0 ⟹ m = 3 m + 3 = […]
If x – 9 is a factor of x² + 5x + 36, what is the other factor?
To find the other factor when x – 9 is a known factor of the polynomial x² + 5x + 36, we can use polynomial long division. 1. Divide the polynomial x² + 5x + 36 by x – 9. 2. The first term of the result will be x because when you multiply x […]
Find all values of x that are not in the domain of g
To determine the values of x that are not in the domain of a function g, we first need to understand the function’s defining characteristics. Generally, values that cause division by zero, square roots of negative numbers, or logarithms of non-positive numbers often lead to restrictions in the domain. For example, suppose g(x) = 1/(x […]
What is 3 minus 3 times 6 plus 2?
To solve the expression 3 – 3 * 6 + 2, we need to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)). 1. First, we handle the multiplication part of the expression. The expression 3 * […]
Which of the following is the solution set of x² – 8x – 12 = 0?
To solve the quadratic equation x² – 8x – 12 = 0, we can use the quadratic formula, which is given by: x = (-b ± √(b² – 4ac)) / (2a) In this equation, a = 1, b = -8, and c = -12. Plugging these values into the formula, we first calculate the discriminant […]
Which of the following is a factor of the polynomial x² + 20?
To determine the factors of the polynomial x² + 20, we first look at its structure. This polynomial is a sum of squares, and it does not factor nicely over the real numbers. The expression can be checked for possible rational factors using the Rational Root Theorem or by trying to factor it directly. The […]