To factor the quadratic expression 48×2 + 26x + 3, we first identify the coefficients: a = 48, b = 26, and c = 3. We will use the factoring method where we find two numbers that multiply to a * c = 48 * 3 = 144 and add up to b = 26. … Read more
Austin’s annual income is $18,000, and he falls into the 15% tax bracket for his income level. To calculate the tax owed, we will use a simple formula: Tax Owed = Annual Income x Tax Rate Substituting Austin’s figures into the equation, we get: Tax Owed = $18,000 x 0.15 Now, performing the calculation: Tax … Read more
To determine the number of winners in a competition where there are 63 participants, we first need to define the criteria for winning. Generally, the number of winners can vary considerably depending on the format of the competition. However, let’s explore a couple of common scenarios: 1. Single Winner Format:If the competition is designed to … Read more
To find the value of x in the expression given, let’s examine the equation carefully. Initially, your expression combines two instances of x alongside some numbers. However, there seems to be a formatting issue in the question as it may not strictly resemble a solvable equation. Therefore, we need to interpret the equation in standard … Read more
The empty set, often denoted by the symbol ∅ or by a pair of curly braces {}, is a fundamental concept in mathematics. It represents a set that contains no elements. In simple terms, if you were to imagine a box that is supposed to hold items, the empty set is like a box that … Read more
To verify the expression sin(90°) + cos(θ), we can utilize the sine and cosine values in trigonometry. First, it’s essential to recall that sin(90°) equals 1. This is a fundamental value in trigonometric functions: sin(90°) = 1 Using this, we can rewrite our expression: sin(90°) + cos(θ) = 1 + cos(θ) This indicates that the … Read more
To find the correct graph representing the solution for the equation x^4, you need to follow a series of steps. 1. **Understand the Equation**: The equation x^4 represents a polynomial function of degree 4. This means its general shape will be a smooth curve, typically resembling a ‘U’ shape. 2. **Identify Key Features**: The function … Read more
Inverse proportion is a relationship between two variables in which an increase in one variable results in a decrease in the other, and vice versa. Here are some real-life examples: Speed and Travel Time: When driving a car, if you increase your speed, the time it takes to reach your destination decreases. For instance, if … Read more
To find the general solution of the differential equation x²y” + 2y’ = e^x, we first identify the type of equation we are dealing with. This is a linear second-order ordinary differential equation. Here’s a systematic approach to solving it: Rewrite the equation: The given differential equation can be expressed as: x²y” + 2y’ – … Read more
To find a function that models the area A of a circle in terms of its circumference C, we can start by recalling the formulas for the area and circumference of a circle: The area of a circle is given by the formula: A = πr² The circumference of a circle is given by the … Read more