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To find the equation of the tangent line to the curve defined by y = 4x – 3x² at the point (2, 4), we follow these steps: Find the derivative: The derivative of a function gives us the slope of the tangent line at any point on that curve. Let’s find the derivative of the … Read more

To check the sum of the numbers 27, 15, and 12, you simply add these three numbers together. Here’s how you can do it step by step: Start by adding the first two numbers: 27 and 15. 27 + 15 = 42 Next, take the result from the previous addition (42) and add the third … Read more

The exact value of sin(30°) is 1/2. This sine value can be derived from the properties of a 30-60-90 triangle, where the sides are in the ratio of 1 : √3 : 2. In this type of triangle, the side opposite the 30-degree angle is half the length of the hypotenuse, which confirms that the … Read more

To check the answer to the division problem 120 divided by 30, you can follow a few straightforward steps: Perform the Division: Start by dividing 120 by 30. You can do this using long division, a calculator, or even mental math if you’re comfortable with it. Using a Calculator: If you prefer a quick solution, … Read more

No, the ratios of 3 to 4 and 4 to 3 are not the same. Let’s break it down to understand why. A ratio expresses the relationship between two quantities. When we say the ratio of 3 to 4, we can express this mathematically as: Ratio of 3 to 4: 3:4 or 3 ÷ 4 … Read more

Finding the Composition of Functions gf Given the functions: f(x) = 3x + 6 g(x) = x + 2 We want to find the composition gf, which means we need to substitute f(x) into g(x). Step 1: Substitute f(x) into g(x) First, let’s identify the function g with f(x) as input: g(f(x)) = g(3x + … Read more

A number that has more than two distinct factors is called a composite number. In simple terms, a composite number can be divided evenly by numbers other than just 1 and itself, meaning it has multiple positive divisors. To understand this better, let’s consider the definition of the two primary types of numbers in terms … Read more

Solving the Quadratic Equation: 5x + 6x² + 3 = 0 To solve the quadratic equation 5x + 6x² + 3 = 0, we first need to rearrange it in the standard form: 6x² + 5x + 3 = 0 The quadratic formula is given by: x = (-b ± √(b² – 4ac)) / 2a … Read more

To solve the system of equations y = 3x + 7 and y = x + 9, we will set the two equations equal to each other since both are equal to y. Thus, we can write: 3x + 7 = x + 9 Next, we’ll isolate the variable x. Start by subtracting x from … Read more

When we talk about numbers that have 5 as a factor, we are referring to numbers that are divisible by 5. One important characteristic of such numbers is their ones place digit. A number is divisibly specifically by 5 if its last digit (the ones place) is either 0 or 5. This is due to … Read more