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Sure! When it comes to identifying rational numbers between two given decimal values, it’s essential to remember that rational numbers are those that can be expressed as a fraction of two integers. Let’s dive into the specific ranges you provided. 1. Rational Numbers Between 1.1 and 2.2 1.2 1.5 1.8 2.0 2.1 Each of these … Read more

Determining if a number is divisible by 7 can be done using a simple method. Here’s a step-by-step guide: Take the number: Start with the number you want to check for divisibility by 7. For example, let’s say the number is 203. Double the last digit: Take the last digit of the number (in this … Read more

To find the first term of the quotient resulting from the division of x³ + 1 by x², we can approach this division step by step. 1. **Set up the division**: We want to divide x³ + 1 by x². To make this easier, we can express this as:     x³ + 1 ÷ x² 2. … Read more

Finding the Surface Area of Revolution To calculate the area of the surface generated by rotating the curve described by the equation y = x3 around the x-axis from x = 0 to x = 2, we can use the formula for the surface area of revolution. Surface Area Formula The surface area S of … Read more

To convert the equation 3x + y = 1 into the general form ax + by + c = 0, you need to rearrange the equation to fit this format. Here are the steps to achieve this: Start with the original equation: 3x + y = 1. Subtract 1 from both sides of the equation … Read more

The graph of the equation x2 + y = 0 intersects the x-axis where the value of y is equal to zero. To find these intersection points, we can set y to zero and solve for x. Start with the equation: x2 + y = 0 Setting y = 0 gives us: x2 + 0 … Read more

The roots of the quadratic equation 3x² + 4x + 5 = 0 can be found using the quadratic formula: x = (-b ± √(b² – 4ac)) / 2a In this equation, a = 3, b = 4, and c = 5. First, let’s calculate the discriminant, which is the part under the square root: … Read more

To find the derivative of the function f(x) = 2x² + 4x + 1, we will use basic rules of differentiation. The derivative, denoted as f'(x), measures how the function changes as x changes. We’ll differentiate each term of the function separately: The term 2x²: Using the power rule, which states that the derivative of … Read more

Expressing the number 9 as a fraction with a denominator of 7 is straightforward. To do this, you simply need to create a fraction where the numerator (top part of the fraction) is the number 9 and the denominator (bottom part of the fraction) is the number 7. Therefore, you can write it as: 9/7 … Read more

To factor the expression xy + 4x + 2y + 8, we first look for common patterns and grouping possibilities within the terms. 1. **Grouping the Terms**: We can group the expression as follows: (xy + 2y) + (4x + 8) 2. **Factoring Out Common Factors**: In the first group (xy + 2y), we can … Read more