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To find the remainder when dividing the polynomial x3 + 2 by x + 1, we can use the Remainder Theorem. The Remainder Theorem states that the remainder of the polynomial f(x) when divided by x – c is equal to f(c). In our case, we want to divide by x + 1, which can … Read more

To determine which sequence is correct, we first need to analyze the provided sequences: Sequence 1: 23 35 1115 Sequence 2: 35 23 1115 Sequence 3: 1115 35 23 Sequence 4: 35 115 23 Next, let’s explore these sequences and try to identify any potential rules or patterns that would indicate correctness: Analysis of Each … Read more

To find the dimensions of the rectangular deck, we can start by letting the width of the deck be represented by the variable x. Given that the length of the deck is 5 feet longer than the width, we can express the length as x + 5. The area A of a rectangle is calculated … Read more

To determine the value of x for which line l is parallel to line m, we need to apply the properties of parallel lines and use the concept of corresponding angles, alternate interior angles, or the slopes of the lines depending on how they are defined in the problem. Here is a step-by-step approach: Identify … Read more

To find the quotient of the polynomial x³ + 2 – 5x + 3x – 1, we first need to rearrange and simplify the polynomial by combining like terms. So, let’s simplify it step by step: Combine the x terms: -5x + 3x results in -2x. Now the polynomial can be expressed as: x³ – … Read more

To find the value of x in the equation 7x + 2y = 48 when y = 3, we can follow these steps: Substitute the value of y: Replace y in the equation with 3: 7x + 2(3) = 48 Calculate: Next, simplify the equation: 7x + 6 = 48 Isolate 7x: Subtract 6 from … Read more

The function y = sin(2x) is periodic and reaches its maximum value at specific points within its cycle. To find the smallest positive value of x where y = sin(2x) reaches its maximum, we first need to identify the properties of the sine function. The sine function achieves its maximum value of 1 whenever its … Read more

Calculating the mean and range of a set of numbers is a fundamental aspect of descriptive statistics, which helps in understanding the data better. Let’s break down each computation step-by-step. Calculating the Mean The mean, often referred to as the average, is found by adding all the numbers in a dataset and then dividing that … Read more

To evaluate the limit as h approaches 0 for the expression √(9h + 3h), we start by simplifying the expression inside the square root. 1. **Combine the terms:** The expression can be rewritten as: √(9h + 3h) = √(12h) 2. **Substituting h = 0:** Now, we replace h with 0 to see how the expression … Read more

The function f(x) = 3x² + 6x + 8 is a quadratic function, which means it has the general form of f(x) = ax² + bx + c, where a, b, and c are constants. In this case, a = 3, b = 6, and c = 8. To find the range of this quadratic … Read more