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The expression given is x²y³ + 11x²y + 6y² + 66. To find a factor, we can first try to factor this polynomial completely by grouping or using other factoring techniques. 1. Let’s rewrite the expression: we have terms with y

Finding the 32nd Term of an Arithmetic Sequence To determine the 32nd term of the arithmetic sequence where the first term is 32 (denoted as a1 = 32) and the ninth term is 120 (denoted as a9 = 120), we can follow these steps: Step 1: Understand the Formula The general formula for the nth … Read more

To find the focus and directrix of the given parabola described by the equation x = 1 + 8y2, we start by rewriting the equation in the standard form of a parabola. The standard form for a parabola that opens to the right is: x = a(y – k)2 + h In this case, comparing … Read more

Certainly! Prime numbers are numbers greater than 1 that have no positive divisors other than 1 and themselves. Pairs of prime numbers that differ by 2 are often referred to as twin primes. Here are three pairs: (3, 5): Both 3 and 5 are prime numbers, and their difference is 2. (5, 7): The numbers … Read more

To determine the distance between two points on a coordinate grid, we can use the Distance Formula, which is derived from the Pythagorean theorem. The formula is: D = √((x2 – x1)² + (y2 – y1)²) In this case, we have the points A(0, 0) and B(0, 5). Let’s denote these points as follows: A … Read more

To calculate the surface area of a sphere when given its circumference, you can follow these steps: Understand the relationship between circumference and radius: The formula for the circumference (C) of a sphere is given by: C = 2πr Where r is the radius of the sphere and π (pi) is approximately 3.14159. Calculate the … Read more

Solving the Equation To find the value of x in the equation 2x + 3 = 11 – 5x, we need to isolate x step by step. Step 1: Combine like terms First, let’s get all the x terms on one side. We can achieve this by adding 5x to both sides of the equation: … Read more

To find the range of a data set, you need to perform a few simple steps that involve basic arithmetic. The range is a measure of how spread out the values in a data set are. Here’s how you can calculate it: Collect Your Data: Start by gathering all the numbers in your data set. … Read more