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To find the 27th term of an arithmetic sequence, we first need to understand how the sequence works. An arithmetic sequence is defined by its first term and a common difference between consecutive terms. In this case, we are given: First term ( a1 ) = 38 17th term ( a17 ) = 74 To … Read more

To determine the vertical and horizontal asymptotes of the function f(x) = 3x² + 2x + 4, we need to analyze the function’s limits and behavior as x approaches certain values. Vertical Asymptotes Vertical asymptotes occur when the function approaches infinity or negative infinity as x approaches a specific value. These typically occur at values … Read more

The Fundamental Theorem of Arithmetic states that every integer greater than 1 can be expressed as a unique product of prime numbers. To find the highest common factor (HCF) of the numbers 26, 51, and 91, we’ll first break each number down into its prime factorization. 1. **Finding Prime Factorizations:** 26: The prime factorization of … Read more

When solving word problems in math, certain words or phrases signal the need for division. Understanding these indicators can help you identify when to divide quantities to find the correct answer. Some common words associated with division include: Divided by: This term directly indicates that a number should be divided by another. For instance, in … Read more

A geometric sequence is a sequence of numbers where each term is found by multiplying the previous term by a fixed, non-zero number known as the common ratio. In your case, the sequence begins with the terms 4, 16, and 64. Let’s find the common ratio by dividing the second term by the first term: … Read more

To find the next number in the series 13, 18, 16, 21, 19, we need to analyze the pattern between the numbers. Let’s look at the series closely: The sequence starts with 13, and the next number is 18. The difference between these two numbers is: 18 – 13 = 5 The next number is … Read more

To rewrite the inequality 12x + 2y < 42 in slope-intercept form (which is generally written as y < mx + b, where m is the slope and b is the y-intercept), we need to isolate y on one side of the inequality. Here are the steps: Start with the original inequality: 12x + 2y … Read more

To solve the system of equations given by y = 2x + 4 and 2y = 6x + 12, we can follow several steps to find the values of x and y. Step 1: Substitute We start with the first equation: y = 2x + 4. We can substitute this expression for y into the … Read more

Determining the Vertex of the Function To find the vertex of the quadratic function f(x) = \frac{1}{2} x^{2} – 3x + \frac{3}{2} , we can utilize the vertex formula for a quadratic equation in the standard form f(x) = ax^2 + bx + c. In our case, the coefficients are: a = 1/2 b = … Read more

The associative property in mathematics states that the way in which numbers are grouped in addition or multiplication does not change their sum or product. This means when you have an expression, you can rearrange the grouping of terms without affecting the result. To demonstrate how to write an equivalent expression using the associative property … Read more