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To find the 12th term of a geometric sequence, we first need to identify the relationship between the terms. A geometric sequence can be described by the formula for its nth term, which is: an = a1 * r(n-1) Where: an is the nth term, a1 is the first term, r is the common ratio, … Read more

To determine the relationship between the sets a and b, we start by defining them: a = {101, 202, 303, 404, 505} b = {101, 404} Now, let’s analyze both sets: The set a contains five values: 101, 202, 303, 404, and 505. On the other hand, b includes two values: 101 and 404. We … Read more

To solve the problem, we first need to substitute the values of x and y into the expressions given: 1. **Calculate 3x² + 2y:** Substituting x = 3 and y = 5, we get: 3(3²) + 2(5) 3(9) + 10 = 27 + 10 = 37 2. **Calculate 2x² + 3y:** Substituting x = 3 … Read more

To determine the next number in the sequence 2, 9, 5, 13, 10, 19, 17, we first need to analyze the pattern. Let’s break down the sequence: The first set of numbers: 2, 5, 10, 17 The second set of numbers: 9, 13, 19 We can observe the following: The first numbers of each pair … Read more

To identify how much fabric Erica has left, we first need to clarify the total amount of fabric she purchased. Erica bought three pieces of fabric, each measuring twelve yards. Therefore, the total amount of fabric can be calculated as follows: Total Fabric = Number of Pieces × Length of Each Piece Total Fabric = … Read more

Writing and Factoring the Equation To rewrite the equation in standard form and factor it, we start with the expression: 3x² + 19x + 14 Step 1: Writing in Standard Form This expression is already in standard form, which generally looks like: Ax² + Bx + C In this case, A = 3, B = … Read more

Factoring by Grouping the Expression 7x³ + 21x² + 3x + 9 To factor the expression 7x³ + 21x² + 3x + 9 by grouping, we will follow these steps: Step 1: Group the Terms We start by grouping the first two terms and the last two terms: (7x³ + 21x²) + (3x + 9) … Read more

To rewrite the expression the fourth root of 7 to the fifth power using a rational exponent, we need to understand how roots and exponents are related. The fourth root of a number can be expressed as a rational exponent. The fourth root of a number x can be written as: x1/4 Therefore, the fourth … Read more

To find dz/dt using the chain rule, we first need to understand how z depends on x and y, and how these, in turn, depend on t. Given the function: z = sin(x)cos(y) where x = t and y = 5t, we can define the partial derivatives of z with respect to x and y. … Read more