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To find the equation of the line that passes through the points (6, 3) and (4, 9), we can follow these steps: Find the slope (m): The slope of a line passing through two points (x1, y1) and (x2, y2) is calculated with the formula: m = (y2 – y1) / (x2 – x1) Using … Read more

To find the value of DG in triangle DEF, we need to first evaluate the expression for DG given that CG is equal to 5 units. The expression provided for DG is 3x + 2. Since the question revolves around finding DG, we need to understand if there is any additional information connecting CG and … Read more

Let the number of days taken by B to finish the work alone be denoted as x. Therefore, the number of days taken by A to finish the work alone will be x – 6 (since A takes 6 days less than B). When A and B work together, their combined work rate can be … Read more

Verifying the Identity To verify the identity cos(x) * cos(y) + cos(x) * cos(y) – 2 * sin(x) * sin(y), we first need to simplify the expression. 1. Start with the left-hand side: cos(x) * cos(y) + cos(x) * cos(y) 2. Combine like terms: 2 * cos(x) * cos(y) 3. Now, we have: 2 * … Read more

The terms sequence and series are fundamental concepts in mathematics, particularly in the study of numbers and functions. While they may seem similar at first glance, they refer to different ideas. A sequence is an ordered list of numbers, typically following a specific rule or pattern. For example, the sequence of natural numbers can be … Read more

To determine whether a polynomial is a difference of two squares, you can use the mathematical identity: a² – b² = (a – b)(a + b) In this case, a² represents the first term, and b² represents the second term. A polynomial can be classified as a difference of two squares if it can be … Read more

To understand the relationship between angles QPR and QOR, we first need to establish how these angles are positioned relative to each other. Angle QPR is given as 80 degrees. Assuming that points Q, P, R, and O are arranged in a specific geometric configuration, we can explore the measure of angle QOR. There are … Read more

To find f(g(4)), we need to first evaluate g(4) using the function g(x) = 3x + 7. Let’s break down the steps: Calculate g(4): Substitute 4 into the function g: g(4) = 3(4) + 7 g(4) = 12 + 7 g(4) = 19 Now calculate f(g(4)) or f(19): Substitute 19 into the function f: f(19) … Read more

To find out how many fish can fit into a fish tank, you can use the formula: Number of Fish = Volume of Tank × Density of Fish In this case, the volume of the fish tank is 30 cubic feet and the density of fish is 0.3 fish per cubic foot. Let’s calculate: Number … Read more

To find the value of the integral ∫ 2cos(x) * 2cos(x^2) dx from 0 to 2, we start by rewriting the integral in a more manageable form: ∫ 2cos(x) * 2cos(x^2) dx = 4∫ cos(x) cos(x^2) dx. We can apply the product-to-sum formulas from trigonometry to simplify the product of cosines: cos(A)cos(B) = 1/2[cos(A-B) + … Read more