To factor the expression x³ + 3x², we first look for common factors in both terms. Both terms have x² as a common factor. We can factor x² out of the expression: x²(x + 3) Thus, the complete factorization of the expression x³ + 3x² is: x²(x + 3) This factorization tells us that if … Read more
To solve the equation 4x – 12 = 0, we need to isolate the variable x. Here are the steps: Add 12 to both sides: This gives us: 4x = 12 Divide both sides by 4: This simplifies to: x = 3 Since we find a single value of x (which is 3) that satisfies … Read more
To evaluate the expression cos(60°) × cos(30°) × sin(60°) × sin(30°), we can start by calculating the trigonometric values for each angle involved. cos(60°): The cosine of 60 degrees is 0.5. cos(30°): The cosine of 30 degrees is approximately 0.866 or \\( rac{ oot{3}}{2}\\). sin(60°): The sine of 60 degrees is approximately 0.866 or \\( rac{ oot{3}}{2}\\). … Read more
Finding the missing sides of a right triangle can be straightforward if you understand the Pythagorean theorem and some basic trigonometric concepts. Here’s a detailed guide on how to do it. 1. Understand the Pythagorean Theorem: In a right triangle, the relationship between the lengths of the sides is given by the Pythagorean theorem, which … Read more
A pint is a unit of volume commonly used in the United States and the United Kingdom, but its measurement slightly differs between these two systems. In the United States, a pint is defined as: 16 fluid ounces 473.176 milliliters In contrast, the UK pint is larger, defined as: 20 fluid ounces 568.261 milliliters This … Read more
To transform the expression x² + 3x into a perfect square trinomial, we follow the steps outlined below: A perfect square trinomial takes the general form of (a + b)², which expands to a² + 2ab + b². In our expression, we have a = x (since it corresponds to x²), and we need to … Read more
To solve the equation x^4 + 3x^2 + 2 = 0 using u substitution, we first transform the equation to make it simpler to work with. We start by letting u = x^2. Consequently, the equation can be rewritten in terms of u: u^2 + 3u + 2 = 0 This is now a standard … Read more
To simplify the expression 6m + 2m + 7 + 3, we will combine like terms. Here are the steps in detail: Identify like terms: In this expression, the terms with ‘m’ are 6m and 2m. The constant terms are 7 and 3. Combine the ‘m’ terms: Add 6m and 2m: 6m + 2m = … Read more
Finding the General Solution of the Differential Equation To solve the second-order differential equation given by: y”” + 4y” = 0 Step 1: Rewrite the Equation We can rewrite this equation by letting y” = z. This transforms the original equation into: z” + 4z = 0 Step 2: Characteristic Equation The next step is … Read more
To determine how far a man has run in an hour and a half at a speed of 8 miles per hour, we can use the formula for distance: Distance = Speed × Time In this case: Speed = 8 miles per hour Time = 1.5 hours (which is equivalent to 1 hour and 30 … Read more