Mathematics Questions

Short Answer To find how many **1/2 cup** measurements equal **3/4 cup**, set up the equation **1/2 x n = 3/4**. Solving for **n** gives **1.5**, meaning you need **1 and 1/2** of the **1/2 cup** measurements to reach **3/4 cup**. Step 1: Understanding the Requirement To determine how many times you need a 1/2 […]

Short Answer Weight is a scalar quantity measured in various units, including kilograms, pounds, and stones. To convert 50 kilograms, it equates to approximately 110.231 pounds and 7.8767 stones. Step 1: Understand Weight and Its Units Weight is a scalar quantity that measures the amount of matter in an object and can be expressed in

Short Answer The problem involves evaluating trigonometric expressions for three pairs of angles (A) and (B). Using the cosine difference identity, ( cos(A-B) ) was calculated for each pair, showing values of approximately 0.866, 0.5, and 0, respectively, while ( cos A – cos B ) provided results of approximately -0.366, -0.985, and 0, confirming

Short Answer To find the equation of a linear function using two points, first identify their coordinates (e.g., (0, 2) and (2, 0)). Then, use the slope formula to derive the equation, which simplifies to y + 2 = -x + 4. Step 1: Identify the Points To find the equation of a linear function,

Short Answer The solution involves identifying a pattern based on the product of the digits of the numbers provided. By calculating the product for each number, we find that for 2353, the product of its digits is 90. Step 1: Identify the Pattern To solve the puzzle, we need to analyze the numbers and their

Short Answer The factor (x + 2b) is found only in Option D: 3x² + 39x + 18b after performing synthetic division on all options. Therefore, the correct polynomial is Option D. Step 1: Select the Polynomials We need to check four polynomials to see if (x + 2b) is a factor: Step 2: Perform

Short Answer To convert grams to tablespoons, it’s essential to understand density, as it varies among substances. For general conversions, assuming a density similar to water, 50 grams equals approximately 3.33 tablespoons, but for other substances, using conversion tools or charts is recommended for accuracy. Step 1: Understand Density To convert grams to tablespoons effectively,

Short Answer The expression is simplified by first combining like terms, resulting in 5x¬≤ for the x¬≤ terms, 12x for the x terms, and -7 for the constant terms. Finally, presenting the result yields the simplified expression: 5x¬≤ + 12x Р7. Step 1: Identify and Combine Like Terms To solve the expression, first, identify

Short Answer The explanation covers the concept of multiplication as repeated addition, using an example involving houses, cats, mice, ears of corn, and sacks of grain. It details the calculations leading to a total of 19,607 items derived from successively multiplying and adding individual counts. Step 1: Understanding Multiplication Multiplication is a fundamental mathematical operation

Short Answer A year is approximately 365.24 days, rounded to 365 days for calendar purposes, translating into about 52.14 weeks, with each year containing 52 full weeks plus 1 or 2 extra days. To organize this into a calendar, months are structured with varying lengths (30 or 31 days) and February is adjusted to 28