devyy Regrouping in math addition, often referred to as carrying, is a technique used to solve addition problems that involve multi-digit numbers. When the sum of digits in a particular column exceeds 9, regrouping allows us to manage this overflow by carrying over the extra value to the next column on the left. To illustrate regrouping, … Read more
To determine what number 51 is 85% of, we can use a simple mathematical formula. The percentage can be converted to a decimal by dividing it by 100. Therefore, 85% becomes 0.85. We can set up the equation as follows: Let x be the unknown number. Then the equation is: 0.85 * x = 51 … Read more
The expression you’re working with is x² – 25 – 10x. To determine whether this is a difference of two squares, we first need to rearrange and simplify the expression. We can rewrite the expression as: x² – 10x – 25 Next, let’s look for a way to express this polynomial in the form of … Read more
To determine the next number in the series 100, 96, 104, 88, 120, 56, we need to identify a pattern among the numbers. Let’s break down the series step by step: Starting with 100 Subtract 4 to get 96 Add 8 to get 104 Subtract 16 to get 88 Add 32 to get 120 Subtract … Read more
To integrate the function cot2(x)dx, we can use a well-known trigonometric identity and substitution method to simplify our work. Here’s a detailed step-by-step explanation: Recall the identity for cot2(x): cot2(x) = csc2(x) – 1. This is useful because it allows us to express cot2(x) in terms of csc2(x). Using this identity, we rewrite the integral: … Read more
A six-digit number is defined as any integer that falls within the range from 100000 to 999999. These numbers start from 100000 and continue all the way up to 999999, inclusive. To find the total number of six-digit numbers, we can use a simple calculation: The smallest six-digit number is 100000. The largest six-digit number … Read more
Finding Solutions to the Polynomial Equation x³ + 8 = 0 The equation you provided is a cubic polynomial equation: x³ + 8 = 0. To solve this, we can start by rewriting the equation: x³ = -8 Next, we can take the cube root of both sides to find the real solution: x = … Read more
Measuring the height of a tree can be an interesting challenge, but with the principles of trigonometry, it becomes an achievable task. Here’s a step-by-step guide to help you calculate the height of a tree accurately. Materials Needed: A measuring tape or a ruler A protractor or a clinometer (a device to measure angles) A … Read more
To find the roots of the equation f(x) = x² – 48, we need to set the function equal to zero: x² – 48 = 0 Next, we can rearrange this equation to isolate x²: x² = 48 Now, we can find the roots by taking the square root of both sides. Remember that taking … Read more
To solve the equation 2x + 53x + 1 = 0, we first need to combine like terms. The equation simplifies as follows: 2x + 53x = 55x, so the equation becomes: 55x + 1 = 0 Next, we can isolate the variable x by moving the constant term to the other side of the … Read more