devyy To solve the equation y3 + y9 + y + 1 = y3 + y6 + y9, we first simplify the equation by subtracting similar terms from both sides. Starting with the original equation: y3 + y9 + y + 1 = y3 + y6 + y9 We can subtract y3 and y9 from both … Read more
To find the equation for the nth term of the arithmetic sequence 20, 16, 12, 8, we first identify the common characteristics of the sequence: First Term (a): The first term of the sequence (denoted as a) is 20. Common Difference (d): The common difference (denoted as d) can be calculated by subtracting the second … Read more
To solve the system of equations using the elimination method, we start with the given equations: Equation 1: 2x + 2y = 8 Equation 2: x + 2y = 1 The goal of the elimination method is to manipulate the equations such that one variable can be eliminated when we add or subtract the equations. … Read more
To find the length of each side of a square when the area is known, you can use the following formula: Area = side × side Area = side2 Given that the area of the square is 400 square miles, you can set up the equation: side2 = 400 To find the length of one … Read more
When you add or multiply a non-zero rational number with an irrational number, the result will always be an irrational number. Let’s break down why this is the case. A rational number is any number that can be expressed as the quotient of two integers, where the denominator is not zero. For example, numbers like … Read more
Estimating fractions can be quite helpful in understanding whether a specific answer is reasonable. To estimate 22 out of 78, you can simplify the numbers involved to make mental calculations easier. First, consider rounding the denominator, 78, to the nearest 10. In this case, you can approximate 78 to 80. Now, consider the fraction: Original … Read more
To find the area of a square park when you know its perimeter, you can follow these steps: Understand the relationship between perimeter and side length: The formula for the perimeter P of a square is given by: P = 4 × s Where s is the length of one side of the square. Given … Read more
The expression you’ve provided, ‘if x² then x² + 6x² + 4,’ is somewhat ambiguous but can be interpreted in the context of algebraic manipulation. First, let’s clarify the components of the expression: x²: This is the square of the variable x. 6x²: This term indicates six times the square of x. 4: This is … Read more
To find a quadratic model for the given set of values, we start by denoting the data points as follows: (0, 4) (2, 20) (4, 20) We want to find a quadratic equation of the form: y = ax² + bx + c where a, b, and c are constants we need to determine using … Read more
The area of a circle can be calculated using the formula: A = πr2 where A is the area, π is a constant (approximately 3.14), and r is the radius of the circle. First, we need to determine the radius from the given diameter. The radius is half of the diameter: r = diameter / … Read more