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To solve the system of equations: 1. Equation 1: y = x^2 – 10x + 11 2. Equation 2: y = x^2 + x – 7 We will set the two equations equal to one another since they both equal y: x^2 – 10x + 11 = x^2 + x – 7 Next, we can … Read more

To find the sum of the expressions 7×6, 10×2, 10, 3×6, 6×3, and 4, we’ll have to calculate each multiplication first: 7 x 6 = 42 10 x 2 = 20 3 x 6 = 18 6 x 3 = 18 Now, we sum these results along with the number 10 and 4: 42 + … Read more

To determine the factors of the expression 3x²y² + 6x² + 12y² + 24 + 6x² + 2y² + 6x² + 4, we first simplify it. Let’s combine like terms: 1. Start with the expression: 3x²y² + 6x² + 12y² + 24 + 6x² + 2y² + 6x² + 4 2. Combine the terms: The … Read more

To find the value of x that makes line rq tangent to circle p at point q, we first need to understand the geometric relationship between the line and the circle. A tangent line to a circle intersects the circle at exactly one point. In this scenario, point q is the point of tangency. The … Read more

To understand the implications of g being an even function and h being an even function of g, let us first define what we mean by an even function. An even function is one that satisfies the condition f(-x) = f(x) for all x in its domain. This symmetry about the y-axis means that the … Read more

To find the quotient of the expression 65y³ ÷ 15y² ÷ 25y ÷ 5y, we can break it down step by step. Step 1: Simplify the expression We can rewrite the expression for clarity. Instead of doing all the divisions at once, let’s start by simplifying: Quotient = 65y³ ÷ 15y² ÷ 25y ÷ 5y … Read more

The factors of a number are the integers that divide that number without leaving a remainder. To find the factors of 32,256, we can start with the prime factorization of the number. First, let’s perform the prime factorization: 32,256 can be expressed as: 32,256 = 2^{8} imes 3^{2} This means that 32,256 is the product … Read more

To analyze the statement regarding the difference between 2 times the square root of 7 and the square root of 28, we need to first express these quantities mathematically: Step 1: Calculate each expression. 2 times the square root of 7 is written as 2√7. The square root of 28 can be simplified: √28 = … Read more

The number 10,90,909 can be expressed in words as ten lakh ninety thousand nine hundred nine. To break it down: 10 lakh: This refers to one million, and is the term used in the Indian numeral system for one hundred thousand. In this case, we have ten times that, which equals one million. 90 thousand: … Read more

To solve for f(4, 35, 14, 2, 17), we first need to understand the function f that relates the inputs to the output given in the problem. It’s important to notice that we have the original value, f(2, 2) = 30, but we need more information about how f behaves or transforms its arguments. Unfortunately, … Read more