devyy Determining if a Graph is Even or Odd To determine whether a graph is even, odd, or neither, you need to analyze its symmetry properties concerning the y-axis and the origin. Here’s a detailed breakdown: 1. Definitions Even Function: A function is considered even if its graph is symmetric about the y-axis. This means that … Read more
Calculating the Area of a Trapezoid The area of a trapezoid can be calculated using the formula: Area = 1/2 * (b1 + b2) * h b1 = length of the first base b2 = length of the second base h = height of the trapezoid (the perpendicular distance between the bases) Even if the … Read more
To prove that in the obtuse triangle DABC, where angle B is obtuse, the equation AC² + AB² = BC² + 2BC * BD holds, we will utilize the Law of Cosines and properties of obtuse triangles. 1. **Understanding Triangle DABC**: First, let’s identify that since angle B is obtuse, this means that the internal … Read more
To solve the system of equations given by 2x + 5y = 13 and 3x + 4y = 8, we can use either the substitution method or the elimination method. Here, we will use the elimination method to find the values of x and y. Step 1: Align the equations We have the two equations: … Read more
To find the perimeter of a rectangular garden, you can use the formula: Perimeter (P) = 2 × (Length + Width) In this case, we know the width and length of the garden: Width (W) = √13 Length (L) = 7√13 Now, we can substitute these values into the perimeter formula: P = 2 × … Read more
To find and simplify the difference quotient for the function f(x) = x² + 5, we follow these steps: Recall the definition of the difference quotient: The difference quotient is given by the formula: Difference Quotient = \\frac{f(x + h) – f(x)}{h} Calculate f(x + h): We start by substituting x + h into the … Read more
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