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To simplify the expression containing the terms 4w2, 4w, 8, 2w2, 3w, and 6, we first need to group similar terms based on their variables and degrees. The terms can be classified as follows: Quadratic terms (w2): 4w2 and 2w2 Linear terms (w): 4w and 3w Constant terms: 8 and 6 Now, let’s combine each … Read more

To calculate the slope of a line that passes through two points, we use the slope formula: Slope (m) = (y2 – y1) / (x2 – x1) In this case, we have two points: (1, 5) and (4, 1). We can assign: (x1, y1) = (1, 5) (x2, y2) = (4, 1) Now, we can … Read more

Choosing the Correct Graph for the System of Equations To identify the correct graph for the given system of equations, we need to understand each equation and find their graphical representation. Step 1: Rewriting the Equations The two equations are: Equation 1: y = 2x + 1 Equation 2: 3y = x + 4 Equation … Read more

To classify the polynomial 5x⁵ + 2x² + 8, we first need to determine its degree and the number of terms it contains. 1. Number of Terms This polynomial consists of three distinct terms: 5x⁵ 2x² 8 Because it has three terms, we can classify it as a trinomial. 2. Degree The degree of a … Read more

Finding the Zeros of the Function The function you provided is: f(x) = 5x³ + 5x² – 30x To find the zeros of this function, we need to solve for x when f(x) = 0: 5x³ + 5x² – 30x = 0 We can factor out the common term: 5x(x² + x – 6) = … Read more

To determine whether the equation 5x = 3y represents a direct variation, we first need to understand what direct variation means. A direct variation exists when one variable is a constant multiple of another variable. The general form of a direct variation equation is y = kx, where k represents the constant of variation. We … Read more

To solve the system of equations 2xy = 7 and 5xy = 9, we can start by isolating one variable in terms of the other from one of the equations. In this case, both equations involve the product of x and y, so let’s first express y in terms of x from the first equation. … Read more

To find a unit vector that has the same direction as the vector 5i + 9j, we first need to understand what a unit vector is. A unit vector is a vector that has a length (or magnitude) of 1, but points in the same direction as the original vector. Here’s how you can find … Read more

To find the point on the curve y = √x that is closest to the point (3, 0), we will use the concept of distance in coordinate geometry. First, express the distance d from the point (3, 0) to any point (x, y) on the curve. Since y = √x, we can rewrite the distance … Read more

To find the exact length of the curve defined by the function y = ln(1 + x²) over the interval [0, 1.5], we can use the formula for the arc length of a curve in Cartesian coordinates: L = ∫ab √(1 + (dy/dx)²) dx Here, dy/dx is the derivative of the function with respect to … Read more