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To solve the system of equations using the substitution method, we will follow these steps: Identify the equations: Equation 1: 3x + 5y = 3 Equation 2: x + 2y = 0 Rearrange one of the equations to express one variable in terms of the other: From Equation 2, we can solve for x: x … Read more

To determine how many solutions exist for the system of equations: 1. First equation: 2x + 6y = 5 2. Second equation: x + 3y = 2 we can use substitution or elimination methods to analyze it. Step 1: Solve the second equation for x Rearranging the second equation gives us: x = 2 – … Read more

The problem involves calculating the acceleration of a bus that slows down from an initial speed to a lower speed over a specific time frame. Let’s break this down step by step. 1. **Identify Initial and Final Velocities**: The initial speed (u) of the bus is 80 kilometers per hour (km/h), and the final speed … Read more

To find the equation of a plane given three points, we can use the vector method. The points given are: Point A: (0, 5, 5) Point B: (5, 0, 5) Point C: (5, 5, 0) First, we can find two vectors that lie on the plane. We can create these vectors by subtracting the coordinates … Read more

To find the difference between the given polynomials, we first need to simplify each expression individually. 1. **First Polynomial**: 5x³ + 4x² + 6x² + 2x + 9 Combine like terms: 4x² + 6x² = 10x² This gives us: 5x³ + 10x² + 2x + 9 2. **Second Polynomial**: x³ + 6x² + 9 + … Read more

To find the value of x in the equation 8 = 4x + 2x + 4, we will follow a series of algebraic steps. Step 1: Simplify the equation Start by combining the like terms on the right side of the equation. The terms 4x and 2x can be added together: 4x + 2x equals … Read more

The end behavior of a polynomial function refers to how the graph behaves as the input (or ‘x’ value) approaches positive and negative infinity. For the polynomial function y = 10×9 – 4x, we can analyze its end behavior by considering the leading term, which is the term with the highest power of ‘x’. In … Read more

Finding the Midpoint of a Line Segment The midpoint of a line segment is the point that is exactly halfway between the two endpoints. To find the midpoint between the endpoints (7, 5) and (7, 11), we use the midpoint formula. Midpoint Formula The formula to calculate the midpoint M of a line segment with … Read more

To find the image vertices for a dilation centered at the origin (0, 0) with a scale factor of 4, you’ll follow a straightforward process. A dilation transformation involves enlarging or reducing the size of a shape based on a given center point and scale factor. In this case, our center is the origin and … Read more