When reflecting a point across the x-axis, we only change the sign of the y-coordinate. The x-coordinate remains the same. For the point (1, 6): The x-coordinate is 1. The y-coordinate is 6. After reflection, it becomes -6. Thus, the new coordinates after reflection across the x-axis will be: (1, -6) So, the coordinates of … Read more
Finding the x-coordinates of the solutions To solve for the x-coordinates of the solutions to the system of equations given by: x² + y² = 36 y = x + 6 we can substitute the second equation into the first. Here are the steps: Start with the first equation: x² + y² = 36. Next, … Read more
To find the equation of a line that is perpendicular to the given line and passes through the specified point, follow these steps: Step 1: Determine the slope of the original line The given line’s equation is in the slope-intercept form: y = mx + b, where m is the slope. Here, the slope of … Read more
The conjugate of a complex number is obtained by changing the sign of its imaginary part. A complex number is typically written in the form a + bi, where a is the real part and b is the imaginary part. For the complex number 6 + 7i, the real part is 6 and the imaginary … Read more
The axis of symmetry for a quadratic function is a vertical line that runs through the vertex of the parabola represented by the equation. For the general form of a quadratic equation, y = ax² + bx + c, the axis of symmetry can be found using the formula: x = - rac{b}{2a} In your case, … Read more
To determine the value of g(f(2x)), we start with the definitions of the functions given: Function f(x) = 4×2 Function g(x) = 5x We will first calculate f(2x): f(2x) = 4(2x)2 = 4(4×2) = 16×2 Next, we take this result and substitute it into the function g(x): g(f(2x)) = g(16×2) = 5(16×2) = 80×2 Therefore, … Read more
The quadratic equation you’re looking at is given by: 0x² + 6x + 8 = 0 However, it’s important to point out that the term ‘0x²’ essentially means that the equation is not a quadratic equation in the conventional sense, as any expression multiplied by zero yields zero, which leads us to focus on the … Read more
To convert grams and milligrams to kilograms, we need to remember the following unit conversions: 1 kilogram (kg) = 1,000 grams (g) 1 kilogram (kg) = 1,000,000 milligrams (mg) Now, let’s break down the conversion: 1. **Convert grams to kilograms:** 87 grams = 87 / 1,000 = 0.087 kilograms. 2. **Convert milligrams … Read more
The slope of the line tangent to the graph of a function at a given point is determined by the derivative of that function evaluated at that point. In this case, we want to find the slope of the tangent line to the graph of y = ln(1 + x) at x = 1. To … Read more
The equation for the line of reflection that maps a trapezoid onto itself involves understanding the geometric properties of trapezoids and the concept of symmetry. In geometry, a trapezoid has at least one pair of parallel sides, which we will refer to as bases. To find the line of reflection for a trapezoid, follow these … Read more