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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

To find the point on the line y = 5x + 4 that is closest to the origin (0, 0), we can use the concept of distance. The distance D from any point (x, y) to the origin can be calculated using the distance formula: D = √(x² + y²) However, since our line is … Read more

To express a number as the sum of three odd primes, we start by identifying odd prime numbers that can be combined to reach the target number. Below, we break down how to achieve this for each of the specified numbers: 1. Expressing 21 as the sum of three odd primes: 7 + 7 + … Read more