What are the real and imaginary parts of the complex number 6 + 2i?
A complex number is generally expressed in the form a + bi, where a represents the real part and b represents the imaginary part. In the case of the complex number 6 + 2i, we can identify the real and imaginary parts as follows: Real Part: 6 Imaginary Part: 2 Therefore, for the complex number […]
If x^2 then x^2 + 6x + 4?
To solve the expression x2 + 6x + 4, we start by recognizing that we are dealing with a quadratic equation in the standard form of ax2 + bx + c, where a = 1, b = 6, and c = 4. Next, we can examine this equation to check if it can be factored […]
How do you graph f(x) = x² + 4x + 5?
Graphing the function f(x) = x² + 4x + 5 involves a few steps to understand its shape and position. 1. Identify the type of function: This is a quadratic function, which means its graph will be a parabola. Since the coefficient of x² is positive, the parabola opens upwards. 2. Find the vertex: To […]
How do you find the vertex of the parabola defined by the equation y = x² + 8x + 12?
To find the vertex of the parabola given by the equation y = x² + 8x + 12, we can use the formula for the vertex of a quadratic equation in the standard form y = ax² + bx + c. The x-coordinate of the vertex can be found using the formula: x = -b […]
How to Find Domain and Range of a Square Root Function
To find the domain and range of a square root function, we first need to understand the general form of the function, which is usually expressed as f(x) = √(x – k), where k is a constant. Finding the Domain: The domain of a square root function consists of all the values of x for […]
How to Find the Distance Between a Point and a Line
To find the distance between a point and a line, you can use a straightforward formula that involves both the coordinates of the point and the equation of the line. Suppose you have a line represented by the equation Ax + By + C = 0 and a point with coordinates (x0, y0). The distance […]
What is the solution to the equation 9x + 1 = 27?
To solve the equation 9x + 1 = 27, we need to isolate the variable x. First, we can subtract 1 from both sides to get: 9x = 27 – 1 9x = 26 Next, we divide both sides by 9 to solve for x: x = 26 / 9 This simplifies to: x = […]
What are the two solutions of x² + 2x – 4 = 3x + 9?
To find the two solutions of the equation x² + 2x – 4 = 3x + 9, we first need to rearrange it into a standard quadratic form. Start by moving all terms to one side: x² + 2x – 4 – 3x – 9 = 0 Combine like terms: x² – x – 13 […]
What is the integral of sin(x) cos(x) from 0 to π/2?
To find the integral of sin(x) cos(x) from 0 to π/2, we can use a simple trigonometric identity. We know that: sin(2x) = 2 sin(x) cos(x) This leads us to rewrite sin(x) cos(x) as: sin(x) cos(x) = (1/2) sin(2x) Now, we can set up the integral: ∫ sin(x) cos(x) dx = ∫ (1/2) sin(2x) dx […]
How to Simplify Square Root of 10 Times Square Root of 8?
To simplify the expression √10 × √8, we can use the property of square roots that states: √a × √b = √(a × b). So, we can rewrite the expression as follows: √10 × √8 = √(10 × 8) Now we can calculate 10 × 8, which equals 80: √(10 × 8) = √80 Next, […]