To simplify the expression 2 ÷ (2 + 5i), we can multiply both the numerator and the denominator by the complex conjugate of the denominator. The complex conjugate of 2 + 5i is 2 – 5i. By doing this, we can eliminate the imaginary part from the denominator: 2 2 – 5i —– × ———– … Read more
To solve the quadratic equation x² – 7x – 12 = 0 using the zero product property, follow these steps: Rearrange the equation in standard form: The equation is already in standard form, which is ax² + bx + c = 0, where a = 1, b = -7, and c = -12. Factor the … Read more
To convert the Cartesian equation x² + y² = 2cx into its polar form, we start by recalling the relationships between Cartesian and polar coordinates. In polar coordinates, x and y are expressed as: x = r * cos(θ) y = r * sin(θ) Where r is the radial distance from the origin and θ … Read more
To find the possible values of n in the quadratic equation 2n² + 7n + 6 = 0, we can use the quadratic formula: n = (-b ± √(b² – 4ac)) / 2a In this equation, a is the coefficient of n² (which is 2), b is the coefficient of n (which is 7), and … Read more
The vertex of a quadratic function in the form of g(x) = ax² + bx + c can be found using the vertex formula. For the given function g(x) = 8x² – 64x + 128, we identify the coefficients: a = 8, b = -64, and c = 128. The x-coordinate of the vertex is … Read more
Factoring the Expression by Grouping To factor the polynomial expression x³ + 4x² + 7x + 28 by grouping, we can follow these steps: Step 1: Group the Terms We start by dividing the polynomial into two groups: (x³ + 4x²) + (7x + 28) Step 2: Factor Out the Common Factors Next, we factor … Read more
To find the height of the airplane above the atoll, we can use some basic trigonometry. In this scenario, we form a right triangle where: The angle of depression is 5 degrees. The horizontal distance to the atoll (adjacent side) is 4629 meters. The height of the airplane (opposite side) is what we want to … Read more
In circle E, angle G is defined as a circumscribed angle that intercepts the major arc FD, which measures 280 degrees. This situation presents an interesting geometrical concept where the position of angle G relative to the circle and the arc significantly influences its measurement. A circumscribed angle is one that is formed outside the … Read more
To write the equation of a line in slope-intercept form, we can use the formula: y = mx + b Where: y is the dependent variable (the value we’re trying to find). m is the slope of the line. x is the independent variable. b is the y-intercept (the point where the line crosses the … Read more
A rough drawing that is drawn without a scale is commonly referred to as a sketch. Sketches serve as preliminary drawings that capture ideas or concepts quickly without the precise measurements that would be found in technical drawings. These sketches can vary widely in their purpose and form, from artistic expressions to practical representations in … Read more