The conjugate of a complex number is obtained by changing the sign of the imaginary part. Given the complex number 6 + 7i, the conjugate can be expressed as follows: Original Complex Number: 6 + 7i Conjugate: 6 – 7i Thus, the conjugate of the complex number 6 + 7i is 6 – 7i.
To convert the quadratic function f(x) = x2 + 3x + 2 into vertex form, we will complete the square. The vertex form of a quadratic equation is given as: f(x) = a(x – h)2 + k, where (h, k) is the vertex of the parabola. Here are the steps to convert our function: Start … Read more
To determine the measure of arc EF in circle H, we need to gather some information regarding the circle’s radius, center, and the angles that create arc EF. Generally, the measure of an arc is closely related to the central angle that subtends it. First, identify the center of circle H and ensure you understand … Read more
To find a rational number equivalent to 5/7, we can simply multiply both the numerator and the denominator of the fraction by the same non-zero integer. This process will create an equivalent fraction because it maintains the same ratio. For example, if we multiply both the numerator (5) and the denominator (7) by 2, we … Read more
The property of real numbers demonstrated in the sequence 3, 5, 6, 3, 5, 6 is known as the Identity Property of Addition. This property states that when you add a number to zero, the result is the original number. However, in this context, the focus is not solely on the addition of zero but … Read more
The smallest two-digit composite number is 10
Understanding the Difference Between Two Polynomials When comparing two polynomials, we need to perform subtraction to find the difference between them. In this case, we are looking at: Polynomial A: 9x² + 8x Polynomial B: 2x² + 3x Step-by-Step Subtraction The difference can be calculated as: (9x² + 8x) – (2x² + 3x) Distributing the … Read more
Transformations from f(x) to g(x) The graphs of the two functions, f(x) = 7x² and g(x) = 35x² + 5, can be understood in terms of several key transformations: 1. Vertical Stretch The first transformation involves a vertical stretch of the graph. The coefficient of x² in f(x) is 7, while in g(x) it is … Read more
To determine the value of x for the triangle with sides 3x, 5x, and 12 (assuming there’s a typo in the original question about sides that can also be interpreted as x and 20), we need to satisfy the condition for the triangle to be isosceles. An isosceles triangle has at least two sides that … Read more