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To find the area of the surface of the part of the plane defined by the equation 2xy + 3z = 1 that lies within the cylinder described by x^2 + y^2 = 3, we can follow these steps: Rearranging the Plane Equation: First, we need to express the plane equation in terms of z, … Read more

Josie’s new mirror, with its five sides, is classified as a pentagon. In geometry, a pentagon is a five-sided polygon, and it can have various forms. When visualizing a pentagonal mirror, it could either be: Regular Pentagon: All sides and angles are equal, giving it a symmetrical appearance. Irregular Pentagon: The sides and angles are … Read more

To find the slope of the line given by the equation 6x + 8y = 12, we first need to get it into the slope-intercept form, which is y = mx + b, where m stands for the slope and b represents the y-intercept. Here’s a step-by-step guide: Start with the original equation: 6x + … Read more

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