To find the area of the portion of the plane defined by the equation 3x + 2y + z = 6 that lies in the first octant, we will follow these steps: Identify intercepts: The first octant is where all coordinates (x, y, z) are non-negative. To find where this plane intercepts the axes, we … Read more
To solve the inequality 43 > 5x + 6x + 9, the first step is to combine the like terms on the right side of the inequality. The terms 5x and 6x can be added together, which gives: 5x + 6x = 11x This simplifies the inequality to: 43 > 11x + 9 Next, to … Read more
In a 45-45-90 triangle, the legs are of equal length, and the relationship between the lengths of the legs and the hypotenuse is defined by the Pythagorean theorem. Specifically, in a 45-45-90 triangle, the hypotenuse is equal to the length of a leg multiplied by the square root of 2. Since both legs measure 12 … Read more
The conjugate of a complex number is found by changing the sign of its imaginary part. For the complex number 7 + 2i, the conjugate is calculated as follows: Identify the real part: 7 Identify the imaginary part: 2i To find the conjugate, simply change the sign of the imaginary part: Complex Number Conjugate 7 … Read more
The cumulative standardized normal distribution is a function that gives you the probability that a standard normal random variable is less than or equal to a given z-value. In this case, we are looking for the value of z for which the cumulative distribution function (CDF) equals 0.8770. To find this z-value, you can use … Read more
To solve for the measure of wut, we start with the expressions provided: mvuw = 4x mwut = 6x + 10 First, we need to recognize the relationships and variables in the problem. Here, mvuw and mwut may represent measures of angles or segments, depending on the context, but they can also be viewed as … Read more
To solve this problem, we need to set up some equations based on the information provided. Let’s denote Amy’s current age as A and Sam’s current age as S. According to the problem, we know two key pieces of information: Sam is 4 years younger than Amy: S = A – 4 Five years ago, … Read more
A line segment that passes through the center of a circle is referred to as a diameter. The diameter is a significant feature of circles, as it represents the longest possible chord of the circle. It measures the distance across the circle, connecting two points on its circumference while passing through the center. Essentially, the … Read more
Understanding the Translation of the Function The original function given is y = 4x. To translate this function with respect to the given asymptotes at x = 7 and y = 6, we first need to understand what translating a function means. Translating a function involves shifting it horizontally and/or vertically without changing its shape. … Read more
Finding the factors of the polynomial x³ + 5x² + 6x – 30 can be achieved through a method known as grouping. This technique involves rearranging and grouping terms in such a way that we can factor out common elements. Step 1: Group the Terms First, we will split the polynomial into two groups. We … Read more