To write the equation of a sphere in standard form, you first need to understand what the equation entails. The standard form of the equation of a sphere is given by: (x – h)² + (y – k)² + (z – l)² = r² Here, (h, k, l) represents the coordinates of the center of … Read more
The expression “23 of 24” can be interpreted in a couple of ways depending on the context. Generally, it refers to a proportion or a fraction, specifically, it means 23 out of 24 parts or elements of a whole. In numerical terms, you can represent this as a fraction: 23/24. This means that if you … Read more
Identifying the Triangle Given the side lengths of 6, 8, and 10, we can first determine the type of triangle by applying the Pythagorean theorem, which states: a2 + b2 = c2 In this case, let’s assign: a = 6 b = 8 c = 10 Now, we can calculate: 62 + 82 = 36 … Read more
To express the number 105 as a fraction, we can use its basic definition as a whole number. A whole number can be represented as a fraction by placing it over 1. Therefore, 105 as a fraction is: 105/1 This means that 105 is equal to 105 parts of 1. Fractions are often used to … Read more
Factoring the expression x² + y² can be a bit tricky because it doesn’t factor in the same straightforward way as other algebraic expressions. Unlike expressions that can be easily factored into real-number products, x² + y² does not have real factors when considered over the set of real numbers. However, we can still express … Read more
The expression 14 3 represents a mixed number, which is a whole number combined with a fraction. In this case, 14 3 can be interpreted as 14 + rac{3}{1} or simply 14 with an additional whole part of 3 that exceeds one unit. To convert this expression into a proper mixed number, we begin by … Read more
To find the positive solution to the quadratic equation 0x² + 2x + 1 = 0, we first notice that the term with x² is 0. This means we can simplify the equation to 2x + 1 = 0. Next, we’ll solve for x: Subtract 1 from both sides: 2x = -1 Now, divide by … Read more
To simplify the expression 1sin x, we need to understand the components involved in this mathematical expression. Firstly, the term ‘1’ can be thought of as a coefficient, and multiplying it by sin x gives us a straightforward expression: 1sin x = sin x. Thus, simplifying 1sin x essentially removes the unnecessary multiplication by 1, … Read more
To find out how many standard deviations a specific data point is from the mean in a dataset, you can follow these steps: Calculate the Mean: First, you need to compute the mean (average) of your dataset. To do this, sum all the data points and then divide by the number of points. The formula … Read more
A fortnight is a unit of time that equals 14 consecutive days. The term “fortnight” is derived from the Old English words “feowertyne niht”, which literally means “fourteen nights”. This period is commonly used in various cultures to denote a two-week span, making it a practical measure for scheduling events, planning vacations, or even determining … Read more