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
The slope of a line is calculated using the formula: Slope (m) = (y2 – y1) / (x2 – x1) For the points (3, 0) and (3, 3), we have: (x1, y1) = (3, 0) (x2, y2) = (3, 3) Plugging these values into the slope formula: m = (3 – 0) / (3 – … Read more
To find the length of a line segment within a circle, you can follow these steps: Method 1: Using the Radius and Central Angle 1. **Identify the Circle’s Attributes**: Begin by noting the radius of the circle (denoted as r) and the central angle (denoted as θ) that subtends the line segment you wish to … Read more
To determine what percentage 15 is of 20, you can use the following formula: Percentage = (Part / Whole) * 100 In this case, the Part is 15, and the Whole is 20. Now, plug the values into the formula: Percentage = (15 / 20) * 100 Next, perform the division: 15 / 20 = … Read more
Finding the value of x in a triangle can involve different methods depending on the information provided and the type of triangle in question. Here are some common approaches: 1. Using the Triangle Sum Theorem One of the fundamental rules of triangles is that the sum of all internal angles must equal 180 degrees. If … Read more