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To find out what 5% of 300 is, you can use a simple formula. First, understand that percentages are just a fraction of a whole. In this case, 5% can be expressed as: 5% = 5/100 = 0.05 Next, multiply this decimal by 300: 0.05 x 300 = 15 So, 5% of 300 is 15. … Read more

The distance between two points on the real number line, ‘a’ and ‘b’, is calculated using a simple mathematical formula. This distance, denoted as d(a, b), is found using the absolute difference between the two points. The formula for computing this distance is: d(a, b) = |a – b| Here’s how it works: If ‘a’ … Read more

The given sequence is 2, 4, 6, 8, 10. To find the general term of this sequence, it’s essential to identify the pattern within the numbers. First, observe the numbers: each term increases by a value of 2. This is a clear indication that we are dealing with an arithmetic sequence. In an arithmetic sequence, … Read more

The equation x² – 5x + 5 = 0 is a quadratic equation. To find its solution set, we can use the quadratic formula, which is given by: x = (-b ± √(b² – 4ac)) / 2a In this case, the coefficients are as follows: a = 1 b = -5 c = 5 Next, … Read more

To find out when the traffic lights will change simultaneously again, we need to calculate the least common multiple (LCM) of the three time intervals: 48 seconds, 72 seconds, and 108 seconds. The first step is to determine the prime factorization of each time interval: 48 = 24 × 31 72 = 23 × 32 … Read more

To calculate the perimeter of rhombus WXYZ, you’ll need to know the length of one of its sides. A rhombus, by definition, has four equal sides. Therefore, the formula for calculating the perimeter (P) is: P = 4 × s Where s is the length of one side of the rhombus. For example, if one … Read more

To calculate the perimeter of a parallelogram, we need to add the lengths of all its sides. For a parallelogram, opposite sides are equal in length. This means that if we have a parallelogram WXYZ, we can assume that one set of sides are equal in length. Let’s denote the sides as follows: Side WX … Read more

To find the inverse of the function y = 2×2 + 2, we need to follow several steps: Start with the original function: Write the equation with y on one side: y = 2×2 + 2 Swap y and x: To find the inverse, we interchange x and y in the equation: x = 2y2 … Read more

To express the fractions 12/316 and 7/8 with a least common denominator (LCD), follow these steps: Step 1: Determine the Denominators The denominators of our fractions are 316 and 8. Step 2: Find the Prime Factorization Next, we need to find the prime factorization of each denominator: 316: It can be factored as follows: 316 … Read more

To find the exact length of the polar curve defined by the equation r = e^(3θ), we can use the formula for the arc length of a polar curve. The arc length L from θ = a to θ = b is given by: L = \int_a^b \sqrt{\left(\frac{dr}{dθ}\right)^2 + r^2} \, dθ. In our case, … Read more