devyy To find the zeros of the quadratic function f(x) = 16x² + 32x + 9, we need to solve the equation 16x² + 32x + 9 = 0 We can use the quadratic formula, which is given by: x = (-b ± √(b² – 4ac)) / 2a In our case, the coefficients are: a = … Read more
When adding two vectors, their resultant vector’s magnitude can be calculated using the triangle inequality theorem. For two vectors, A and B, the possible range of magnitudes for the resultant vector R can be defined as: |A| – |B| < |R| < |A| + |B|. In this specific case, we have a vector A with … Read more
To determine which equation best represents the data in a scatter plot with a trend line, follow these steps: Visual Analysis: Start by observing the scatter plot. Look for general patterns, clusters, and the direction of the data points. Identify if the trend appears linear, exponential, quadratic, etc. Choose Candidate Equations: Based on your visual … Read more
The least natural number that is divisible by three different prime numbers can be calculated by multiplying the smallest three prime numbers. The three smallest primes are: 2 3 5 To find the least natural number: Least number = 2 × 3 × 5 Now let’s do the multiplication: First, multiply 2 and 3: 2 … Read more
A recursive formula defines a sequence of numbers in terms of its preceding terms. To determine the recursive formula for a specific sequence, you first need to identify the pattern or relationship between the elements of the sequence. For example, let’s consider the Fibonacci sequence, which starts with 0 and 1. The recursive formula is … Read more
The Pythagorean Theorem is a fundamental principle in geometry that establishes a special relationship between the sides of a right triangle. It states that: a² + b² = c² In this formula: a and b represent the lengths of the two legs (the sides that form the right angle) of the triangle. c represents the … Read more
To calculate the number of fish that can fit in a fish tank, you can use the formula: Number of Fish = Volume of Tank × Density In this case, the volume of the fish tank is 40 cubic feet, and the density is 0.4 fish per cubic foot. Plugging in these values, we get: … Read more
To find the value of q in the equation q³ = 64, we need to perform a specific calculation known as taking the cube root of both sides of the equation. Here’s how you can do it step by step: Start with the original equation: q³ = 64 Take the cube root: The cube root … Read more
To solve this problem, we need to first understand the properties of unit vectors and the geometric arrangement they form. A unit vector is defined as a vector with a magnitude of 1. When we have three unit vectors forming an equilateral triangle, there are specific relationships between these vectors that we can use. Step … Read more
To solve the equations 5x + 6y = 38 and 3x + 4y = 0, we can use the method of substitution or elimination. Here, I will demonstrate the elimination method: Step 1: Align the Equations Write the two equations one below the other: Equation 1: 5x + 6y = 38 Equation 2: 3x + … Read more