devyy In the quadratic function expressed as f(x) = ax² + bx + c, the term a represents the leading coefficient. This coefficient plays a crucial role in determining the shape and direction of the parabola represented by the equation. For the given function f(x) = x² + 8x + 4, we can identify the coefficients … Read more
To find the 7th term in the sequence defined by the formula a_n = 30 + 4n, we need to substitute n with 7. The formula for the nth term can be rewritten specifically for this case: a_7 = 30 + 4(7) Now, let’s calculate: First, calculate the multiplication: 4 x 7 = 28. Next, … Read more
To find the zeros of the quadratic function f(x) = 6x² + 12x – 7, we need to solve the equation f(x) = 0. This leads us to: 6x² + 12x – 7 = 0 We can use the quadratic formula, which is: x = (-b ± √(b² – 4ac)) / (2a) In our quadratic … Read more
To solve for f(g(x)) when x = 1, we will first evaluate g(x) for x = 1 and then substitute that result into f(x). Find g(1): Since the function g(x) = x + 3, we can substitute x with 1: g(1) = 1 + 3 = 4. Now, we substitute g(1) into f(x): The function … Read more
When dealing with a population that has an established mean ( extit{μ}) of 80 and a standard deviation ( extit{σ}) of 7, we can apply concepts of inferential statistics to understand how a sample of 49 observations behaves. First, it’s important to note that when we take a sample from a population, the sample mean … Read more
To express 3 raised to the power of 2, you simply multiply 3 by itself. This is known as exponentiation, where the base is 3 and the exponent is 2. So, you perform the following calculation: 32 = 3 × 3 = 9 Thus, 3 to the power of 2 equals 9. This mathematical expression … Read more
The equation you have is somewhat ambiguous, but if we interpret it as: x * x = 5, or x2 = 5 Then we can find the solution set by solving for x. To solve the equation x2 = 5, we take the square root of both sides: x = ±√5 This means there are … Read more
To find the coordinates of the vertex of the quadratic function given by y = x² + 6x + 11, we can use the vertex formula. The vertex of a parabola described by the equation y = ax² + bx + c can be found at the point (h, k), where: h = -b / … Read more
To find the length of the arc subtended by an angle in a circle, you can use the formula: Arc Length (L) = (θ / 360) * 2 * π * r Where: L = arc length θ = angle in degrees (70 degrees in this case) r = radius of the circle (6 inches) … Read more
Understanding Set Intersection In mathematics, the intersection of two sets refers to the elements that are common to both sets. This is often denoted as A ∩ B. Given Sets Set A: {10, 20, 30, 40, 50, 60} Set B: {10, 40, 60} Finding the Intersection To find the intersection of these two sets, we … Read more