devyy To solve the system of equations using elimination, we start by stating the equations clearly: Equation 1: 3x + 4y = 9 Equation 2: 3x + 2y = 9 The goal of the elimination method is to eliminate one of the variables, allowing us to solve for the other. In this case, we can eliminate … Read more
Finding the Linearization of the Function To find the linearization of a function at a given point, we need to use the formula for the linearization, which is given by: L(x) = f(a) + f'(a)(x – a) In this case, we will find the linearization L(x) of the function f(x) = x^4 + 5x + … Read more
The variance of a binomial distribution can be calculated using the formula: Variance (σ²) = n * p * (1 – p) In this formula: n represents the number of trials, p is the probability of success on each trial, and (1 – p) is the probability of failure. For this particular case, you have: … Read more
The transition from the graph of y = 2x² to the graph of y = 2x² + 5 can best be described as a vertical shift upwards by 5 units. To understand this, let’s break down the equation: The original graph, y = 2x², is a standard parabola that opens upwards with its vertex located … Read more
In a right triangle, the sine of an angle is defined as the ratio of the length of the opposite side to the length of the hypotenuse. If we have an acute angle θ such that sin(θ) = 6/7, we can use this relationship to find the value of cotangent (cot) for the angle. The … Read more
To find the perimeter of an equilateral triangle when given the altitude, we need to follow a few mathematical steps. An equilateral triangle has all three sides of equal length, and the altitude creates two 30-60-90 right triangles. This property of the triangle can be used to find the side length. In a 30-60-90 triangle, … Read more
To find two positive numbers that meet the criteria of their sum being 100 when the first number is added to twice the second number, as well as maximizing their product, we can use a bit of algebra and calculus. Let’s denote the first number as x and the second number as y. According to … Read more
Finding five rational numbers between any two numbers, such as 1 and 2, is quite simple. A rational number is any number that can be expressed as a fraction where both the numerator and denominator are integers, and the denominator is not zero. Here’s a step-by-step guide to help you find five rational numbers between … Read more
To determine cos(8) given that sin(8) = 21/29, we will utilize the Pythagorean identity: sin2(θ) + cos2(θ) = 1 This identity states that for any angle θ, the square of the sine of the angle plus the square of the cosine of that same angle is equal to 1. Now, let’s calculate: sin2(8) = (21/29)2 … Read more
To find the quotient of the expression (64y³) / (20y²) / (28y) / (4y), we can start by simplifying the expression step by step. Step 1: Simplify 64y³ / 20y² First, we divide the numerical coefficients and the variables separately: Numerical part: 64 / 20 simplifies to 16 / 5 by dividing both numerator and … Read more