To graph the function f(x) = x² + 4x + 5, follow these steps: 1. Understand the Function: This is a quadratic function in the form of f(x) = ax² + bx + c, where: a = 1 b = 4 c = 5 Since a > 0, the parabola opens upwards. 2. Find the … Read more
To find the equation of the line that passes through the point (2, 2) and is parallel to the given line y = rac{1}{2}x + 8, we need to follow these steps: Identify the slope: The given line has a slope (m) of rac{1}{2}, as indicated by the coefficient of x in the slope-intercept form … Read more
To evaluate the numbers 10, 43, 2, 5, 12, and 6, we can analyze different characteristics such as their statistical properties, range, mean, mode, and median, as well as their relevance in various contexts. 1. Basic Characteristics Count: There are a total of 6 numbers in the set. Minimum: The smallest number is 2. Maximum: … Read more
To find the radian measure of a central angle in a circle, we can use the relationship between the arc length, the radius, and the angle measured in radians. The formula to calculate the angle in radians (θ) is given by: θ = s / r Where: θ is the angle in radians. s is … Read more
To convert the fraction 7/12 into a decimal, you simply need to perform the division of the numerator (7) by the denominator (12). Here’s how you can do it: Start by dividing 7 by 12. You can use a calculator for precise results, or do it manually. The calculation gives you 0.5833333…, which is a … Read more
Finding HCF and LCM by Prime Factorization To find the Highest Common Factor (HCF) and Lowest Common Multiple (LCM) of the numbers 90 and 144 using the prime factorization method, follow these steps: Step 1: Prime Factorization First, we need to express both numbers as a product of their prime factors. Prime factorization of 90: … Read more
To solve this problem, we can use the concept known as the Birthday Paradox. This paradox demonstrates that in a relatively small group of people, the odds of two individuals having the same birthday can be surprisingly high. The approach involves calculating the probability that no two students share a birthday and then subtracting that … Read more
To determine the value of the discriminant for the quadratic equation in the form: ax² + bx + c = 0 we need to identify the coefficients a, b, and c from the given equation 5x² + 7x + 6 = 0. a: The coefficient of x² is 5. b: The coefficient of x is … Read more
To find the probability of not rolling a 3 on a regular number cube, we can start by looking at how a standard six-sided die works. Each face of the cube has an equal chance of landing face up, and there are a total of 6 faces: 1, 2, 3, 4, 5, and 6. When … Read more
To determine the equivalent system of the given equations, we first need to analyze the equations: 1. Equation 1: 23x + y = 2 2. Equation 2: x + 12y = 3 Next, we will solve these equations to find an equivalent system that may present the same solution set. Step 1: Solve Equation 1 … Read more