How to Tell if a Number is Prime or Composite
To determine if a number is prime or composite, follow these simple steps: Definition Check: A prime number is greater than 1 and has no divisors other than 1 and itself. A composite number is also greater than 1 but has additional divisors. Start with 2: If the number is 2, it’s prime. If it’s […]
What is the vertex of the graph of f(x) = x^3 + 7?
The vertex of the graph of a function describes the point where the function reaches its maximum or minimum value. However, for the given function f(x) = x^3 + 7, we are dealing with a cubic function rather than a quadratic function. In a cubic function, there isn’t a single vertex like there is for […]
Use the Quadratic Formula to Solve the Equation 2x² + 5x + 5 = 0
To solve the quadratic equation 2x² + 5x + 5 = 0 using the quadratic formula, we need to identify the coefficients a, b, and c from the general quadratic form ax² + bx + c = 0. In this case: a = 2 b = 5 c = 5 The quadratic formula is given […]
How to Convert the Equation x² + y² + 8x + 22y + 37 = 0 to Standard Form?
To convert the given equation into standard form, we need to rearrange it and complete the square for both the x and y terms. The equation is: x² + y² + 8x + 22y + 37 = 0 First, let’s move the constant term to the other side: x² + y² + 8x + 22y […]
How to Find the Area of a Regular Hexagon with a 48 Inch Perimeter?
To calculate the area of a regular hexagon when given the perimeter, we first need to break down the steps. 1. **Determine the side length of the hexagon**: A regular hexagon has six equal sides. To find the length of one side, we divide the perimeter by the number of sides. In this case, the […]
What is the likelihood of selecting adults with an IQ over 130 in a sample of 200?
To determine the likelihood of selecting adults with an IQ over 130 from a population where the mean IQ is 112 and the standard deviation is 20, we can use the properties of the normal distribution. The first step is to calculate the z-score for an IQ of 130 using the formula: z = (X […]
How do you solve the equation 2y + 3x + 4y = 20?
To solve the equation 2y + 3x + 4y = 20, we first combine the like terms involving y. 1. Combine like terms: 2y + 4y = 6y So the equation simplifies to: 6y + 3x = 20 2. Next, we can isolate one of the variables. Let’s isolate y. To do this, we can […]
What is the area of a square as a function of its perimeter?
The area A of a square can be expressed as a function of its perimeter P. Let’s explore how. A square’s perimeter is given by the formula: P = 4s where s represents the length of one side of the square. To find the area, we use the formula: A = s2 Now, we can […]
How is the graph of y = 8x² + 1 different from the graph of y = 8x²?
The graph of y = 8x² + 1 is similar to the graph of y = 8x² in that both represent parabolic shapes that open upwards due to the positive coefficient of x². However, there is a key difference between the two graphs regarding their position on the coordinate plane. Specifically, the graph of y […]
If f(x) = 3x + 2 and g(x) = x + 5, what is the value of f(g(8))?
To find the value of f(g(8)), we first need to calculate g(8) and then use that result to find f(g(8)). We start with the function g(x): g(x) = x + 5 Now, we substitute 8 into g(x): g(8) = 8 + 5 = 13 Next, we will use the result from g(8) to find f(g(8)), […]