Given the function f(x) = 2x + 8, find x if f(x) = 12
To find x when f(x) = 12, we start with the function definition: f(x) = 2x + 8 Now we set f(x) equal to 12: 2x + 8 = 12 Next, we will solve for x: Subtract 8 from both sides: 2x + 8 – 8 = 12 – 8 2x = 4 Now, divide […]
How do you find an equation of the plane through the points (2, 1, 2), (3, 8, 6), and (2, 3, 1)?
To find the equation of a plane given three points, we can use the formula derived from the determinant of three vectors formed by these points. 1. **Identify the points**: Let the points be A(2, 1, 2), B(3, 8, 6), C(2, 3, 1). 2. **Form vectors**: Create two vectors from these points: AB = B […]
If x varies inversely with y and x is 4 when y is 8, find x when y is 16?
To solve this problem, we start by understanding that if x varies inversely with y, it can be represented mathematically as: x = k / y where k is a constant. We need to find the value of k first, using the initial conditions provided. Given that x = 4 when y = 8, we […]
Which factors are not included in the prime factorization of a composite number?
In the prime factorization of a composite number, the only factors included are prime numbers. By definition, a composite number is a whole number greater than one that is not prime, meaning it has more than two distinct positive divisors: 1 and itself. For example, let’s take the composite number 12. The prime factorization of […]
Determine Whether the Function is Linear or Nonlinear – If Linear, Determine the Slope
To determine if a function is linear, we can analyze its equation. A linear function can be expressed in the form y = mx + b, where m represents the slope and b is the y-intercept. A key characteristic of linear functions is that they graph as straight lines. In contrast, nonlinear functions do not […]
Which of the following represents the zeros of f(x) = 6x³ + 31x² + 4x – 5?
To determine the zeros of the polynomial function f(x) = 6x³ + 31x² + 4x – 5, we need to find the values of x for which f(x) = 0. This can typically be done through various methods such as factoring, using the Rational Root Theorem, or applying synthetic division if applicable. For a cubic […]
What is the difference between an integer x and 9 if it is 6? Find all possible values of x.
To find the possible values of x, we start by interpreting the statement: the difference between an integer x and 9 is 6. This can be expressed mathematically as: |x – 9| = 6 This absolute value equation implies there are two scenarios to consider: x – 9 = 6 x – 9 = -6 […]
What is the interval notation for the compound inequality x 5?
To express the compound inequality x < 4 or x > 5 in interval notation, we need to break it down into the individual parts. The inequality x < 4 means that x can take any value less than 4. In interval notation, this is represented as (-∞, 4). The parentheses indicate that 4 is […]
If you take out a $1000 loan for college at 7% interest, what is the principal?
The principal of a loan is the original sum of money borrowed before any interest is added. In this case, if you take out a loan for college for $1000, the principal amount is simply $1000. The interest rate of 7% will apply to this amount, which means that over time, you will repay the […]
Find all polar coordinates of point p where p = 9π/5
To find the polar coordinates of the point where the angle is given as θ = 9π/5, we first need to understand the basic concept of polar coordinates. In polar coordinates, a point in a plane is represented by two values: the radius (r) and the angle (θ). The angle 9π/5 is more than 2π […]