For the function f(x) = 8 + 2x², find f(1) and determine whether f(1) is a function.
To find f(1), we will substitute x with 1 in the function f(x) = 8 + 2x². Substituting, we get: f(1) = 8 + 2(1)² This simplifies to: f(1) = 8 + 2(1) = 8 + 2 = 10 So, f(1) = 10. Now, regarding whether f(1) is a function: the notation f(1) refers to […]
What is the solution set of the given system: 2x + y ≥ 4 and 3x + y ≤ 9?
To find the solution set of the inequalities 2x + y ≥ 4 and 3x + y ≤ 9, we need to graph these inequalities and determine the region that satisfies both conditions. 1. **Graphing the first inequality (2x + y ≥ 4)**: Convert to equality: y = -2x + 4 (this is a line […]
What are the values of x in the equation x² + 6x + 9 = 25?
To find the values of x in the equation x² + 6x + 9 = 25, we first need to rearrange the equation. We can start by moving 25 to the left side of the equation: x² + 6x + 9 – 25 = 0 This simplifies to: x² + 6x – 16 = 0 […]
Can a rational number be written as the ratio of one to another and represented by a repeating or terminating decimal?
A rational number is defined as a number that can be expressed as the ratio of two integers, where the numerator is an integer and the denominator is a non-zero integer. This means that any rational number can be written in the form a/b, where a and b are integers and b ≠ 0. Moreover, […]
What is the LCM of 7.56 and 5?
To find the least common multiple (LCM) of 7.56 and 5, we first express the numbers in a form that’s easier to work with. A common approach is to convert the decimal into a fraction. 7.56 can be expressed as 756/100. Next, we can simplify this fraction. Both the numerator and denominator can be divided […]
Prove that 5 is irrational and hence prove that 2√5 is also irrational
To prove that 5 is irrational, we first need to recall the definition of an irrational number. A number is considered irrational if it cannot be expressed as a fraction of two integers, i.e., it cannot be written in the form p/q, where p and q are integers and q ≠ 0. Next, we need […]
Which function below is the inverse of f(x) = x² + 25?
To find the inverse of the function f(x) = x² + 25, we need to follow a few steps. 1. Start by replacing f(x) with y: y = x² + 25 2. Next, swap x and y: x = y² + 25 3. Now, solve for y. Start by isolating y²: y² = x – […]
Which polynomials are listed with their correct additive inverse? Check all that apply.
To determine which polynomials are listed with their correct additive inverses, we need to understand what an additive inverse is. An additive inverse of a polynomial is another polynomial that, when added to the original polynomial, results in zero. For example, if you have a polynomial like P(x) = 3x^2 + 2x + 1, its […]
How do you solve log4y 9 log44 log464?
To solve the expression log4y 9 log44 log464, we need to break it down step by step. Let’s start simplifying each logarithm: 1. **Calculating log44**: We know that logbb = 1 for any base b (in this case, base 4). So, log44 = 1. 2. **Calculating log464**: Since 64 is equal to 4 raised to […]
What is the average arithmetic mean of 8, 7, 7, 5, 3, 2, and 2?
To find the average arithmetic mean of the numbers 8, 7, 7, 5, 3, 2, and 2, you need to follow a simple process. First, you add all the numbers together: 8 + 7 + 7 + 5 + 3 + 2 + 2 = 34 Next, you count how many numbers there are. In […]