Which statements are true about the graph of the function f(x) = 6x^4 – x^2?
The function f(x) = 6×4 – x2 is a polynomial function, and its graph has some important characteristics: Degree and Leading Coefficient: The degree of the polynomial is 4, and the leading coefficient is positive (6). This means that as x approaches positive or negative infinity, the graph will rise towards positive infinity on both […]
If x – 8 is a factor of f(x), which of the following must be true?
When we say that x – 8 is a factor of f(x), we can apply the Factor Theorem, which states that if a polynomial f(x) has a factor of the form x – c, then f(c) = 0. In this case, we have c = 8. This means that if x – 8 is a […]
What is the average rate of change of the function over the interval x = 0 to x = 5, f(x) = 42x + 1?
The average rate of change of a function over a specific interval can be found using the formula: Average Rate of Change = (f(b) – f(a)) / (b – a) In this case, we have the function f(x) = 42x + 1, and we are interested in the interval [0, 5]. Here, a = 0 […]
Suppose g is an even function; is h(fg) always an even function?
To determine whether h(fg) is always an even function given that g is an even function, we first need to understand the definition of an even function. A function f(x) is called even if it satisfies the condition f(-x) = f(x) for all x in its domain. Since g is an even function, we have: […]
What is the solution of the linear quadratic system of equations y = 25x^2 + 3y = x^2?
To solve the system of equations given by y = 25x^2 and y = x^2, we start by setting the two expressions for y equal to each other: 25x^2 = x^2 Next, we can rearrange this equation: 25x^2 – x^2 = 0 24x^2 = 0 Dividing both sides by 24 gives: x^2 = 0 Taking […]
What is the quotient of 65y³, 15y², 25y, and 5y?
To find the quotient of the polynomial terms 65y³, 15y², 25y, and 5y, we need to divide each term by the common factor, which in this case is 5y. Let’s break it down: For the first term, 65y³ divided by 5y is: 65y³ ÷ 5y = (65 ÷ 5)(y³ ÷ y) = 13y² For the […]
Find the area under the standard normal curve between z = 0 and z = 3
To find the area under the standard normal curve between z = 0 and z = 3, we can use the standard normal distribution table, often called the Z-table. This table provides the area (or probability) to the left of a given z-score. First, we look up the z-score of 0 in the Z-table. The […]
How to Calculate the Expression: 7×6 + 10×2 + 10 + 3×6 + 6×3 + 4?
To evaluate the expression 7×6 + 10×2 + 10 + 3×6 + 6×3 + 4, we need to follow the proper order of operations (also known as PEMDAS/BODMAS rules), which stands for Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). Let’s break it down step by step: […]
Classify the following expression by degree and term: x³y + 5xyz
To classify the expression x³y + 5xyz, we first need to break it down into its individual components. 1. **Identifying Terms:** The expression consists of two terms: x³y 5xyz 2. **Degree of Each Term:** The degree of a term is determined by the sum of the exponents of the variables in that term. For the […]
If the smallest angle of rotation for a regular polygon is 18 degrees, how many sides does the polygon have?
To find the number of sides of a regular polygon based on its smallest angle of rotation, we can use the formula for the angle of rotation. The angle of rotation for a regular polygon with n sides is given by: Angle of rotation = 360° / n Given that the smallest angle of rotation […]