Which functions have an axis of symmetry of x = 2? Check all that apply.
The functions that have an axis of symmetry at x = 2 will reflect symmetrically across the line x = 2. To determine which functions meet this criterion, we can consider several types: Quadratic functions: A general quadratic function is in the form of f(x) = a(x-h)^2 + k, where (h, k) is the vertex. […]
What is the product of the radical expression 7 sqrt 28 sqrt 2?
The product of the radical expression 7 √28 √2 can be simplified step by step. First, we start by simplifying each radical in the expression: √28 can be simplified because 28 = 4 × 7, and √4 = 2. So, √28 = √(4 × 7) = √4 × √7 = 2√7. We don’t need to […]
If the area of the rectangle is 500 square centimeters, what is the length of the rectangle?
To find the length of a rectangle when you know the area, you also need to know the width, because the formula for the area of a rectangle is: Area = Length × Width In this case, we know the area is 500 square centimeters. So, we can rearrange the formula to find the length: […]
Line AB Contains Points A(4, 5) and B(9, 7) What is the Slope of AB?
To find the slope of line AB that connects the points A(4, 5) and B(9, 7), we can use the slope formula, which is given by: m = (y2 – y1) / (x2 – x1) Here, (x1, y1) is point A and (x2, y2) is point B. Substituting the coordinates: m = (7 – 5) […]
Find an equation of the tangent line to the curve at the given point y = √x at point (36, 6)
To find the equation of the tangent line to the curve y = √x at the point (36, 6), we will follow these steps: Calculate the derivative: The derivative of the function gives us the slope of the tangent line. The function is y = √x, which can also be written as y = x^(1/2). […]
Must the Difference Between Two Rational Numbers Be a Rational Number?
Yes, the difference between two rational numbers is always a rational number. To understand why, let’s first define what rational numbers are. A rational number is any number that can be expressed as the quotient or fraction of two integers, where the denominator is not zero. For example, numbers like 1/2, -3/4, and 5 are […]
What is the solution of the system of equations x + 2y = 7 and x + 2y = 1?
To solve the system of equations, we start by writing down the two equations: x + 2y = 7 x + 2y = 1 If we look closely at these two equations, we can see that they both have the same left-hand side: x + 2y. This means that both equations are representing the same […]
Given f(x) = x² – 12x + 26, how do you write the quadratic function in vertex form?
To rewrite the quadratic function f(x) = x² – 12x + 26 in vertex form, we first need to complete the square. 1. Start with the original equation: f(x) = x² – 12x + 26 2. Focus on the x² – 12x part. To complete the square, take the coefficient of x (which is -12), […]
How many variable terms are in the expression 3x^3y + 5x^2y + 9?
In the expression 3x3y + 5x2y + 9, we are looking for the number of variable terms. A variable term is defined as a term that includes at least one variable. In this expression, we have three terms: 3x3y, 5x2y, and 9. – The first term, 3x3y, contains the variables x and y. – The […]
Find the value of x if necessary round your answer to the nearest tenth
To find the value of x, we need a specific equation or context. However, I can provide you with a general method for solving for x in various types of equations. For example, if we have a simple linear equation like: 2x + 5 = 15 Here’s how you solve it: First, subtract 5 from […]