The range of which function is 2 infinity: y = 2x, y = 25x, y = 5x^2, or y = 5x^2?
To determine the range of the given functions, let’s analyze them one by one: y = 2x: This is a linear function. As x approaches negative infinity, y will also approach negative infinity, and as x approaches positive infinity, y will approach positive infinity. Thus, the range of y = 2x is all real numbers. […]
Determine whether the function f(x) = 3x^4 is even or odd
To determine whether the function f(x) = 3x^4 is even or odd, we can use the definitions of even and odd functions. A function is considered even if, for every x in the domain of the function, f(-x) = f(x). Conversely, a function is odd if f(-x) = -f(x). Let’s apply these definitions to our […]
What is the length of AC rounded to the nearest tenth?
To determine the length of AC, we first need to have the necessary measurements that relate to the triangle or figure in question. Assuming we are dealing with a right triangle where AC is one of the sides, we would typically use the Pythagorean theorem if we have the lengths of the other two sides. […]
Which is a correct first step in solving the inequality 42x + 15 > 3x?
To solve the inequality 42x + 15 > 3x, the first step is to isolate the variable terms on one side of the inequality. This can be achieved by subtracting 3x from both sides. After performing this action, the inequality will then be: 42x – 3x + 15 > 0 Which simplifies to: 39x + […]
Find the value of two numbers if their sum is 12 and their difference is 4
To find the two numbers, let’s denote them as x and y. We have two equations based on the problem: Equation 1: x + y = 12 Equation 2: x – y = 4 Now, we can solve these equations simultaneously. From Equation 1, we can express y in terms of x: y = 12 […]
The circumference of a circle is 628. What is the area of the circle?
To find the area of a circle when given the circumference, we can use the relationships between the two. The formula for the circumference (C) of a circle is: C = 2πr where r is the radius of the circle. We are given that the circumference is 628: 2πr = 628 Now, we can solve […]
How to Write Each Mixed Number as a Fraction?
To convert a mixed number into a fraction, you need to follow a simple process. A mixed number consists of a whole number and a fraction. Here’s how to do it: Multiply the whole number by the denominator of the fractional part. Add that result to the numerator of the fractional part. Place the sum […]
What are the domain, range, and asymptote of h(x) = 0.5x + 9?
The function h(x) = 0.5x + 9 is a linear function, which means it can be represented with a straight line on a graph. Domain The domain of a function is the set of all possible input values (x-values) for which the function is defined. Since h(x) is a linear function, it is defined for […]
Prove that √2√5 is irrational
To prove that √2√5 is irrational, we can start by simplifying the expression. The product √2√5 can be rewritten as √(2 * 5), which equals √10. Thus, we need to show that √10 is irrational. An irrational number is defined as a number that cannot be expressed as a fraction of two integers. To prove […]
One fifth of a number is 9. Find the number.
To find the number when one fifth of it equals 9, we first represent the unknown number as x. According to the problem, we can set up the equation: 8 = 9 To find x, we will multiply both sides of the equation by 5, since we want to isolate x. x = 9 7; […]