Which of the following represents the range of the function f(x) = 4x + 1 for the domain { -5, -1, 0, 2, 10 }?
To find the range of the function f(x) = 4x + 1 for the given domain { -5, -1, 0, 2, 10 }, we need to calculate the function’s output for each value in the domain. For x = -5: f(-5) = 4(-5) + 1 = -20 + 1 = -19 For x = -1: […]
What is the inverse of the function f(x) = x^4 + 12?
To find the inverse of the function f(x) = x4 + 12, we first need to express y in terms of x: Let y = x4 + 12. To find the inverse, we switch x and y: x = y4 + 12 Next, we solve for y: Subtract 12 from both sides: x – 12 […]
How do I find an equation of the tangent line to the curve y = x³ + 2x² at the point (2, 6)?
To find the equation of the tangent line to the curve at a given point, we need to follow these steps: Find the derivative of the function: The first step is to compute the derivative of the function, which gives us the slope of the tangent line at any point on the curve. For the […]
If d is the HCF of 468 and 222, find the value of integers x and y which satisfy the equation 468 = d × x and 222 = d × y.
To find integers x and y such that 468 = d × x and 222 = d × y, we first need to determine the highest common factor (HCF) of the numbers 468 and 222. We can calculate the HCF using the prime factorization method or the Euclidean algorithm. For simplicity, let’s use the Euclidean […]
The length of a long rod is measured first by using pace span and then by using foot span of a person. What is the length of the rod in terms of foot span?
To convert the length of the rod measured in pace spans to foot spans, we start by understanding the relationship between the two measurements. A pace span generally refers to the distance covered in one step of a person, while a foot span is the length of a person’s foot, typically about 12 inches. Let’s […]
How to Find the Diameter of a Circle with the Circumference
To find the diameter of a circle when you have the circumference, you can use the relationship between the circumference (C) and the diameter (D) of a circle. The formula for the circumference of a circle is: C = πD Where π (pi) is a constant approximately equal to 3.14159. To find the diameter from […]
Find the point on the line y = 4x + 5 that is closest to the origin
To find the point on the line y = 4x + 5 that is closest to the origin (0, 0), we can use the method of minimizing the distance from the origin to any point on the line. The distance d from the origin to a point (x, y) on the line can be expressed […]
The square of a number is 12 less than 7 times the number. What is the number?
To find the number, let’s represent it with a variable. We can use x to represent the unknown number. According to the problem, the square of the number can be expressed as x2. The phrase ‘7 times the number’ can be written as 7x. Since the square of the number is 12 less than 7 […]
What is the sum of the arithmetic sequence 3, 9, 15 if there are 26 terms?
The arithmetic sequence starts with the first term (a) as 3 and continues with a common difference (d) of 6 (since 9 – 3 = 6 and 15 – 9 = 6). To find the sum of the first n terms of an arithmetic sequence, we can use the formula: Sn = n/2 * (2a […]
If 9x + 49x + 4 = ax^2 + b, what is the value of a?
To find the value of a, we first need to simplify the left side of the equation. The expression on the left is: 9x + 49x + 4 Combine the like terms: (9x + 49x) + 4 = 58x + 4 Now we have: 58x + 4 = ax^2 + b In order to compare […]