Find an equation of the line that passes through the point (2, 3) and is perpendicular to the line 4x – 3y = 10
To find the equation of the line that passes through the point (2, 3) and is perpendicular to the given line, we first need to determine the slope of the given line. The equation of the line is given in standard form: 4x – 3y = 10 To find the slope, we can rewrite this […]
Given the function f(x) = 2x, find the value of f(116)
To find the value of f(116) for the function f(x) = 2x, we will simply substitute x with 116 in the function. Here’s the calculation: f(116) = 2 * 116 = 232 Therefore, the value of f(116) is 232.
What is the sum of the geometric sequence 1, 3, 9 if there are 14 terms?
To find the sum of the geometric sequence where the first three terms are 1, 3, and 9, we first need to identify the first term and the common ratio. Here, the first term (a) is 1 and the common ratio (r) can be calculated by dividing the second term by the first term: r […]
Two complementary angles have measures in the ratio of 1 to 5. Find the measure of each angle.
To find the measures of the two complementary angles that are in the ratio of 1 to 5, we can start by defining the angles in terms of a variable. Let’s say the first angle is represented by x. Since the angles are in the ratio of 1 to 5, we can express the second […]
What are the first four terms of the sequence given by the formula below an 2n 4?
To find the first four terms of the sequence defined by the formula an = 2n + 4, we simply substitute the values of n from 1 to 4 into the formula. 1. For n = 1: a1 = 2(1) + 4 = 2 + 4 = 6 2. For n = 2: a2 = […]
What is the set of prime numbers that are less than 15?
The set of prime numbers that are less than 15 is {2, 3, 5, 7, 11, 13}. In order to understand why these numbers are considered prime, we need to define what a prime number is. A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural […]
What do you understand by the term vector space?
A vector space is a fundamental concept in linear algebra and mathematics as a whole. It is essentially a collection of objects called vectors, which can be added together and multiplied by scalars (numbers). To qualify as a vector space, a set must satisfy certain properties regarding these operations. The key properties include closure under […]
How to Write an Equation in Point-Slope Form for the Line Through the Point (8, 3) with Given Slope?
To write the equation of a line in point-slope form, we use the formula: y – y1 = m(x – x1) Here, m is the slope of the line, and (x1, y1) is a point on the line. In this case, we are given the point (8, 3) and the slope m = 8. Plugging […]
Find Parametric Equations for the Line through (2, 4, 6) that is Perpendicular to the Plane x + y + 3z = 7
To find the parametric equations for the line that passes through the point (2, 4, 6) and is perpendicular to the plane defined by the equation x + y + 3z = 7, we need to determine the direction of the line and then use the point to create the equations. The normal vector of […]
What is the image of e for a dilation with center (0, 0) and a scale factor of 6?
To find the image of the point e under a dilation with center at (0, 0) and a scale factor of 6, we need to apply the dilation formula. The formula for dilation centered at the origin is given by: D(x, y) = (kx, ky) where (x, y) is the original point, k is the […]