The slope of the line tangent to the graph of a function at a given point is determined by the derivative of that function evaluated at that point. In this case, we want to find the slope of the tangent line to the graph of y = ln(1 + x) at x = 1. To … Read more
The equation for the line of reflection that maps a trapezoid onto itself involves understanding the geometric properties of trapezoids and the concept of symmetry. In geometry, a trapezoid has at least one pair of parallel sides, which we will refer to as bases. To find the line of reflection for a trapezoid, follow these … Read more
To find the point on the line y = 5x + 4 that is closest to the origin (0, 0), we can use the concept of distance. The distance D from any point (x, y) to the origin can be calculated using the distance formula: D = √(x² + y²) However, since our line is … Read more
To express a number as the sum of three odd primes, we start by identifying odd prime numbers that can be combined to reach the target number. Below, we break down how to achieve this for each of the specified numbers: 1. Expressing 21 as the sum of three odd primes: 7 + 7 + … Read more
To find the quotient of the polynomial 3x² + 17x + 10 when it is divided by 5, we will perform polynomial division. First, let’s rewrite the polynomial: 3x² is the term of degree 2. 17x is the term of degree 1. 10 is the constant term. Next, we will divide each term of the … Read more
To find out how many whole numbers are between 31 and 73, we start by identifying the two numbers we are interested in. Whole numbers are the set of non-negative integers, which include zero but exclude fractions and decimals. When we talk about whole numbers between two numbers, we want to look at all the … Read more
Finding the Value of x To solve the equation 92x + 9x = 18, we will first combine like terms on the left side of the equation. 1. **Combine Like Terms**: We have: 92x + 9x = 101x So the equation simplifies to: 101x = 18 2. **Isolate x**: To isolate x, we need to … Read more
The algebraic expression 3x + 7 – 10 can be simplified and interpreted in various ways. First, let’s combine the constant terms: 1. Simplifying the expression: Start with: 3x + 7 – 10 Combine the constants: 7 – 10 = -3 This simplifies to: 3x – 3 This expression can represent different phrases depending on … Read more
The function f(x) = x² + 3 is a quadratic function, where the term x² indicates that it is a parabola. Let’s explore how to find its range step by step. 1. **Understand the Parabola’s Shape**: The graph of the function is a parabola that opens upwards because the coefficient of x² is positive. 2. … Read more