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
The relationship between a semicircle and the diameter of a circle is fundamental to understanding the geometry of circles. A semicircle is defined as half of a circle, and it is formed when you take a diameter of the circle and rotate it around one of the endpoints. This means that the diameter serves as … Read more
A complex number is a number that can be expressed in the form a + bi, where a is the real part, b is the imaginary part, and i is the imaginary unit, which is defined as the square root of -1. The ‘real part’ (a) represents a point on the standard number line, while … Read more
To completely factor the expression 49x² + 81 + 7x + 92 + 7x + 92 + 7x + 97x + 9 + 7x + 9, we first need to simplify it. 1. **Combine like terms**: The expression has several x terms and constant terms that can be combined. Combine the x terms: 7x + … Read more
To solve the quadratic equation x² + 5x + 3 = 0, we can use the quadratic formula, which is given by: x = (-b ± √(b² – 4ac)) / 2a In our equation, the coefficients are: a = 1 (the coefficient of x²) b = 5 (the coefficient of x) c = 3 (the … Read more