devyy To find the roots of the polynomial equation x³ + 2x² + 16x + 32 = 0, we can use various methods such as factoring, synthetic division, or the Rational Root Theorem. Let’s start by trying to find any rational roots using the Rational Root Theorem, which suggests that any rational solution p/q (where p … Read more
Understanding Volumes of Composite Figures A composite space figure, like a rectangular pyramid resting on a rectangular prism, can be analyzed by calculating the volumes of its individual components and then summing them up. To determine the volume of the entire figure, we must first know the dimensions of both the rectangular prism and the … Read more
The function f(x) = x² – 2 is a quadratic function, which is a type of polynomial function that can be represented graphically as a parabola. To determine its range, we should first identify its vertex and behavior as x approaches positive and negative infinity. 1. **Finding the Vertex**: The standard form of a quadratic … Read more
To find the sum of the two complex numbers, we start by identifying the components of each number. The first complex number is 12 + 5i, where 12 is the real part and 5i is the imaginary part. The second complex number is 3 + 4i, with 3 as the real part and 4i as … Read more
To determine how many 45-degree angles it takes to make a full turn, we first need to understand what a full turn actually means. A full turn, or full rotation, is equal to 360 degrees. This is the complete circle that you might visualize if you think about spinning around in a circle. Now, since … Read more
To convert square inches to square feet, we first need to know the relationship between those two units. There are 12 inches in a foot, so we can calculate the square footage from square inches by using the following conversion: 1 square foot = (12 inches) x (12 inches) = 144 square inches. Now, to … Read more
To convert degrees Celsius to Kelvin, you can use the formula: K = °C + 273.15 Where K represents the temperature in Kelvin and °C is the temperature in degrees Celsius. So, if we want to convert 100 degrees Celsius to Kelvin: Start with the temperature in Celsius: 100 °C Add 273.15 to this value: … Read more
To find two points on the line described by the equation y = 3x + 11, you can choose any two values for x and then use the equation to solve for y. Here’s a step-by-step process: Choose a value for x: Let’s start by choosing x = 0. Calculate y: Plugging x = 0 … Read more
To factor the expression involving the terms 26r3s, 52r5, and 39r2s4, we need to find the greatest common factor (GCF) for the coefficients and the variable parts separately. Step 1: Factor the Coefficients The coefficients are 26, 52, and 39. Factors of 26: 1, 2, 13, 26 Factors of 52: 1, 2, 4, 13, 26, … Read more
When comparing the numbers 29 and 0, it’s clear that 29 is the greater number. This is because the number 29 is positive and significantly larger than 0, which is the baseline or starting point in the number system. To put this in perspective, on a number line, 0 is located at the center, with … Read more