How do you subtract 2k³ + k² + 9 from 5k³ + 3k + 7?
To perform the subtraction of the polynomials 2k³ + k² + 9 from 5k³ + 3k + 7, we follow a straightforward process. First, we write down the two expressions: 5k³ + 3k + 7 – (2k³ + k² + 9) Next, we distribute the negative sign across the second polynomial: 5k³ + 3k + […]
Find the area of the regular polygon pentagon with a side of 6 m
To find the area of a regular pentagon (a five-sided polygon) with a given side length, we can use the formula: Area = (1/4) * √(5(5 + 2√5)) * s² where s is the length of a side of the pentagon. In this case, the side length is 6 m. Substituting the value of s […]
Complete this statement: A polygon with all sides of the same length is said to be
A polygon with all sides of the same length is said to be equilateral. In geometry, polygons are classified based on their sides and angles. An equilateral polygon specifically refers to any polygon whose sides have equal length. The most common example of an equilateral polygon is an equilateral triangle, where all three sides and […]
How do I find a vector function representing the curve of intersection of the cylinder x^2 + y^2 = 4 and the surface z = xy?
To find a vector function that represents the curve of intersection of the two given surfaces, we need to analyze both equations: Cylinder: The equation of the cylinder is given by x2 + y2 = 4, which represents a circular cylinder with a radius of 2 centered along the z-axis. Surface: The surface is defined […]
What is the volume of a swimming pool with dimensions of 10 meters, 5 meters, and 1 meter?
To calculate the volume of a swimming pool, you can use the formula for the volume of a rectangular prism, which is: Volume = Length × Width × Height In this case, the dimensions of the swimming pool are: Length = 10 meters Width = 5 meters Height = 1 meter Now, plug the dimensions […]
How to Write an Equation of a Line with a Given Slope and Y-Intercept?
To write the equation of a line when you have the slope (m) and the y-intercept (b), you can use the slope-intercept form of a linear equation, which is: y = mx + b In this case, we are given: Slope (m) = 5 Y-intercept (b) = 3 Now, substituting the given values into the […]
How do you solve the system of equations 2x – y = 3 and 4x + 2y = 2 using a graph?
To solve the system of equations 2x – y = 3 and 4x + 2y = 2 using a graph, follow these steps: Rewrite the equations in slope-intercept form: For the first equation, isolate y: 2x – y = 3 ⇒ y = 2x – 3 For the second equation, also isolate y: 4x + […]
How do you get 24 from 9, 6, 11, and 3 using addition, subtraction, multiplication, or division?
To achieve the target number 24 using the numbers 9, 6, 11, and 3, we can use a combination of arithmetic operations. One possible way is to perform the following calculations: First, we can multiply 6 and 3: 6 × 3 = 18 Next, we can add 9 to this result: 18 + 9 = […]
Is the product of two integers positive, negative, or zero?
The product of two integers can be positive, negative, or zero depending on the values of those integers. 1. **Positive Product**: If both integers are positive (e.g., 3 and 5), their product will also be positive (3 × 5 = 15). Similarly, if both integers are negative (e.g., -3 and -5), the product will also […]
Solve the following system of equations: x + 3y + z = 2, x + 2y + 3z = 7, x + 2y + 5z = 21
To solve the given system of equations, we have: 1. x + 3y + z = 2 2. x + 2y + 3z = 7 3. x + 2y + 5z = 21 First, let’s label our equations for convenience: Equation (1): x + 3y + z = 2 Equation (2): x + 2y + […]