Evaluate the summation of 2n plus 5 from n equals 1 to 12
To evaluate the summation of the expression 2n + 5 from n = 1 to n = 12, we can break it down into two separate summations. First, we calculate the summation of 2n: The summation of n from 1 to 12 is given by the formula: Σn = n(n + 1)/2. Thus, for n […]
What Does Cartesian System Mean?
The Cartesian system, often referred to as the Cartesian coordinate system, is a mathematical framework used for describing the position of points in a space using numbers. It is named after the French mathematician René Descartes, who developed this system in the 17th century. In a two-dimensional Cartesian system, any point can be represented by […]
If Two Lines are Parallel to the Same Line, Are They Parallel to Each Other?
Yes, if two lines are parallel to the same line, then they are parallel to each other. The reasoning behind this is based on the definition of parallel lines. When two lines are parallel, it means they never intersect, regardless of how far they are extended. If line A is parallel to line B, and […]
Derive the equation of the parabola with a focus at (2, 4) and a directrix of y = 8
To derive the equation of the parabola given a focus and a directrix, we start with the focus at the point (2, 4) and the directrix as the line y = 8. 1. **Understanding the basics**: A parabola is defined as the set of all points (x, y) that are equidistant from the focus and […]
How Do You Find the Circumference of a Circle with the Radius?
To find the circumference of a circle when you have the radius, you can use the formula: C = 2πr In this formula, C represents the circumference, π (pi) is a constant approximately equal to 3.14159, and r is the radius of the circle. For example, if the radius of the circle is 5 units, […]
A cylinder has a height of 53 cm and a diameter of 30 cm. What is its volume?
To find the volume of a cylinder, we can use the formula: Volume = π × r² × h Where: π (pi) is approximately 3.14 r is the radius of the cylinder h is the height of the cylinder First, we need to find the radius of the cylinder. The diameter is given as 30 […]
How to Solve and Check the Expression 1x + 3x + 10x² from Least to Greatest?
To solve the expression, we start by simplifying it. Combine like terms in the expression: 1x + 3x = 4x This gives us the simplified expression: 4x + 10x² Next, we will set this expression to zero to find the roots: 10x² + 4x = 0 We can factor this equation: 2x(5x + 2) = […]
How do you simplify the expression (x² – 15x + 36) / (5x – 60)?
To simplify the expression (x² – 15x + 36) / (5x – 60), we will start by factoring both the numerator and the denominator. First, let’s factor the numerator: The expression is x² – 15x + 36. We need to find two numbers that multiply to 36
What is the area of a sector with a central angle of 160 degrees and a diameter of 58m?
To find the area of a sector, we can use the formula: Area of Sector = (θ / 360) × π × r² where: θ is the central angle in degrees r is the radius of the circle First, we need to find the radius of the circle. Given that the diameter is 58m, we […]
What is the length of x round to the nearest tenth 9 7 m 10 4 m 37 3 m 38 6 m?
To find the length of x rounded to the nearest tenth, we first need to determine the average of the given lengths: 9.7 m, 10.4 m, 37.3 m, and 38.6 m. Let’s break it down: Step 1: Add the values together: 9.7 + 10.4 + 37.3 + 38.6 = 96.0 m Step 2: Count the […]