When you take out a loan, the principal is the original sum of money that you borrow, which you are obligated to pay back, not including any interest. In your case, if you take out a $1000 loan for college, the principal amount is simply $1000. To further clarify, let’s break down the components of … Read more
To find all the polar coordinates of a point with a given angle, we need to understand the relationship between polar and Cartesian coordinates. In polar coordinates, a point in the plane is represented as (r, θ), where r is the radial distance from the origin, and θ is the angle measured from the positive … Read more
The temperature of 5 degrees Celsius (°C) is equivalent to 41 degrees Fahrenheit (°F) when converted using the standard formula for temperature conversion. Here’s how the conversion works: To convert Celsius to Fahrenheit, you can use the formula: °F = (°C × 9/5) + 32. Substituting 5°C into the formula gives you: °F = (5 … Read more
When an equilateral triangle is rotated about a line that runs parallel to one of its sides, the resulting shape is a triangular prism. In this case, if we consider a triangle where its base lies along the line of rotation and the triangle revolves around this line, it creates a solid 3D object that … Read more
To determine the fraction of the areas of circles that contain Xs, we first need to understand the total area of each circle and the area covered by the Xs within them. Here’s a step-by-step guide: Step 1: Calculate the Total Area of the Circles The area of a circle can be calculated using the … Read more
The function given is y = 0.96x. To determine the percentage rate of change and whether this function represents exponential growth or decay, we need to analyze the base of the exponent. In the case of functions of the form y = ax, the behavior of the function is largely dependent on the value of … Read more
When we say that a variable z varies directly with another variable or a combination of variables, it means that there exists a constant k such that: z = k * (x2 + y2) In this case, we understand that z is proportional to the sum of the squares of x and y. This relationship … Read more
To find the ratio of the radii of the circles given the areas in the ratio of 4:9:25, we need to use the relationship between the area of a circle and its radius. The area (A) of a circle is calculated using the formula: A = πr2, where r is the radius of the circle. … Read more
To determine the value of x in the equation xy = 30 when y = 15, we can follow these steps: First, substitute the value of y into the equation. The equation now looks like this: x * 15 = 30. Next, to isolate x, divide both sides of the equation by 15. This will … Read more
To find the value of k for which one root of the quadratic equation kx² + 14x + 80 = 0 is zero, we can follow these steps: Step 1: Set the root to zero If we want one of the roots of the equation to be zero, we can substitute x = 0 into … Read more