To find the solution set of the equation x² = 80, we start by solving for x. We can rewrite the equation as: x² = 80 Next, we can take the square root of both sides to find the values of x: x = ±√80 Now, simplifying √80, we get: √80 = √(16 * 5) … Read more
In the given scenario, we have a parallelogram ABCD where line AE is perpendicular to line DC and line CF is perpendicular to line AD. This setup introduces important geometric relationships and properties. First, since AE is perpendicular to DC, it means that angle AEB measures 90 degrees. Therefore, triangle ABE is a right triangle. … Read more
Converting a rational number into a decimal is a straightforward process. A rational number is any number that can be expressed as the quotient or fraction p/q, where p is the numerator and q is the denominator, with q not equal to zero. Here are the steps to convert a rational number to a decimal: … Read more
To identify the type of conic section from the given equation x² – 4y + 2y² = 0, we first need to rearrange and rewrite it in a standard form. 1. **Rearranging the Equation**: We start by rearranging the equation: 2y² – 4y + x² = 0 2. **Completing the Square**: We will complete the … Read more
To solve the system of equations given by 3x + 2y = 5 and x + y = 10, we can use the substitution or elimination method. Here, we’ll use the substitution method for clarity. Step 1: Solve one of the equations for one variable Let’s solve the second equation for y: x + y … Read more
To complete the square for the quadratic equation x² + 8x + 4, we follow a systematic approach. Completing the square allows us to transform the quadratic equation into a perfect square trinomial, facilitating easier analysis and solving. First, let’s isolate the variable terms: x² + 8x + 4 Next, we focus on the expression … Read more
To solve the inequality np < 5 + 4c – 2, let’s simplify and isolate n. 1. Start by simplifying the right side of the inequality: 5 + 4c – 2 = 3 + 4c Now the inequality looks like this: np < 3 + 4c 2. Next, isolate n by dividing both sides by … Read more
The function y = x^9 is a polynomial function, which means it is continuous and defined for all real numbers. Let’s examine its domain and range in detail. Domain: The domain of a function is the set of all possible input values (x-values). For the function y = x^9, you can input any real number … Read more
To find an angle that is coterminal with a given angle, you can add or subtract full rotations (360 degrees for degrees or 2π radians for radians) until you bring the angle within the desired range. Part A: Finding a Coterminal Angle for 600 Degrees The first step is to determine how many full circles … Read more
To calculate the interest due on an amount of money, you can use the simple interest formula: Interest = Principal × Rate × Time. Here’s how you can do it step by step: Identify the values: Principal (P): $800 Annual Interest Rate (R): 12%, which is 0.12 in decimal form Time (T): 120 days. To … Read more