To determine which equations have both x = 5 and x = -5 as solutions, we need to consider the characteristics of the equations that yield these values. A polynomial equation can have multiple roots, and if we want both x = 5 and x = -5 to be solutions, we can formulate an equation … Read more
To solve this problem, we start with the understanding that in a right triangle, the two non-right angles are complementary. This means that angle L and angle M add up to 90 degrees: L + M = 90° Given that: sin L = 1920 Now, the sine function gives us the ratio of the length … Read more
Finding the Completely Factored Form of the Polynomial To factor the polynomial 6x³ + 13x² + 4x – 15, we can follow a systematic approach that involves several steps: Step 1: Use the Rational Root Theorem The Rational Root Theorem suggests that any rational solution (root) of the polynomial equation can be expressed as a … Read more
The equation a = pr²π is an expression that combines several important mathematical constants and variables, usually in the context of geometry or physics. Here’s a detailed breakdown of each component of the equation: a: This variable typically represents the area in geometric contexts. The specific area calculated could vary based on the context of … Read more
Point symmetry about the origin means that for every point (x, y) in a set, there is a corresponding point (-x, -y) also in the set. In simpler terms, you can visualize this as if you have a point on one side of the origin, you should have an identical point on the opposite side … Read more
To find the equation of a hyperbola when you have been given the center, focus, and vertex, you’ll follow a series of steps that relate these elements to the general form of a hyperbola’s equation. Here’s how: Step 1: Identify the Components A hyperbola can be characterized by its center, foci (plural of focus), vertices, … Read more
To find the 25th term of the arithmetic sequence 3, 9, 15, 21, 27, we first need to identify the pattern of the sequence. An arithmetic sequence is a sequence of numbers where the difference between consecutive terms is constant. In this case, we can calculate the common difference: 9 – 3 = 6 15 … Read more
Graphing the Inequality x + 2y < 4 Graphing the inequality x + 2y < 4 involves several steps: Rewrite the Inequality: Start by isolating y. You can do this by rearranging the terms: 2y < 4 – x Now, divide by 2 to solve for y: y < 2 – 0.5x Graph the Boundary … Read more
To solve for y in the equation 2x + y = 6, you will need to isolate the variable y. This is done through simple algebraic manipulation. Here’s a step-by-step guide: Start with the original equation: 2x + y = 6 Subtract 2x from both sides: This gives you: y = 6 – 2x You … Read more
To solve the equation p = 2w + 2l for w, follow these steps: Start with the original equation: p = 2w + 2l Isolate the terms involving w on one side of the equation. To do this, you can subtract 2l from both sides: p – 2l = 2w Now, to isolate w, divide … Read more