To write the equation of a line, you can use the slope-intercept form, which is expressed as: y = mx + b In this equation: y is the dependent variable (output). x is the independent variable (input). m represents the slope of the line. b signifies the y-intercept, which is the point where the line … Read more
To find the x-intercept and y-intercept of the equation y = x² + 6, we need to evaluate the function at specific points. X-Intercept: The x-intercept occurs when y = 0. To find it, we set the equation equal to zero: 0 = x² + 6 Rearranging gives us: x² = -6 Since the square … Read more
To determine the values of x that are not in the domain of a function g, you first need to understand what makes a value invalid for that function. In general, the domain of a function includes all the possible input values (x-values) for which the function is defined. Here are some common reasons why … Read more
Understanding the Values of Sine, Cosine, and Tangent To find the sine, cosine, and tangent values for the angle 8π/4 radians, we first simplify the angle: 8π/4 = 2π (since 8 divided by 4 equals 2). The angle 2π radians corresponds to a full rotation (360 degrees) around the unit circle. Therefore, it lands on … Read more
To find the sale price of a cell phone that is currently available for $15 off its regular price of $75, we can follow a simple calculation. First, we start with the regular price of the cell phone, which is $75. From this amount, we then subtract the discount amount of $15. This calculation is … Read more
The international system of numeration is a method for writing numbers that helps to distinguish the value of each digit according to its position. Here’s how you would write the given numbers: 1. 78921092 This number can be broken down as follows: 70 million 9 hundred thousand 80 thousand 2 hundred 10 tens 2 units … Read more
Whole numbers, fractions, and decimals are all terms used in the realm of mathematics to describe different types of numbers. While ‘whole number’ is a term that specifically refers to non-negative integers (like 0, 1, 2, 3, etc.), ‘fraction’ represents a part of a whole, such as 1/2 or 3/4, and ‘decimal’ conveys numbers in … Read more
Solution Set for the Equation 6x² – 24 = 0 To find the solution set for the equation 6x² – 24 = 0, we can follow these steps: Step 1: Add 24 to both sides First, let’s isolate the term with x² by adding 24 to both sides of the equation: 6x² – 24 + … Read more
To find the x-intercept of the graph given by the equation 4x + 3y + 5, we need to determine the point where the graph intersects the x-axis. This occurs when the value of y is equal to zero. Start by setting y = 0 in the equation: 4x + 3(0) + 5 = 0 … Read more
To find the solution set for the equation 7x² + 3x = 0, we start by factoring out the common term: Step 1: Factor the equation. This equation can be factored as: x(7x + 3) = 0 Here, we see that we can set each factor to zero to find the individual solutions. Step 2: … Read more