How do you solve for x in the equation 3x + 1 = 2x + 6?
To solve for x in the equation 3x + 1 = 2x + 6, follow these steps: Start with the original equation: 3x + 1 = 2x + 6. Subtract 2x from both sides to get the terms involving x on one side: 3x – 2x + 1 = 6 This simplifies to: x + […]
Can You Conclude That A ⊆ B If A ⊆ B And C Are Sets Such That?
In set theory, when we say that A ⊆ B, we mean that set A is a subset of set B. This means that every element of set A is also an element of set B. Now, let’s analyze the relationship between three sets: A, B, and C. If we know that A ⊆ B, […]
How to Differentiate the Function v = 13x^2?
To differentiate the function v = 13×2, we’ll apply the power rule of differentiation. The power rule states that if you have a term in the form of axn, its derivative will be n * a * x(n-1). In our function, v = 13×2, we identify a = 13 and n = 2. Using the […]
Find the area under the standard normal distribution curve between z = 2.05 and z = 2.05
The area under the standard normal distribution curve between z = 2.05 and z = 2.05 is effectively zero. This is because when we are asked for the area between two identical z-scores, we are referencing a single point on the curve. In statistical terms, the area under the curve represents the probability of the […]
What are the x intercepts of the graph of the function f(x) = x² + 4x – 12?
To find the x-intercepts of the function f(x) = x² + 4x – 12, we need to set the function equal to zero and solve for x. So, we start with: x² + 4x – 12 = 0 This is a quadratic equation, which we can solve by factoring, completing the square, or using the […]
What are the zeros of the polynomial function f(x) = x³ + 10x² + 24x?
ABC is an Equilateral Triangle. What is the Value of X?
In an equilateral triangle, all three sides are of equal length, and all three angles measure 60 degrees. Given that triangle ABC is equilateral, if we assume that x represents the measure of one of the angles, then we can confidently say that: x = 60 degrees. This is because each angle in an equilateral […]
How do you solve the equation x² – 18x + 81 = 25?
To solve the equation x² – 18x + 81 = 25, we first need to rearrange it into standard form. This involves moving all terms to one side of the equation. 1. Start by subtracting 25 from both sides: x² – 18x + 81 – 25 = 0 This simplifies to: x² – 18x + […]
Given the equation 3x + 25 = 7x + 5, which order of operations completely solves for x?
To solve the equation 3x + 25 = 7x + 5, we need to isolate x. Here’s how we can do it step by step: Subtract 3x from both sides: This helps us get all the x terms on one side of the equation. So, we subtract 3x from both sides: 3x + 25 – […]
How is the graph of y = 6x² + 4 different from the graph of y = 6x²?
The graph of y = 6x² + 4 is a parabola that opens upwards, just like the graph of y = 6x². However, there is a key difference between the two graphs. In the equation y = 6x², the vertex of the parabola is located at the origin (0, 0). This means the lowest point […]