What is the sum of the first 30 terms of this arithmetic sequence 6, 13, 20, 27, 34?
To find the sum of the first 30 terms of the arithmetic sequence 6, 13, 20, 27, 34, we first need to identify the first term and the common difference. The first term (a) is 6, and we can find the common difference (d) by subtracting the first term from the second term: d = […]
Prove that Angle ABD is Congruent to Angle ACD
To prove that angle ABD is congruent to angle ACD, we can use the properties of parallel lines and transversals. Let’s assume that line AB is parallel to line CD, and line AC acts as a transversal that intersects both lines at points A and D. According to the properties of parallel lines, when a […]
What are the coordinates of the vertex for f(x) = x² + 4x – 10?
To find the coordinates of the vertex for the quadratic function f(x) = x² + 4x – 10, we can use the vertex formula. For a quadratic in the standard form f(x) = ax² + bx + c, the x-coordinate of the vertex is given by: x = -b / (2a) In our case, a […]
Choose the correct simplification of the expression 2b over c all to the power of 3
To simplify the expression (2b/c)³, we start by applying the power to both the numerator and the denominator. This means we raise both the numerator (2b) and the denominator (c) to the power of 3. So, we have: (2b)³ in the numerator and c³ in the denominator. Calculating the numerator: (2b)³ = 2³ * b³ […]
What is the coefficient in 6, 65, 10, 4?
In mathematical terms, a coefficient is a numerical or constant factor in a term of an algebraic expression. In the sequence of numbers you’ve provided—6, 65, 10, 4—it’s important to specify what you mean by ‘coefficient’ as these numbers do not form a traditional algebraic expression. If you’re referring to the first number, which is […]
How to Write a Decimal as a Mixed Number
To convert a decimal into a mixed number, follow these simple steps: Identify the Whole Number: Look at the decimal and determine if there is a whole number part. If so, note that down. For instance, in the decimal 3.75, the whole number is 3. Convert the Decimal Fraction to a Fraction: Take only the […]
How to Solve the Expression 2 + 5x – 3 + 7 – 1 + 4 – 3 + 7x + 3 – 5?
To solve the expression, we will combine like terms step by step. Begin with the original expression: 2 + 5x – 3 + 7 – 1 + 4 – 3 + 7x + 3 – 5 Now, let’s rearrange and group the constant terms and the terms involving x: Constant terms: 2 – 3 + […]
If an object moves 40m north, 40m west, 40m south, and 40m east, what’s the total displacement?
The total displacement of the object is 0 meters. To understand this, let’s break down the movements: The object moves 40 meters north. Then, it moves 40 meters west. Next, it moves 40 meters south. Finally, it moves 40 meters east. If we visualize this path, we can see that the object effectively forms a […]
What comes next in this sequence of prime numbers 11, 13, 17, 19?
The next number in the sequence is 23. To understand why, let’s look at the given sequence: 11, 13, 17, 19. These are all prime numbers, which means they are numbers greater than 1 that have no positive divisors other than 1 and themselves. The prime numbers follow a specific pattern, but they are not […]
How to Determine if a Function is Differentiable at a Point
To determine if a function is differentiable at a specific point, you need to check a few conditions: Continuity: First, the function must be continuous at that point. If there is any kind of discontinuity, like a jump or an asymptote, the function cannot be differentiable there. Existence of the Derivative: You need to confirm […]