HCF of 2 Consecutive Odd Numbers
The highest common factor (HCF) of two consecutive odd numbers is always 1. This is because consecutive odd numbers differ by 2, making them co-prime. To understand this better, let’s consider two consecutive odd numbers, for example, 5 and 7. The factors of 5 are 1 and 5, while the factors of 7 are 1 […]
What is the slope of the line represented by the equation y = 5x?
The slope of the line represented by the equation y = 5x is 5. In this equation, the format is a linear equation in slope-intercept form, which is typically written as y = mx + b, where m represents the slope and b represents the y-intercept. In our case, the equation has no constant term […]
What is the first step when rewriting y = 4x² + 2x + 7 in the form y = a(x – h)² + k?
The first step in rewriting the quadratic equation y = 4x² + 2x + 7 in vertex form y = a(x – h)² + k is to complete the square. To complete the square, you need to focus on the quadratic and linear terms, which are 4x² + 2x. Here’s how you can do it: […]
The polynomial 8x² + 8x + 2 + 5x is simplified to 8x² + gx + h. What are the values of g and h?
To simplify the given polynomial, we first combine like terms. The original polynomial is: 8x² + 8x + 2 + 5x We can group the terms with x: 8x² + (8x + 5x) + 2 This simplifies to: 8x² + 13x + 2 Now, we can compare this with the simplified form, which is: 8x² […]
Which Property of Addition is Shown Below: a + b + c + d = a + c + b + d?
The property demonstrated in the equation a + b + c + d = a + c + b + d is known as the Commutative Property of Addition. This property states that changing the order of the addends does not affect the sum. In the equation, you can see that the terms are rearranged. […]
Enter a Recursive Rule for the Geometric Sequence 4, 16, 64, 256
The given sequence is 4, 16, 64, 256. To find the recursive rule, we first need to identify the common ratio between the terms. We can see that: 16 / 4 = 4 64 / 16 = 4 256 / 64 = 4 Each term is obtained by multiplying the previous term by 4. Therefore, […]
What is the converse of the statement ‘If two angles are supplementary, then they are not equal’?
The converse of the statement ‘If two angles are supplementary, then they are not equal’ is: ‘If two angles are not equal, then they are supplementary.’ This means that if we have two angles that do not measure the same, according to the converse, we can conclude that they must sum up to 180 degrees, […]
Find the Common Ratio of the Sequence 125, 25, 5, 1
The common ratio of a geometric sequence can be found by dividing any term by its preceding term. In the given sequence, we have: 1. The first term (a1) is 125. 2. The second term (a2) is 25. 3. The third term (a3) is 5. 4. The fourth term (a4) is 1. To find the […]
How do you solve x² + 12x + 5 = 0 using the completing the square method?
To solve the quadratic equation x² + 12x + 5 = 0 by completing the square, follow these steps: Start with the equation: x² + 12x + 5 = 0 Move the constant term to the other side of the equation: x² + 12x = -5 To complete the square, take half of the coefficient […]
If an exterior angle of a regular polygon measures twenty four degrees, how many sides does the polygon have?
To find the number of sides of a regular polygon given an exterior angle, we can use the formula: Number of sides (n) = 360 / Exterior angle In this case, we know that the exterior angle is 24 degrees. Plugging this value into the formula gives: n = 360 / 24 Calculating this, we […]