The Correct Answer and Explanation is:
Of course. Based on the exercises provided in the worksheet, here is the solution and detailed explanation.
The correct answer to the riddle is formed by solving each problem and matching the result to one of the lettered options. By solving the problems in order, we find the following matches:
- G (2x + 1)
- E (3x – 2)
- I (3x² + 5x)
- C (10x + 10)
- A (5x + 3)
Arranging these letters in the order of the problems gives the sequence G-E-I-C-A. It is possible there is an error on the worksheet, as this does not form a coherent punchline. However, the mathematical solutions are correct.
Explanation
Here is a step by step breakdown of how to solve each problem on the worksheet.
1. Find the quotient of (4x² + 2x) and 2x.
To find the quotient, you must divide the polynomial (4x² + 2x) by the monomial 2x. This is done by dividing each term of the polynomial by 2x separately.
(4x² / 2x) + (2x / 2x) = 2x + 1.
This result, 2x + 1, matches letter G in the answer list.
2. What is the result when (12x² – 8x) is divided by 4x?
Similar to the first problem, divide each term of (12x² – 8x) by 4x.
(12x² / 4x) – (8x / 4x) = 3x – 2.
This solution, 3x – 2, corresponds to letter E.
3. A rectangular prism has a volume of (15x³ + 25x²) and a base area of 5x. Find the height.
The formula for the volume of a prism is Volume = Base Area × Height. To find the height, you rearrange the formula to Height = Volume / Base Area.
Height = (15x³ + 25x²) / 5x.
Dividing each term gives: (15x³ / 5x) + (25x² / 5x) = 3x² + 5x.
The height of the prism is 3x² + 5x, which matches letter I.
4. The area of a rectangle is (6x² + 10x) and the width is 2x. Find the perimeter.
This is a two step problem. First, find the length. The formula for area is Area = Length × Width, so Length = Area / Width.
Length = (6x² + 10x) / 2x = 3x + 5.
Next, find the perimeter using the formula P = 2(Length + Width).
P = 2((3x + 5) + 2x) = 2(5x + 5) = 10x + 10.
The perimeter is 10x + 10, which is letter C.
5. Find how many times the remaining fundraiser amount is of the second day’s collection.
First, calculate the remaining amount by subtracting the first day’s collection from the goal.
Remaining = (35x² + 20x) – (10x² + 5x) = 25x² + 15x.
Next, divide this remaining amount by the second day’s collection, 5x.
(25x² + 15x) / 5x = (25x² / 5x) + (15x / 5x) = 5x + 3.
This answer, 5x + 3, corresponds to letter A.
