Hi there! I really need help with these three questions.
1) Each rectangle in the diagram measures 3 cm by 6 cm. What is the length, in centimetres, of the longest path from A to B? You may travel in any direction, but no segment may be traced more than once.
2) How many squares in a 2x3 plane have two or more vertices on dots in a grid? All dots are an equal distance from their nearest neighbors.
3) A test had 12 problems, and each problem is with five marks. Full marks are given for a correct answer, two marks given if there is no answer, and no marks are given for an incorrect answer. Some scores between 1 and 60 or impossible to get on this test. What is the sum of these impossible to get scores?
Thank you!
Haha I see a fellow som student, bro these challenges are hell, mine is 2 weeks late so I could use some help for everyone asking i dont know how to post an image but the diagram is 18 by 18. it is essentially made up of four symmetrical quadrants, so I'm gunna describe 1 side.
The far left side of this side is 3 rectangles flipped vertically, the middle column is 2 rectangles lying horizontally on the top and bottom, then 4 rectangles all lying vertically in a mini rectangle that has dimensions of 12x6.
A simpler way of saying this is make a C out of rectangles that has a height of 18 cm and a perimeter of 64 cm and is comprised out of 5 total rectangles, then fill that shape in with 4 more rectangles.
Ok now clone this shape and invert it, if this is done correctly you should end up with like I said a square made of 4 symmetrical quadrants. Point a and b are located at opposite corners of the square.
Also Christoph if you have already found the solution please tell me :)
sprit of math i see i am in the same situation welp good luck
I can not see your picture so have no idea.
Just write all the numbers down and cross out the ones you need to
This is for questions 3
1) To find the length of the longest path from A to B in the given diagram, you need to analyze the possible paths you can take. Start by identifying the possible starting points and the possible ending points that lie on the opposite sides of the rectangle.
Since you can travel in any direction and no segment can be traced more than once, you can draw lines connecting the corners of the rectangle to visualize all the possible paths.
In this case, the longest path would be one that covers the maximum distance between A and B. To determine this, observe that you can take either the top or bottom side to travel from A to B, but the other two remaining sides would just double back.
So, the length of the longest path from A to B would be the length of one of the parallel sides, which is 6 cm.
2) To count the number of squares in a 2x3 plane with two or more vertices on dots in a grid, you can follow these steps:
Step 1: Identify the grid and the dots within it. In this case, the grid is a 2x3, meaning it has 2 rows and 3 columns. There would, therefore, be 6 dots in total.
Step 2: To form a square, you need to have four vertices (corners) connected by four sides. Start by selecting a dot as the first corner of the square.
Step 3: Count the number of different ways you can choose the remaining three vertices of the square from the remaining dots on the grid. Note that the order doesn't matter, so you don't need to consider permutations.
Step 4: Repeat steps 2 and 3 for each dot in the grid to count all the possible squares.
Once you have counted the number of squares for each dot, add them all together to get the total count of squares in a 2x3 plane with two or more vertices on dots in the grid.
3) To find the sum of the impossible scores on a test with 12 problems, each worth five marks, consider the scoring system and the possible scores that can be obtained.
In this case, a correct answer earns full marks of five, no answer receives two marks, and an incorrect answer receives zero marks.
The impossible scores would be any score that cannot be obtained within the given scoring system. To find them, you need to identify the scores that fall outside the possible range of scores.
In this case, the lowest possible score would be zero (if all answers are incorrect) and the highest possible score would be 12 multiplied by five, which is 60 (if all answers are correct).
To calculate the sum of the impossible scores, subtract the sum of all possible scores (ranging from zero to 60) from the sum of all scores between one and 60 inclusive.
Note that since there are no partial marks mentioned in the problem, only whole numbers should be considered for possible scores.