I need help understanding this so please help me??
1. A table is 4 ft high. A small model of the table is 6 in. high. What is the ratio of the height of the model table to the height of the real table?
2 : 3
1 : 6
1 : 8
2 : 6
2. If a/b = 9/10, complete this statement: a/9 = ?/?
Solve each proportion.
3. y/6 = 18/54
4. 5/7 = x-2/4
5. The scale of a scale drawing is 2 in. = 5 ft. A room is 5 in. long on the scale drawing. Find the actual length of the room.
12.5 ft
20.5 ft
15.2 ft
18.5 ft
6. A postcard is 6 in. by 4 in. A printing shop will enlarge it so that the longer side is any length up to 3 ft. Find the dimensions of the biggest enlargement.
3 ft by 2 ft
6 ft by 4 ft
3 ft by 1 ft
2 ft by 1 ft
We do not do your work for you. Once you have attempted to answer your questions, we will be happy to give you feedback on your work. Although it might require more time and effort, you will learn more if you do your own work. Isn't that why you go to school?
I'd be happy to help you understand these questions! Let's go through each one step by step:
1. To find the ratio of the height of the model table to the height of the real table, we need to compare their heights. We know that the model table is 6 inches high and the real table is 4 feet high.
Since there are 12 inches in 1 foot, we convert the height of the real table to inches: 4 feet * 12 inches/foot = 48 inches.
Now we can compare the heights: 6 inches : 48 inches.
To simplify the ratio, we divide both sides by 6: 6/6 inches : 48/6 inches
The simplified ratio is: 1 inch : 8 inches.
So, the answer is 1 : 8.
2. In this problem, if a/b = 9/10, we want to find what a/9 is equal to.
To solve this, we need to isolate a in the given proportion by multiplying both sides by 9:
(a/b) * 9 = (9/10) * 9
Simplifying, we get: (a * 9) / b = 9
Now, we can substitute the value of a/b from the given information (a/b = 9/10):
(9/10 * 9) / b = 9
Simplifying further: 81/10b = 9
To find a/9, we need to multiply both sides by 10b:
(81/10b) * 10b = 9 * 10b
Simplifying, we get: 81 = 90b
Finally, we divide both sides by 90 to solve for b:
81/90 = 90b/90
Simplifying, we find: b = 9/10
So, a/9 is equal to 9/10.
3. To solve the proportion y/6 = 18/54, we can cross-multiply:
y * 54 = 6 * 18
Simplifying, we get: 54y = 108
Dividing both sides by 54, we find: y = 2
Therefore, y is equal to 2.
4. For the proportion 5/7 = (x-2)/4, we can cross-multiply:
5 * 4 = 7 * (x-2)
Simplifying, we get: 20 = 7x - 14
Adding 14 to both sides, we have: 34 = 7x
Finally, dividing both sides by 7: 34/7 = x
Simplifying, x is approximately 4.86.
5. In this question, we are given that the scale of the scale drawing is 2 inches = 5 feet. We are given that the length of the room on the scale drawing is 5 inches.
To find the actual length of the room, we can set up a proportion:
2 inches / 5 feet = 5 inches / x feet
Cross-multiplying, we get: 2x = 5 * 5
Simplifying, we find: 2x = 25
Dividing both sides by 2, we have: x = 25/2
Therefore, the actual length of the room is 12.5 feet.
6. In this problem, we are given that the postcard is 6 inches by 4 inches, and the printing shop can enlarge it so that the longer side is up to 3 feet.
Since there are 12 inches in 1 foot, the maximum length of the longer side can be 3 feet * 12 inches/foot = 36 inches.
To find the dimensions of the biggest enlargement, we need to determine which of the given options (3 ft by 2 ft, 6 ft by 4 ft, 3 ft by 1 ft, or 2 ft by 1 ft) has a longer side of 36 inches.
From the given options, we can see that the only option with a longer side of 36 inches is 6 ft by 4 ft.
Therefore, the dimensions of the biggest enlargement would be 6 feet by 4 feet.
I hope this helps clarify the solutions for each question! Let me know if you have any further questions.