Multiple Choice

1. Write the ratio in the simplest form.

45:15 (1 point)
9:3
3:1
1:3
4:1
2. Solve the following proportion.

r over five equals nine over twenty-one (1 point)
r = 2.14
r = 9
r = 11.66
r = 37.8
3. Sarah’s mother has a miniature village modeled after her home town. The model is 10 feet long and 7 feet wide. The actual village is 7 miles long. What is the village’s actual width? If necessary, round to the nearest tenth of a mile. (1 point)
4.9 miles
10 miles
1 mile
0.7 mile
4. Find the unit rate for 306 miles in 10 hours. (1 point)
0.03 miles/hour
30.6 miles/hour
306 miles/hour
3,060 miles/hour
5. In 10 months, 62.6 gallons were used. Find the unit rate. (1 point)
0.16 gallons/month
10 gallons/month
6.3 gallons/month
626 gallons/month
6. On a recent day, one U.S. dollar was worth 0.81 euros. If you were to exchange 222 euros, how many U.S. dollars would you receive? (1 point)
$88.91
$274.07
$548.15
$179.82
7. The pair of polygons is similar. Find the value of x.

(1 point)
20 in.
15 in.
13 in.
2 in.
8. Two ladders are leaning against a wall at the same angle, as shown. How long is the short ladder?

(1 point)
20 ft
24 ft
30 ft
40 ft
9. The sides of a rectangle are increased by a scale factor of 4. The perimeter of the smaller rectangle is 20 cm. What is the perimeter of the larger rectangle? (1 point)
320 cm
80 cm
120 cm
60 cm
10. A right triangle has an area of 13 m2. The dimensions of the triangle are increased by a scale factor of 3. What is the area of the new triangle? (1 point)
39 m2
169 m2
117 m2
142 m2
11. Quadrilateral PQRS was dilated to produce quadrilateral P'Q'R'S' on the grid below.

What was the apparent scale factor of the dilation used to produce quadrilateral P'Q'R'S'?

(1 point)

12. The width of a picture is 20 cm. Using a color copier, you reduce the width of the picture to 5 cm. What is the scale factor of the dilation? (1 point)
5
1 over 5
4
1 over 4
13. On a given blueprint, 1 inch = 30 feet. If the dimensions of a meeting room on the blueprint are 1.5 inches × 1.25 inches, what are its actual measurements? (1 point)
4.5 ft × 3.75 ft
20 ft × 24 ft
45 ft × 37.5 ft
15 ft × 12.5 ft
14. Using a scale factor of 1 inch = 5 feet, what are the blueprint dimensions of a bedroom that is 12 feet × 18 feet? (1 point)
2.2 in. × 3.3 in.
2.4 in. × 3.6 in.
2.8 in. × 4.2 in.
2.9 in. × 5.0 in.
15. The scale of a map is 1 inch = 25 miles. How many miles does 1.25 inches represent? (1 point)
25 miles
31.25 miles
62.5 miles
49.25 miles
16. The ramp shown below is used to move crates of apples to loading docks at different heights. When the horizontal distance AB is 12 feet, the height of the loading dock, BC, is 6 feet. What is the height of the loading dock DE?

(1 point)
10 feet
12 feet
17 feet
18 feet

My Answers:1. C
2. A
3.A
4. B
5. C
6. D
7. C
8. B
9. D
10. D
11. B
12. A
13. B
14. A
15. B
16. B
am i right??

1. no 3/1

6. 222/.81 = 274
7. no idea
8. no idea, same ratio of sides of triangle
9. 4*20 = 80
10. 9 * 13 = 117
11. no idea
12. 5/20 = 1/4
13. 1.5 * 30 = 45 !!!
14. 12/5 = 2.4 !!!
15. YES right 1.25 * 25 = 31.25
16. No idea, similar triangles aging, same ratio of corresponding sides.

Wait is 2,3,4 and 5 right?

Based on your answers, here is the feedback:

1. The ratio 45:15 is equal to 3:1, not 3:1.

2. The correct answer is A, r = 2.14.

3. The correct answer is 1 mile, not 4.9 miles.

4. The correct answer is 30.6 miles/hour, not 0.03 miles/hour.

5. The correct answer is 6.3 gallons/month, not 0.16 gallons/month.

6. The correct answer is $179.82.

7. The value of x is 13 in, not 20 in.

8. The length of the shorter ladder is 20 ft, not 24 ft.

9. The perimeter of the larger rectangle is 320 cm, not 80 cm.

10. The area of the new triangle is 117 m2, not 39 m2.

11. The apparent scale factor of the dilation used to produce quadrilateral P'Q'R'S' is 2, not 6.

12. The scale factor of the dilation is 1/4, not 4.

13. The actual measurements of the meeting room are 45 ft × 37.5 ft, not 4.5 ft × 3.75 ft.

14. The blueprint dimensions of the bedroom are 2.4 in. × 3.6 in., not 2.2 in × 3.3 in.

15. 1.25 inches represent 31.25 miles, not 25 miles.

16. The height of the loading dock DE is 12 feet, not 10 feet.

So, some of your answers are correct, but others need to be adjusted.

To determine if your answers are correct, let's go through each question and explain how to find the correct answer.

1. To write the ratio 45:15 in simplest form, you need to find the greatest common divisor (GCD) of the two numbers. In this case, the GCD of 45 and 15 is 15. Dividing both numbers by 15 gives you the simplest form: 3:1. So the correct answer is (C) 3:1.

2. To solve the proportion r/5 = 9/21, you need to cross-multiply and then solve for r. Cross-multiplying gives you r * 21 = 5 * 9. Simplifying it further, you get 21r = 45. Finally, dividing both sides by 21 gives you r = 45/21 = 2.14. So the correct answer is (A) r = 2.14.

3. To find the village's actual width, you need to determine the ratio between the model and the actual village on one dimension. The model is 10 feet long, and the actual village is 7 miles long. Since they are asking for the width of the village in miles, you can set up a proportion with unknown x as the width: 10 feet / 7 miles = x feet / 1 mile. Solving for x gives you x = (10/7) * 1 = 10/7 ≈ 1.43 miles. Rounded to the nearest tenth of a mile, the correct answer is (C) 1 mile.

4. The unit rate is found by dividing the total distance (306 miles) by the total time (10 hours). So the unit rate is 306 miles / 10 hours = 30.6 miles/hour. Therefore, the correct answer is (B) 30.6 miles/hour.

5. To find the unit rate, you need to divide the total gallons used (62.6 gallons) by the total time (10 months). So the unit rate is 62.6 gallons / 10 months = 6.26 gallons/month. However, the answer options provided are not in proper decimal format. To convert 6.26 gallons/month to a decimal, you need to move the decimal point two places to the right, resulting in 626 gallons/month. Therefore, the correct answer is (D) 626 gallons/month.

6. To find how many U.S. dollars you would receive when exchanging 222 euros, you need to multiply the exchange rate (1 U.S. dollar = 0.81 euros) by the amount of euros to be exchanged: 222 euros * (1 U.S. dollar / 0.81 euros) ≈ 274.07 U.S. dollars. So the correct answer is (B) $274.07.

Now, I have explained the steps for questions 1-6. If you would like further explanation or help with the remaining questions, please feel free to ask.