1) Write the ratio in simplest form. 16:24
1:2
4:3
3:4
2:3***
2) Solve the following proportion. r/5=9/21
r= 2.14***
r= 9
r=11.66
r= 37.8
3) James has a model helicopter. The model is 8 inches long and 7 inches wide. The actual helicopter is 56 inches long. What is the helicopters actual width, if we assume the model is proportionate?
40 inches
49 inches***
56 inches
60 inches
4) Find the unit rate for 521 miles in 14 hours.
0.03 miles/hour
37.21 miles/hour***
521 miles/hour
7,294 miles/hour
5) In six months, 33.6 gallons were used. Find the unit rate.
3.6 gallons/month
4.6 gallons/month
5.6 gallons/month***
6.6 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?
$88.91
$274.07***
$548.15
$179.82
7) The pair of polygons is similar. Find the value of x (Figure 1, Side 1= 15 in. Side 2= 60 in. Figure 2, Side 1= 10 in. Side 2= x).
2.5 in.
5 in.
35 in.
40 in.***
8) Two ladders are leaning against the wall at the same angle, as shown. What is the length of the short ladder (Tall ladder, length= 60 ft., width- 40 ft. Short ladder, length= x, width, 10 ft.)?
6 ft
15 ft***
20 ft
30 ft
9) The sides of a square are increased by a scale factor of 7. The perimeter of the smaller square is 16 ft. What is the perimeter of the larger square?
28 ft***
56 ft
64 ft
112 ft
10) A right triangle has an area of 21m^2. The dimensions of the triangle are increased by a scale factor of 4. What is the area of the new triangle?
42m^2
84m^2***
168 m^2
336 m^2
11) Figure A'B'C'D' (A'= (-3, 6) B'= (9, 3) C'= (6, -3) D'= (-3, -3)) is a dilation of figure ABCD (A= (1, 2) B= (3, 1) C= (2, -1) D= (-1, -1)). Find the scale factor. Classify the dilation as an enlargement or a reduction.
Scale factor 1/3; reduction
Scale factor 1/4; reduction
Scale factor 3; enlargement***
Scale factor 4; enlargement
12) The length of a piece of paper is 8.5 inches. Using scissors, you reduce the length of the paper to 4.25 inches. What is the scale factor of the dilation?
1/4
1/2***
2
4
13) On a given blueprint, 1 inch= 12 feet. If the dimensions of a recreation room on the blueprint are 2 inches x 1.75 inches, what are its actual measurements?
1 ft x 12 ft
6 ft x 7 ft
22 ft x 18 ft
24 ft x 21 ft***
14) Using a scale factor of 1 inch = 16 feet, what are the blueprint dimensions of a room that is 20 feet x 28 feet?
1.5 in. x 2.5 in
1.25 in. x 2.25 in
1.25 in. x 1.75 in.***
1.5 in. x 1.75 in.
15) The scale of a map is 1 inch= 30 miles. How many actual miles does 5.25 inches represent?
157.5 miles***
175 miles
1,575 miles
1,750 miles
Well, I accidentally submitted the test, and discovered that three of those were incorrect. Horray.
Please, I'm literally desperate TwT
that's fine with me I just need to get it done
1) To write the ratio 16:24 in simplest form, we need to find the greatest common divisor (GCD) of the two numbers and divide both numbers by it. In this case, the GCD of 16 and 24 is 8. Dividing both numbers by 8 gives us the simplified ratio of 2:3.
2) To solve the proportion r/5 = 9/21, we need to cross multiply and solve for r. Cross multiplying gives us r * 21 = 5 * 9. Simplifying this equation gives us 21r = 45. Dividing both sides by 21 gives us r = 45/21, which simplifies to r = 2.14.
3) If the model helicopter is 8 inches long and 7 inches wide, and the actual helicopter is 56 inches long, we can use a proportion to find the actual width. The proportion is 8/7 = 56/x, where x represents the actual width of the helicopter. Cross multiplying gives us 8x = 56 * 7. Dividing both sides by 8 gives us x = (56 * 7) / 8, which simplifies to x = 49.
4) To find the unit rate for 521 miles in 14 hours, we need to divide the total distance by the total time. Dividing 521 miles by 14 hours gives us a unit rate of approximately 37.21 miles per hour.
5) To find the unit rate for 33.6 gallons in six months, we need to divide the total amount of gallons by the total time. Dividing 33.6 gallons by 6 months gives us a unit rate of 5.6 gallons per month.
6) If one U.S. dollar is worth 0.81 euros, and we want to exchange 222 euros, we can find the amount of U.S. dollars by multiplying the euros by the exchange rate. Multiplying 222 euros by 0.81 gives us approximately $179.82.
7) Since the two polygons are similar, the ratios of corresponding sides will be equal. From Figure 1, we have 15/60 = 10/x. Cross multiplying gives us 15x = 600. Dividing both sides by 15 gives us x = 40.
8) If the length of the tall ladder is 60 ft and the width is 40 ft, we can set up a proportion to find the length of the short ladder. The proportion is 60/40 = x/10, where x represents the length of the short ladder. Cross multiplying gives us 60 * 10 = 40x. Dividing both sides by 40 gives us x = (60 * 10) / 40, which simplifies to x = 15.
9) If the sides of a square are increased by a scale factor of 7, then the perimeter of the larger square will also be increased by the same scale factor. The perimeter of the smaller square is 16 ft, so the perimeter of the larger square will be 16 ft * 7, which equals 112 ft.
10) When the dimensions of a right triangle are increased by a scale factor of 4, the area of the new triangle will increase by the square of the scale factor. The original triangle has an area of 21m^2, so the area of the new triangle will be 21m^2 * 4^2, which equals 84m^2.
11) To find the scale factor of the dilation, we need to compare the corresponding side lengths of the original figure (ABCD) to the corresponding side lengths of the dilated figure (A'B'C'D'). From the given coordinates, we can see that AB has a length of sqrt((3-1)^2 + (1-2)^2) = sqrt(5) and A'B' has a length of sqrt((-3-(-3))^2 + (6-3)^2) = sqrt(18). Therefore, the scale factor is sqrt(18)/sqrt(5) = sqrt(18/5) ≈ 3. Since the scale factor is greater than 1, it is an enlargement.
12) The scale factor of the dilation can be found by taking the ratio of the new length to the original length. In this case, the original length is 8.5 inches and the new length is 4.25 inches. The scale factor is 4.25/8.5 = 0.5.
13) If 1 inch on the blueprint represents 12 feet in actual measurements, we can find the actual dimensions of the recreation room by multiplying the dimensions on the blueprint by 12. The actual measurements of the recreation room are 2 inches x 12 feet and 1.75 inches x 12 feet, which simplifies to 24 ft x 18 ft.
14) Using a scale factor of 1 inch = 16 feet, we can find the blueprint dimensions of a room that is 20 feet x 28 feet by dividing each dimension by 16. The blueprint dimensions are 20 ft / 16 = 1.25 inches and 28 ft / 16 = 1.75 inches.
15) If the scale of a map is 1 inch = 30 miles, we can find the actual miles represented by 5.25 inches by multiplying 5.25 inches by 30. 5.25 inches * 30 miles/inch = 157.5 miles.