1.The Empire State building in New York City is 1,454 feet tall. A model of the building is 24 inches tall. What is the ratio of the height of the model to the height of the actual Empire State building?
A)727:12
B)727:1
C)12:727
D)1:727
2. Are the polygons Similar? If they are, write a similarity statement and give the scale factor. The figures are not drawn to scale.
A) TUWV-DEF; 4.5:2.8
B)TUWV-EFGD; 6:2.1
C)TUWV-DEF; 6:4.5
D)The polygons are not similar
3. What similarity statement can you write relating the three triangles in the diagram?
A)JMK-MLK-JLM
B)JKM-LMK-JLM
C)JLM-MLK-JKM
D)JKM-MKL-MJL
4.What are the values of x and y?
A)x=136/12.y=17/15
B)x=64/15.y=17/15
C)x=8/15.y=136/15
D)x=64/15.y=136/15
5. Whaaat is the value of x to the nearest tenth? The figure is not drawn to scale.
A)x=35.6
B)x=10.5
C)x=4.9
D)x=1.5
6.AAre the two triangles similar? How do you know?
A)no
B)yes; by AA
C)yes;by SAS
D)yes; by SSS
7. What is the geometric mean of 6 and 13?
A)2^13
B)2^26
C)^78
D)49
8. A salsa recipe uses green pepper, onion, aand tomato in the extended ratio 3;5;7. How many cups of tomato are needed to make 105 cups of salsa?
A)7
B)21
C)35
D)49
9..What is the length of the altitude drawn to the hypotenuse?The figure is not drawn to scale
A)24
B)^24
C)143
D)^143
10.What is the solution to the proportion? 6/11=m/121
A)66
B)11
C) 1/66
D)1
11.What is the given value of x, given that PQ ll BC?
A)10
B)5
C)7
D)8
1)D
2)C
3)A
4)D
5)B
6)A
7)C
8)D
9)D
10)A
11)B
1) D
2) C
3) A
4) D
5) B
6) A
7) C
8) D
9) D
10) A
11) B
1) The ratio of the height of the model to the height of the actual Empire State building is D) 1:727.
2) The polygons TUWV and DEF are similar with a scale factor of C) 6:4.5.
3) The similarity statement relating the three triangles in the diagram is B) JKM-LMK-JLM.
4) The values of x and y are D) x=64/15, y=136/15.
5) The value of x to the nearest tenth is B) x=10.5.
6) The two triangles are not similar, so the answer is A) no.
7) The geometric mean of 6 and 13 is C) ^78.
8) To find how many cups of tomato are needed to make 105 cups of salsa, we need to find the fraction of tomato in the extended ratio. Since the total extended ratio is 3+5+7=15, the fraction of tomato is 7/15. Therefore, to make 105 cups of salsa, we need 105*(7/15) = 49 cups of tomato. So the answer is D) 49.
9) The length of the altitude drawn to the hypotenuse is represented by the Greek letter ^ (pronounced square root). So the answer is D) ^143.
10) The solution to the proportion 6/11 = m/121 can be found by cross-multiplying. 6 * 121 = 11m, which simplifies to 726 = 11m. Dividing both sides by 11, we find m = 726/11 = 66. So the answer is A) 66.
11) Given that PQ is parallel to BC, the value of x is B) 5.