24. Yes, they are congruent by the AAS postulate/statement
26. 3/4.5 = 5.2/a -> m-e thm. -> mult. POC -> a = 7.8 in.
30. pythagorean thm. -> 2² + b² = 2.5² -> b = 1.5 m
32. a) v = 1/3πr²h -> v = 1/3*3.14*4.5²*6 (6 is found w/ pythagorean thm.) -> v ≈ 127.2 cm³
b) yes, 130 cm³ > 127.2 cm³
33. a) 4.5/r = 2/7 -> 4.5/2 = r/7 -> 15.75 ≈ 15.8 in.
b) due to the cones being similar in shape, all one-dimensional measurements will be the same, thus, it is 2:7.
Answer:
no change in area
Step-by-step explanation:
The original area is
A = 12*5 = 60 ft^2
The new length and width
l = 12 + .25 (12) = 12+3 =15
w = 5 - .2 (5) =5-1 = 4
The new area is
A = l*w =15*4 = 60 ft^2
The area is the same
15s=2550
(divide both sides by 15)
S=170
170 students went
We know that the sum of the internal angles in each triangle is 180°.
Therefore we have the equation:
![m\angle C+m\angle D+m\angle E=180^o](https://tex.z-dn.net/?f=%20m%5Cangle%20C%2Bm%5Cangle%20D%2Bm%5Cangle%20E%3D180%5Eo%20)
substitute and solve:
![79+(6x+11)+(7x-14)=180\\(6x+7x)+(79+11-14)=180\\13x+76=180\ \ \ |-76\\13x=104\ \ \ |:13\\x=8](https://tex.z-dn.net/?f=%2079%2B%286x%2B11%29%2B%287x-14%29%3D180%5C%5C%286x%2B7x%29%2B%2879%2B11-14%29%3D180%5C%5C13x%2B76%3D180%5C%20%5C%20%5C%20%7C-76%5C%5C13x%3D104%5C%20%5C%20%5C%20%7C%3A13%5C%5Cx%3D8%20)
We have
![m\angle N=3x+18](https://tex.z-dn.net/?f=m%5Cangle%20N%3D3x%2B18)
substitute the value of x to the expression:
![m\angle N=3(8)+18=24+18=42](https://tex.z-dn.net/?f=m%5Cangle%20N%3D3%288%29%2B18%3D24%2B18%3D42)
Answer: m∠N = 42 degrees