Answer:
B). 3 1/2(-2) = -7
Step-by-step explanation:
Let's evaluate the expression so as to be able to get the right estimate.
3 4/7 (-2 1/12)
=3 4/7 (-25/12)
= 25/7 * -25/12
= 25/7 * -25/12
= -625/84
= -7 37/84
Approximately it's equal to ,-7
Priscilla's age was 83,534 while Jack's age was 83,633.
Answer:
Case 1:
![AB = 30](https://tex.z-dn.net/?f=AB%20%3D%2030)
![BC = 50](https://tex.z-dn.net/?f=BC%20%3D%2050)
Case 2:
![AB = 15.9](https://tex.z-dn.net/?f=AB%20%3D%2015.9)
![BC = 36.7](https://tex.z-dn.net/?f=BC%20%3D%2036.7)
Case 3: Not possible
Step-by-step explanation:
Given
See attachment for illustration of each case
Required
Find AB and BC
Case 1:
Using Pythagoras theorem in ANB, we have:
![AB^2 = AN^2 + BN^2](https://tex.z-dn.net/?f=AB%5E2%20%3D%20AN%5E2%20%2B%20BN%5E2)
This gives:
![AB^2 = 24^2 + 18^2](https://tex.z-dn.net/?f=AB%5E2%20%3D%2024%5E2%20%2B%2018%5E2)
![AB^2 = 576 + 324](https://tex.z-dn.net/?f=AB%5E2%20%3D%20576%20%2B%20324)
![AB^2 = 900](https://tex.z-dn.net/?f=AB%5E2%20%3D%20900)
Take square roots of both sides
![AB = \sqrt{900](https://tex.z-dn.net/?f=AB%20%3D%20%5Csqrt%7B900)
![AB = 30](https://tex.z-dn.net/?f=AB%20%3D%2030)
To calculate BC, we consider ANC, where:
![AC^2 = AN^2 + NC^2](https://tex.z-dn.net/?f=AC%5E2%20%3D%20AN%5E2%20%2B%20NC%5E2)
![40^2 = 24^2 + NC^2](https://tex.z-dn.net/?f=40%5E2%20%3D%2024%5E2%20%2B%20NC%5E2)
![1600 = 576 + NC^2](https://tex.z-dn.net/?f=1600%20%3D%20576%20%2B%20NC%5E2)
Collect like terms
![NC^2 = 1600 - 576](https://tex.z-dn.net/?f=NC%5E2%20%3D%201600%20-%20576)
![NC^2 = 1024](https://tex.z-dn.net/?f=NC%5E2%20%3D%201024)
Take square roots
![NC = \sqrt{1024](https://tex.z-dn.net/?f=NC%20%3D%20%5Csqrt%7B1024)
![NC = 32](https://tex.z-dn.net/?f=NC%20%3D%2032)
So:
![BC = NC + BN](https://tex.z-dn.net/?f=BC%20%3D%20NC%20%2B%20BN)
![BC = 32 + 18](https://tex.z-dn.net/?f=BC%20%3D%2032%20%2B%2018)
![BC = 50](https://tex.z-dn.net/?f=BC%20%3D%2050)
Case 2:
Using Pythagoras theorem in ANB, we have:
![AN^2 = AB^2 + BN^2](https://tex.z-dn.net/?f=AN%5E2%20%3D%20AB%5E2%20%2B%20BN%5E2)
This gives:
![24^2 = AB^2 + 18^2](https://tex.z-dn.net/?f=24%5E2%20%3D%20AB%5E2%20%2B%2018%5E2)
![576 = AB^2 + 324](https://tex.z-dn.net/?f=576%20%3D%20AB%5E2%20%2B%20324)
Collect like terms
![AB^2 = 576 - 324](https://tex.z-dn.net/?f=AB%5E2%20%3D%20576%20-%20324)
![AB^2 = 252](https://tex.z-dn.net/?f=AB%5E2%20%3D%20252)
Take square roots of both sides
![AB = \sqrt{252](https://tex.z-dn.net/?f=AB%20%3D%20%5Csqrt%7B252)
![AB = 15.9](https://tex.z-dn.net/?f=AB%20%3D%2015.9)
To calculate BC, we consider ABC, where:
![AC^2 = AB^2 + BC^2](https://tex.z-dn.net/?f=AC%5E2%20%3D%20AB%5E2%20%2B%20BC%5E2)
![40^2 = 252 + BC^2](https://tex.z-dn.net/?f=40%5E2%20%3D%20252%20%2B%20BC%5E2)
![1600 = 252 + BC^2](https://tex.z-dn.net/?f=1600%20%3D%20252%20%2B%20BC%5E2)
Collect like terms
![BC^2 = 1600 - 252](https://tex.z-dn.net/?f=BC%5E2%20%3D%201600%20-%20252)
![BC^2 = 1348](https://tex.z-dn.net/?f=BC%5E2%20%3D%201348)
Take square roots
![BC = \sqrt{1348](https://tex.z-dn.net/?f=BC%20%3D%20%5Csqrt%7B1348)
![BC = 36.7](https://tex.z-dn.net/?f=BC%20%3D%2036.7)
Case 3:
This is not possible because in ANC
The hypotenuse AN (24) is less than AC (40)
Answer is 553 beasts
Step by step:
Multiply 158 by 3 to get 474
Divide 158 by 2 to get 79
Add 474 with 79 and get 553
Answer:
see below
Step-by-step explanation:
72pi cubic inches
1/3 pi r ^2 * h = 72 pi
1/3 r^2 h = 72
You can theoretically find infinite answers to this and get enough points for the semester where you don't have to do work anymore. I will list a couple more possible answers below
r = radius, h = height
r = 2, h = 54
r = 3, h = 24
r = 4, h = 27/2
r = √(1/pi), h = 72pi