Domain: all real numbers
Range: y>-3
While none of these examples can be used as an counterexample i could make one up to prove the conclusion is false. ex: 3-5=-2
Answer:
$98,048.77
Step-by-step explanation:
First you want to find out how much he has put in without interest so you would do 237.95*12 to figure out how much he puts in per year then times that number by 30 to figure out how much he has put in in total, after this you subtract this total from the 183,710.77 to get the total amount of interest
Let the number of article be x,
let the machine required be y
x/42=63
x/y=54
x=63*42
x=54*y
∴42×63=54y
y=49
Answer:
1) ![n = 84](https://tex.z-dn.net/?f=n%20%3D%2084)
2) ![n = 78](https://tex.z-dn.net/?f=n%20%3D%2078)
3) ![n = 24](https://tex.z-dn.net/?f=n%20%3D%2024)
4) ![n = 16](https://tex.z-dn.net/?f=n%20%3D%2016)
5) ![n = 35](https://tex.z-dn.net/?f=n%20%3D%2035)
Step-by-step explanation:
To solve each proportion, we apply cross multiplication.
Question 1:
![\frac{5}{12} = \frac{35}{n}](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B12%7D%20%3D%20%5Cfrac%7B35%7D%7Bn%7D)
![5n = 35*12](https://tex.z-dn.net/?f=5n%20%3D%2035%2A12)
Simplifying both sides by 5
![n = 7*12 = 84](https://tex.z-dn.net/?f=n%20%3D%207%2A12%20%3D%2084)
Question 2:
![\frac{n}{52} = \frac{180}{120}](https://tex.z-dn.net/?f=%5Cfrac%7Bn%7D%7B52%7D%20%3D%20%5Cfrac%7B180%7D%7B120%7D)
![120n = 52*180](https://tex.z-dn.net/?f=120n%20%3D%2052%2A180)
Simplifying both sides by 20
![6n = 52*9](https://tex.z-dn.net/?f=6n%20%3D%2052%2A9)
Simplifying by 3
![2n = 52*3](https://tex.z-dn.net/?f=2n%20%3D%2052%2A3)
Simplifying by 2
![n = 26*3 = 78](https://tex.z-dn.net/?f=n%20%3D%2026%2A3%20%3D%2078)
Question 3:
![\frac{18}{n} = \frac{21}{28}](https://tex.z-dn.net/?f=%5Cfrac%7B18%7D%7Bn%7D%20%3D%20%5Cfrac%7B21%7D%7B28%7D)
![21n = 18*28](https://tex.z-dn.net/?f=21n%20%3D%2018%2A28)
Simplifying both sides by 7
![3n = 18*4](https://tex.z-dn.net/?f=3n%20%3D%2018%2A4)
Simplifying both sides by 3
![n = 6*4 = 24](https://tex.z-dn.net/?f=n%20%3D%206%2A4%20%3D%2024)
Question 4:
![\frac{n}{4} = \frac{24}{6}](https://tex.z-dn.net/?f=%5Cfrac%7Bn%7D%7B4%7D%20%3D%20%5Cfrac%7B24%7D%7B6%7D)
![\frac{n}{4} = 4](https://tex.z-dn.net/?f=%5Cfrac%7Bn%7D%7B4%7D%20%3D%204)
![n = 16](https://tex.z-dn.net/?f=n%20%3D%2016)
Question 5:
![\frac{10}{16} = \frac{n}{56}](https://tex.z-dn.net/?f=%5Cfrac%7B10%7D%7B16%7D%20%3D%20%5Cfrac%7Bn%7D%7B56%7D)
![16n = 56*10](https://tex.z-dn.net/?f=16n%20%3D%2056%2A10)
Simplifying by 2, both sides
![8n = 56*5](https://tex.z-dn.net/?f=8n%20%3D%2056%2A5)
Simplifying by 8, both sides
![n = 7*5 = 35](https://tex.z-dn.net/?f=n%20%3D%207%2A5%20%3D%2035)