Answer:
X = 156
Step-by-step explanation:
52 is a factor of 52, 104, 156, and 208
78 is a factor of 78, 156, and 234.
The commonality here is 156.
The x-intercept is (-12, 0)
The y-intercept is (0, -6)
Let me know if you want to see how I answered it
Using linear functions, it is found that the two planes will be at the same altitude in 7 minutes.
<h3>What is a linear function?
</h3>
A linear function is modeled by:
In which:
- m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
- b is the y-intercept, which is the value of y when x = 0.
For the first plane:
- Initial altitude of 1000 meters, hence
.
- Ascending t a rate of 400 meters per minute, hence
.
Hence, the equation is:
![y_1(x) = 400x + 1000](https://tex.z-dn.net/?f=y_1%28x%29%20%3D%20400x%20%2B%201000)
For the second plane:
- Initial altitude of 5900 meters, hence
.
- Descending t a rate of 300 meters per minute, hence
.
Hence, the equation is:
![y_2(x) = -300x + 5900](https://tex.z-dn.net/?f=y_2%28x%29%20%3D%20-300x%20%2B%205900)
They will be at the same altitude at the value of x for which:
![y_1(x) = y_2(x)](https://tex.z-dn.net/?f=y_1%28x%29%20%3D%20y_2%28x%29)
Hence:
![400x + 1000 = -300x + 5900](https://tex.z-dn.net/?f=400x%20%2B%201000%20%3D%20-300x%20%2B%205900)
![700x = 4900](https://tex.z-dn.net/?f=700x%20%3D%204900)
![x = \frac{4900}{700}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B4900%7D%7B700%7D)
![x = 7](https://tex.z-dn.net/?f=x%20%3D%207)
The two planes will be at the same altitude in 7 minutes.
To learn more about linear functions, you can take a look at brainly.com/question/25823744
You would have to divide 100,000 by 467 which is 214.1327623 then round up so no one is left behind so you would have to make 215 trips
Answer:
Explanation:
12x = 48 - 8y
10x + 8y = 38
———————
12x + 8y = 48
10x + 8y = 38
———————
12x + 8y = 48
-1(10x + 8y = 38)
————————
12x + 8y = 48
-10x - 8y = -38
————————
2x = 10
x = 10/2 = 5
If x = 5 then:
10x + 8y = 38
10(5) + 8y = 38
50 + 8y = 38
8y = 38 - 50
8y = -12
y = -12/8
y = -3/2
Therefore, x = 5 and y = -3/2