Answer:
<u>It takes them 30/11 hours to paint them together.</u>
Step-by-step explanation:
This is known as a work problem (rate * time = work). We are given the individual times for Tom and Huck (6 hours and 5 hours respectively). However, we are not given the rates at which they can paint the fence. Since we know that the total work that they both do individually is 1 (there is 1 job to do), we can calculate the rates at which Tom and Huck paint the fence on their own:
![Tom: R_{T}*6=1\\Huck: R_{H}*5=1](https://tex.z-dn.net/?f=Tom%3A%20R_%7BT%7D%2A6%3D1%5C%5CHuck%3A%20R_%7BH%7D%2A5%3D1)
We can isolate R{t} and R{h} to find the rates at which Tom and Huck work:
![Tom: R_{T}=\frac{1}{6}\\Huck: R_{H}=\frac{1}{5}](https://tex.z-dn.net/?f=Tom%3A%20R_%7BT%7D%3D%5Cfrac%7B1%7D%7B6%7D%5C%5CHuck%3A%20R_%7BH%7D%3D%5Cfrac%7B1%7D%7B5%7D)
Now, we can calculate the time it takes for Tom and Huck to work together using the same formula (the combined rate is just the sum of Tom and Huck's individual rates):
![(\frac{1}{6} +\frac{1}{5})*T=1\\\\T*(11/30)=1 , T = 30/11](https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7B6%7D%20%2B%5Cfrac%7B1%7D%7B5%7D%29%2AT%3D1%5C%5C%5C%5CT%2A%2811%2F30%29%3D1%20%2C%20T%20%3D%2030%2F11)
Therefore, the time it takes them to paint the fence together is <u>30/11 Hours</u>
Answer:
x-2i
Step-by-step explanation:
Complex roots come in pairs, called complex conjugates
If you have a root a+bi, the other root is a-bi
Since you have one root x+2i, the other root is x-2i
The set of points that represents a function is given by:
A {(2, 1), (7, 9), (3, 12), (4, 10)}.
<h3>When does a relation represents a function?</h3>
A set, or a relation, represents a function when <u>each value of x is mapped to only one value of y</u>.
In this problem, we have that option A represents a function, as:
- In option B, x = 2 and x = -2 are mapped to two values.
- In option C, x = 4 is mapped to four values.
- In option D, both x = 1 and x = 2 are mapped to two values.
Hence the set of points that represents a function is given by:
A {(2, 1), (7, 9), (3, 12), (4, 10)}.
More can be learned about relations and functions at brainly.com/question/12463448
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