Answer:
2870 miles and 210 miles per hour
Step-by-step explanation:
Multiply 2 hours by 7 to get to 14, so you multiply 410 by 7 to get to 2870 miles. 410/2 equals 210 miles per hour
Look at the picture the answer is there
Answer:
The correct ratio is 7:8, so no, Emma is not correct.
SOLUTION
From the question, we are told that y varies inversely as x
This is mathematically written as
![\begin{gathered} y\propto\frac{1}{x} \\ \propto\text{ is a sign of proportionality } \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20y%5Cpropto%5Cfrac%7B1%7D%7Bx%7D%20%5C%5C%20%5Cpropto%5Ctext%7B%20is%20a%20sign%20of%20proportionality%20%7D%20%5Cend%7Bgathered%7D)
Now, we will remove the proportionality sign and replace it with equal to sign =
If we do this, we will intoduce a constant k
![\begin{gathered} y\propto\frac{1}{x} \\ y=k\times\frac{1}{x} \\ y=\frac{k}{x} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20y%5Cpropto%5Cfrac%7B1%7D%7Bx%7D%20%5C%5C%20y%3Dk%5Ctimes%5Cfrac%7B1%7D%7Bx%7D%20%5C%5C%20y%3D%5Cfrac%7Bk%7D%7Bx%7D%20%5Cend%7Bgathered%7D)
So we have the formula
![y=\frac{k}{x}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7Bk%7D%7Bx%7D)
We will substitute the values of x for 10 and y for 8 into the formula to get k, we have
![\begin{gathered} y=\frac{k}{x} \\ 8=\frac{k}{10} \\ k=8\times10 \\ k=80 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20y%3D%5Cfrac%7Bk%7D%7Bx%7D%20%5C%5C%208%3D%5Cfrac%7Bk%7D%7B10%7D%20%5C%5C%20k%3D8%5Ctimes10%20%5C%5C%20k%3D80%20%5Cend%7Bgathered%7D)
Now, we will substitute k for 80 back into the formula to get the inverse function, we have
![\begin{gathered} y=\frac{k}{x} \\ y=\frac{80}{x} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20y%3D%5Cfrac%7Bk%7D%7Bx%7D%20%5C%5C%20y%3D%5Cfrac%7B80%7D%7Bx%7D%20%5Cend%7Bgathered%7D)
Hence the answer is option C