12.15 km /h
Step-by-step explanation:
Step 1 :
Given
Distance between Airy Town to Brightvale = 9 km
Speed of Ricky = x km/h
Step 2:
Speed taken by Sam = x + y km/h
Time taken by Sam = 40 min = 40/60 hrs = 2/3 hrs
so we have (x+y) 2/3 = 9
Step 3:
Speed taken by Timothy = x - y km / h
Time taken by Timothy = 50 min = 50/60 = 5/6 hrs
= > (x-y) 5/6 = 9
Step 4 :
Solving the 2 equations
(x+y) 2/3 = 9 and (x-y) 5/6 = 9 we have
(2/3)x + 2/3(y) = 9 = > 2x + 2 y = 27
5/6(x) - 5/6(y) = 9 = > 5 x - 5 y = 54
Multiplying the first equation by 5 and the second by 2 we have ,
10 x + 10 y = 135 and 10 x - 10y = 108
Adding both,
20 x = 243 => x = 12.15.
This gives speed of Ricky as 12.15 km /h
For this case we must find an expression equivalent to:
![(x ^ {\frac {4} {3}} * x ^ {\frac {2} {3}}) ^ {\frac {1} {3}}](https://tex.z-dn.net/?f=%28x%20%5E%20%7B%5Cfrac%20%7B4%7D%20%7B3%7D%7D%20%2A%20x%20%5E%20%7B%5Cfrac%20%7B2%7D%20%7B3%7D%7D%29%20%5E%20%7B%5Cfrac%20%7B1%7D%20%7B3%7D%7D)
By definition of power properties we have to:
![(a ^ n) ^ m = a ^ {n * m}](https://tex.z-dn.net/?f=%28a%20%5E%20n%29%20%5E%20m%20%3D%20a%20%5E%20%7Bn%20%2A%20m%7D)
So, rewriting the expression we have:
![x ^ {\frac {4} {3 * 3}} * x ^ {\frac {2} {3 * 3}} =](https://tex.z-dn.net/?f=x%20%5E%20%7B%5Cfrac%20%7B4%7D%20%7B3%20%2A%203%7D%7D%20%2A%20x%20%5E%20%7B%5Cfrac%20%7B2%7D%20%7B3%20%2A%203%7D%7D%20%3D)
![x ^ {\frac {4} {9}} * x ^ {\frac {2} {9}} =](https://tex.z-dn.net/?f=x%20%5E%20%7B%5Cfrac%20%7B4%7D%20%7B9%7D%7D%20%2A%20x%20%5E%20%7B%5Cfrac%20%7B2%7D%20%7B9%7D%7D%20%3D)
By definition of multiplication of powers of the same base, we put the same base and add the exponents:
![x ^ {\frac {4} {9} + \frac {2} {9}} =\\x ^ {\frac {4 + 2} {9}} =\\x ^ {\frac {6} {9}} =\\x ^ {\frac {2} {3}}](https://tex.z-dn.net/?f=x%20%5E%20%7B%5Cfrac%20%7B4%7D%20%7B9%7D%20%2B%20%5Cfrac%20%7B2%7D%20%7B9%7D%7D%20%3D%5C%5Cx%20%5E%20%7B%5Cfrac%20%7B4%20%2B%202%7D%20%7B9%7D%7D%20%3D%5C%5Cx%20%5E%20%7B%5Cfrac%20%7B6%7D%20%7B9%7D%7D%20%3D%5C%5Cx%20%5E%20%7B%5Cfrac%20%7B2%7D%20%7B3%7D%7D)
Answer:
Option B
Step-by-step explanation:
Yᴏᴜʀ ᴀɴsᴡᴇʀ ɪs ɪɴ ᴛʜᴇ ᴀᴛᴛᴀᴄʜᴍᴇɴᴛ...
Hᴏᴘᴇ ɪᴛ ʜᴇʟᴘs ʏᴏᴜ
Answer:
(a)5 and 8
(b)5 and 5
(c) 7 and 5
(d)6 and 2
(e)6 and -2
Step-by-step explanation:
(a)a negative integer
We consider the integers 5 and 8
Difference = 5-8 =-3
3 is a negative integer.
(b)Zero
We consider the integers 5 and 5
Difference = 5-5 =0
(c) an integer smaller than both the integer.
We consider the integers 7 and 5
Difference = 7-5 =2
2 is smaller than both integers.
(d) an integer smaller than only one of the integers.
We consider the integers 6 and 2
Difference =6-2=4
4 is smaller than only 6.
(e)an integer greater than both the integers
We consider the integers 6 and -2
Difference =6-(-2)=6+2=8
8 is greater than both 6 and -2.