The answer for the exercise shown above is the option B, which is:
<span> B. log5(7)+5log5(a)
The explanation of the problem is shown below:
1. You have the following expression given in the problem above:
</span><span>log5(7)(a^5)
2. To expand it, you must use the logaritms properties, as following:
</span> log5(7)(a^5)
log5(7)+log5(a^5)
log5(7)+5log5(a)
3. Therefore, as you can see, the answer is the option B.
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</span>
Dale drove to the mountains last weekend. there was heavy traffic on the way there, and the trip took 7 hours. when dale drove home, there was no traffic and the trip only took 5 hours. if his average rate was 18 miles per hour faster on the trip home, how far away does dale live from the mountains? do not do any rounding.
Answer:
Dale live 315 miles from the mountains
Step-by-step explanation:
Let y be the speed of Dale to the mountains
Time taken by Dale to the mountains=7 hrs
Therefore distance covered by dale to the mountain = speed × time = 7y ......eqn 1
Time taken by Dale back home = 5hours
Since it speed increased by 18 miles per hour back home it speed = y+18
So distance traveled home =speed × time = (y+18)5 ...... eqn 2
Since distance cover is same in both the eqn 1 and eqn 2.
Eqn 1 = eqn 2
7y = (y+18)5
7y = 5y + 90
7y - 5y = 90 (collection like terms)
2y = 90
Y = 45
Substitute for y in eqn 1 to get distance away from mountain
= 7y eqn 1
= 7×45
= 315 miles.
∴ Dale leave 315 miles from the mountains
Answer:
$270
Step-by-step explanation:
We are given;
- The rate of increase is 8%
- The new amount is $250
We need to determine the value in the next year with the same rate of increase;
Therefore;
250% = 100%
New amount = 100 + 8 = 108%
Therefore;
New amount = (250 × 108)÷ 100
= $270
Therefore, the value in the next year is $270
Answer:
15
Step-by-step explanation:
Set the number of children to n.
The number of adults is, thus, n + 25.
The total price of admission is $720, made up of adult tickets and child tickets.
The children paid $8 per child, or
8 * n
The adults paid $15 per adult, or
15 * (n + 25)
These sum of these is equal to the total cost of $720.
8*n + 15*(n + 25) = 720
8n + 15(n + 25) = 720
Multiplying 15 with both n and 25.
8n + 15n + 25*15 = 720
8n + 15n + 375 = 720
Subtracting 375 from both sides.
8n + 15n + 375 - 375 = 720 - 375
8n + 15n = 345
Adding together 8n and 15n.
23n = 345
Dividing both sides by 23.
n = 345/23 = 15
n = 15
As n is the number of children, there are 15 children in the group.
Answer: 15
