Answer:
Step-by-step explanation:
apply the inverse properties of logarithmic and exponential functions to simplify
all logs has base 'e'
Inverse property of log says that
, the value of ln e=1
we apply this property in our problem. ln has same base 'e' . ln and 'e' gets cancelled
Before combining the real parts and the imaginary parts, line them up vertically as follows:
4 + 4i
-13 - 17i
-------------- Now add up each column.
-9 - 13i (Answer A)
Answer:
Step-by-step explanation:
<u><em>
Options are:
</em></u>
- <em>2 feet
</em>
- <em>3 feet
</em>
- <em>9 feet
</em>
- <em>15 feet
</em>
- <em>19 feet
</em>
- <em>21 feet
</em>
- <em>30 feet</em>
<em>-------------------------------------</em>
Use the triangle inequality theorem: sum of any two side must be greater than the third side by length
- 2 feet ⇒ no, as 2 + 9 < 12
- 3 feet ⇒ no, as 3 + 9 = 12
- 9 feet ⇒ yes
- 15 feet ⇒ yes
- 19 feet ⇒ yes
- 21 feet ⇒ no, as 9 + 12 = 21
- 30 feet ⇒ no, as 9 + 12 < 30
Website A:
c = 10 + 0.25 s
where c is the cost and s is the number of songs.
Website B:
c = 0.75 s
The equation ( answer ):
10 + 0.25 s = 0.75 s
We can solve this equation:
10 = 0.5 s
s = 10 : 0.5
s = 20 ( Marvin would have to buy 20 songs to to make the costs equal )
Answer: the cost of one medium sized jug is $60
the cost of one large sized jug is $10
Step-by-step explanation:
Let x represent the cost of one medium sized jug.
Let y represent the cost of one large sized jug.
Jack bought 2 medium sized jugs and 3 large sized jugs for 150 dollars. This means that
2x + 3y = 150 - - - - - - - - - - - 1
Jill bought 4 medium jugs and 12 large jugs for 360 dollars. This means that
4x + 12y = 360 - - - - - - - - - - - 2
Multiplying equation 1 by 4 and equation 2 by 2, it becomes
8x + 12y = 600
8x + 24y = 720
Subtracting, it becomes
- 12y = - 120
y = - 120/ - 12
y = 10
Substituting y = 10 into equation 1, it becomes
2x + 3 × 10 = 150
2x + 30 = 150
2x = 150 - 30 = 120
x = 120/2 = 60
