Answer:
8 + 4i
Step-by-step explanation:
Put corresponding terms above each other and subtract in the usual way.
z = 3 + 5i
<u> w = -5 + i
</u>
z - w = 8 + 4i: 3 - (-5} = 8; 5i - 1i = 4
i
The answer is 41 miles
Imagine the diagonal distance is called c
Using Pythagorean theorem 40^2 + 9^2 = c^2
1600 + 81 = c^2
The square root of 1681 is 41
So c = 41
Answer:
b
Step-by-step explanation:
denominator(5) stays the same
multiply 2 by 4 since that is 1 fourth of an hour.
So now its 8/5
5 goes into 8 1 time with 3 leftover
So the 1 is a whole number now
the leftover fraction 3/5
=1 3/5
Answer:
Please see attached graph
Step-by-step explanation:
We know that the equation tht represents the boats avlue is given by
A(x) = 400(b)^x + 0 = 400(b)^x
A(x) = 400(b)^x
An increment in the rate of 25% a yeard is given by
b = 1.25
A(x) = 400(1.25)^x
Which graph can be seen below
Answer:
rate of the plane in still air is 33 miles per hour and the rate of the wind is 11 miles per hour
Step-by-step explanation:
We will make a table of the trip there and back using the formula distance = rate x time
d = r x t
there
back
The distance there and back is 264 miles, so we can split that in half and put each half under d:
d = r x t
there 132
back 132
It tells us that the trip there is with the wind and the trip back is against the wind:
d = r x t
there 132 = (r + w)
back 132 = (r - w)
Finally, the trip there took 3 hours and the trip back took 6:
d = r * t
there 132 = (r + w) * 3
back 132 = (r - w) * 6
There's the table. Using the distance formula we have 2 equations that result from that info:
132 = 3(r + w) and 132 = 6(r - w)
We are looking to solve for both r and w. We have 2 equations with 2 unknowns, so we will solve the first equation for r, sub that value for r into the second equation to solve for w:
132 = 3r + 3w and
132 - 3w = 3r so
44 - w = r. Subbing that into the second equation:
132 = 6(44 - w) - 6w and
132 = 264 - 6w - 6w and
-132 = -12w so
w = 11
Subbing w in to solve for r:
132 = 3r + 3(11) and
132 = 3r + 33 so
99 = 3r and
r = 33
