Answer:
Step-by-step explanation:
The given hexagon has interior angles
x,x,x, x/2, x/2, x/2 for a total of S1=4.5x.
We also know that the sum of interior angles of any polygon of n sides is
S2=180(n-2)
For a hexagon, S2 = 180(6-2) = 720°.
Equating S1 and S2
4.5x = 720
x = 720/4.5 = 160.
Therefore substitute x in the given angles to get
{160°,160°.160°,80°,80°,80°}
Answer: 132 degrees
Explanation: a straight line has 180 degrees in it, take away the 48 leaves you with 132.
Answer:
$6000
Step-by-step explanation:
Given the following :
Total planned amount to invest = 10,000 in two funds:
Fund A at rates 4.5% and
Fund B at 5% simple interest
Total Annual Interest should be = 480
What is the smallest amount you can invest in the 5% fund and still meet your objective?
Let ;
Investment in fund A = principal = a at 4.5%(0.045)
Investment in fund B = principal = (10000 - a) at 5%(0.05)
Simple interest = principal * rate * time
a + (10000 - a) = 10000
(a * 0.045) + (10000 - a) * 0.05 = 480
0.045a + 500 - 0.05a = 480
-0.005a = 480 - 500
-0.005a = - 20
a = 20 / 0.005
a = 4000
4000 at 4.5%
Investment in fund B = principal = (10000 - a)
(10,000 - 4000) = 6000
It is often easiest to use "military time". That is, add 12 to all the afternoon numbers and do the subtraction in the usual way. Of course, 1 hour = 60 minutes, so 10 minutes = 10/60 hour = 1/6 hour.
Mon: 15:10 -8:00 = 7:10 = 7 1/6
Tue: 15:25 -8:05 = 7:20 = 7 1/3
Wed: 14:30 -8:00 = 6:30 = 6 1/2
Thur: 14:45 -7:55 = 7:(-10) = 6:50 = 6 5/6
Fri: 15:38 -7:58 = 8:(-20) = 7:40 = 7 2/3
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Some calculators have nice features for working with degrees, minutes, and seconds. In this context, degrees and hours are the same thing. That is, the base-60 arithmetic is the same whether you consider the numbers to be hours or degrees. Similarly, some calculators convert nicely between decimal fractions and mixed numbers. In short, a suitable calculator will almost do this math for you. (You just need to add 12 to all the numbers in the column on the right.)
