Multiply the horizontal side by the vertical side to find the area
<h3>
Answer: D) 3/150</h3>
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Explanation:
With the use of a calculator, we see that,
- 11/19 = 0.57894736842106...., the decimals eventually repeat; but unfortunately my calculator ran out of room to show the repeating portion
- 4/7 = 0.5714285714285714..., the block "571428" repeats forever
- 1/3 = 0.333333.... the 3s go on forever
- 3/150 = 0.02
So 3/150 converts to the terminating decimal 0.02
The word "terminate" means "stop". In the other decimal values, the decimal digits go on forever repeating the patterns mentioned.
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A non-calculator approach will have us simplify 3/150 into 1/50 after dividing both parts by the GCF 3. Then notice how 50 has the prime factorization of 2*5*5. The fact that the denominator 50 can be factored in terms of only 2's and 5's is enough evidence to conclude that the fraction converts to a terminating decimal.
If the denominator factors into some other primes, other than 2s and 5s, then we don't have a terminating decimal. So that's why 11/19, 4/7 and 1/3 convert to non-terminating decimals.
All the triangles are similar, so the ratio of (long leg)/(short leg) is the same. The long leg of ΔADB is
.. AD = AC -DC = 20 -4
.. AD = 16
Then
.. (long leg)/(short leg) = AD/DB = BD/DC
.. 16/h = h/4
.. h^2 = 64
.. h = 8
Selection D is appropriate.
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You may see this again. The altitude (h) from the right angle in a right triangle is the geometric mean of segments AD and DC. That is,
.. h = √((AD)*(DC))
<u>Answer</u>
6,122 hm
<u>Explanation</u>
You can carry out operations on the like terms only. So convert all units to one unit.
I will convert them to dam
1 km =100 dam
73 km = 73 × 100
=7,300 dam
11 km = 11× 100
1100 dam
1 hm = 10 dam
47 hm = 47 × 10
= 470 dam
55 hm = 55× 10
= 550 dam
73km 47hm 2dam - 11km 55hm = (7300+ 470+2) - (1100+550)
= 7,772 - 1,650
= 6,122 hm
1a) 8 / (1/2) = 16 * 3 = 48
1b) 3sqrt(49) = 3 * 7 = 21
1c) (5+2)(-8) / (-2)^3 -3
(7*-8) / (-8 -3)
-56/-11
56/11
