This equates to the division problem 54/3, which is equal to 18.
It would take them 18 weeks to frame all 54 houses.
Let's see.
Let's look at the first 10 natural numbers raised to the 4th power.
1^4 = 1 * 1 * 1 * 1 = 1
2^4 = 2 * 2 * 2 * 2 = 16
3^4 = 3 * 3 * 3 * 3 = 81
4^4 = 4 * 4 * 4 * 4 = 256
5^4 = 5 * 5 * 5 * 5 = 625
6^4 = 6 * 6 * 6 * 6 = 1296
7^4 = 7 * 7 * 7 * 7 = 2401
8^4 = 8 * 8 * 8 * 8 = 4096
9^4 = 9 * 9 * 9 * 9 = 6561
10^4 = 10 * 10 * 10 * 10 = 10000
Notice that of the first 10 natural numbers raised to the 4th power, only 5^4 and 10^4 do not have a 1 or a 6 as its units digit. All other 8 numbers have a 1 or a 6 as their units digit.
Now think of 11. If you raise 11 to the 4th power, it will end in 1 just 1^4 does. 12^4 will end in 6 just like 2^4 does. This holds true for the 4th powers of all of the natural numbers. Every natural number that ends in 1 has a 4th power that ends in 1. Every natural number that ends in 2 has a 4th power that ends in 6, etc. Since 8 out of 10 4th powers have a 1 or a 6 in the units digit, then out of 1000, you get 8/10 * 1000 = 800.
Answer:
- BC = 6
- x = 5
- CE = 16
- Yes, BC║DE
Step-by-step explanation:
1. The parallel lines make the various triangles similar, so the corresponding sides are in proportion.
... BC/AB = FE/A.F
... BC/9 = 4/6
... BC = 9·4/6 = 6
2. As in problem 1, the triangles are similar, so ...
... x/(x+10) = 10/30
... 30x = 10x + 100 . . . . multiply by 30(x+10)
... 20x = 100 . . . . . . . . . subtract 10x
... x = 100/20 = 5
3. As in problems 1 and 2, the triangles are similar, so ...
... AD/DB = CE/EB
... 24/27 = CE/18
... 18·24/27 = CE = 16
4. If the lines of interest are parallel, the triangles will be similar and corresponding measures will be in proportion.
Compare AD/DB = 15/12 = 5/4 to AE/EC = 10/8 = 5/4. These are equal, so corresponding measures are proportional. Therefore we conclude the triangles are similar and BC║DE.
9. Commutative Law, 11. Multiplicative Identity Property, 13. Distributive Law, 15. Inverse Property of Addition, 17. Commutative Law, 19. Distributive property (?)
Good luck, hope this helps!!
Answer:
25 ft
Step-by-step explanation:
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