Answer:
30
Step-by-step explanation:
The factors of 120 are: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, <u>30</u>, 40, 60, 120
The factors of 150 are: 1, 2, 3, 5, 6, 10, 15, 25, <u>30</u>, 50, 75, 150
Then the greatest common factor is 30.
2,4 and 7 do not form a triangle
To form a triangle, knowing the 3 sides, then
The sum of any 2 sides must be greater than the third side
Consider 2, 4, 7
2 + 4 = 6 < 7
2 + 7 = 9 > 4
4 + 7 = 11 > 2
Since 2 + 4 < 7
Then these 3 sides would not form a triangle
Given the expression (2 + i)(3 - i)(1 + 2i)(1 - i)(3 + i), we are to take the product of all the complex values. We must note that i² = -1.
Rearranging the expression [(3 - i)(3 + i)] [(2 + i)(1 - i)](1 + 2i)
On expansion
(3 - i)(3 + i)
= 9+3i-3i-i²
= 9-(-1)
= 9+1
(3 - i)(3 + i) = 10
For the expression (2 + i)(1 - i), we have;
(2 + i)(1 - i)
= 2-2i+i-i²
= 2-i+1
= 3-i
Multiplying 3-i with the last expression (1 + 2i)
(2 + i)(1 - i)(1 + 2i)
= (3-i)(1+2i)
= 3+6i-i-2i²
= 3+5i-2(-1)
= 3+5i+2
= 5+5i
Finally, [(3 - i)(3 + i)] [(2 + i)(1 - i)(1 + 2i)]
= 10(5+5i)
= 50+50i
Hence, (3 - i)(3 + i)(2 + i)(1 - i)(1 + 2i) is equivalent to 50+50i
Answer: 11 1/7
hope this helps
