1 )
1st and 2nd equation (multiply 1st by -2 ):
-2x - 10 y + 8 z = 20
2 x - y + 5 z = -9
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- 11 y + 13 z = 11 / * ( -20 )
1st and 3rd:
- 2 x - 10 y + 8 z = 20
2 x - 10 y - 5 z = 0
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- 20 x + 3 z = 20 / * 11
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220 y - 260 z = -220
- 220 y + 33 z = 220
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z = 0, y = -1, x = - 5
2 )
2 x - y + 5 = -4
- 2 x + 3 y - 5 = - 10
Substitution: y = 2 x + 9
- 2 x + 3(2 x + 9 ) = -5
4 x = - 32, x = -8, y = -7, z = 5
3 )
x + y + z = 11
1.5 x+3 y +1.5 z = 21
x = 2 y
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3 y + z = 11 / * (-2)
6 y + 1.5 z = 21
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- 6 y - 2 z = -22
6 y + 1.5 z = 21
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-0.5 z = -1, z = 2, y = 3, z = 6
Answer: the store used 6 pounds of peanuts, 3 pounds of almonds and 2 pounds of raisins.
Answer:
6 ways
Step-by-step explanation:
Given:
Books: Spanish, Maths and History textbooks (1 each)
Required
Determine the number of arrangements
In total, Nathan has 3 books.
The number of arrangements (n) is as follows:
The first book can be lined in 3 ways
The second book can be lined in 2 ways
The third book can be lined in 1 way
So,
Answer:
<h2>
76 cm</h2>
Step-by-step explanation:
Answer:
6 lengths
Step-by-step explanation:
You essentially want the smallest integer solution to ...
60x ≥ 350
x ≥ 350/60
x ≥ 5 5/6
The smallest integer solution to this is x = 6.
The minimum number of lengths of hose needed is 6.
_____
Informally, you know that dividing the required total length by the length of one hose will tell you the number of required hoses. You also know the ratio 350/60 is equivalent to 35/6 and that this will be between 5 and 6. (5·6 = 30; 6·6 = 36) The next higher integer value will be 6.
17.5x12=210
210 divided by 14=15
15x2.50=37.5
37.5
17.5 is feet so you need to divide by 12 for inches which gets 210 and you need each necklace to be 14 inches so you need to divide 210 by 14 which is 15 each necklace costs 2.50 so you multiply 2.50x15
You get 37.5
