The net for a triangular prism consists of
2 identical triangles, here all nets have sides 5,12, and 13.
3 rectangles, all with a common dimension: the height H=14 of the prism.
Each of the 3 rectangles should have dimensions
H=14 plus one of the following:
each of 5, 12, 13 corresponding to one side of the base (triangle).
So the dimensions of the rectangles are
5x14, 12x14, 13x14
And dimensions of the triangles are
5,12 and 13.
The total surface area is therefore
(5+12+13)*14 + 2*(5*12/2)
=420+60
=480.
There is only one net that satisfies this condition.
<span>Equation:
0.15x + 0.10(5-x) = 0.11*5
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Multiply thru by 100:
15x + 10*5 - 10x = 11*5
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5x = 5
x = 1 liter (amt. 15% oj needed)
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5-x = 4 liters (amt of 10% oj needed)
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Answer:
1,750 ÷5= 350
Step-by-step explanation:
there are 350 calories in each serving 1,750 is the total
True!! If you multiply -3 x -7 you get 21!!
Answer:
α² +β² = 3 4/9
Step-by-step explanation:
Assuming α and β are solutions to the equation, it can be factored as ...
(x -α)(x -β) = 0
Expanding this, we get ...
x² -(α +β)x +αβ = 0
Dividing the original equation by 3, we find ...
x² +(1/3)x -5/3 ≡ x² -(α+β)x +αβ ⇒ (α+β) = -1/3, αβ = -5/3
We know that the square (α+β)² can be expanded to ...
(α +β)² = α² +β² +2αβ
α² +β² = (α +β)² -2αβ . . . . . . subtract 2αβ
Substituting the values for (α+β) and αβ, we find the desired expression is ...
α² +β² = (-1/3)² -2(-5/3) = 1/9 +10/3 = 31/9
α² +β² = 3 4/9
