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Nastasia [14]
2 years ago
11

Which size of carton has the lowest price for egg?

Mathematics
1 answer:
Leviafan [203]2 years ago
8 0
D, Each egg costs about 13 cents
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P and q are complex numbers such that ∣p∣ = 2/5 x + 2 , ∣q∣ = −3/4 x − 1 , and ∣p+q∣ = 2x + 4 .
Leya [2.2K]

Answer: (b)

Step-by-step explanation:

Given

\left |  p\right |=\dfrac{2}{5}x+2

\left |  q\right |=\dfrac{-3}{4}x-1

\left |  p+q\right |=2x+4

for two complex number, z_1,z_2

\left |  z_1+z_2\right |\leq \left |  z_1\right |+\left |  z_2\right |

Apply the above the property

\Rightarrow 2x+4\leq \dfrac{2}{5}x+2-\dfrac{3}{4}x-1\\\\\Rightarrow 2x+4\leq \dfrac{8x-15x}{20}+1\\\\\Rightarrow 2x+3\leq -\dfrac{7x}{20}\\\Rightarrow x\leq -\dfrac{60}{47}

Also, the absolute value of each complex number must be greater than or equal to zero

\text{Case-1}\\\\\Rightarrow \dfrac{2}{5}x+2\geq 0\\\\\Rightarrow x\geq -5\\\\\text{Case-2}\\\\\Rightarrow -\dfrac{3}{4}x-1\geq 0\\\\\Rightarrow x\leq -\dfrac{4}{3}\\\\\text{Case-3}\\\\\Rightarrow 2x+4\geq 0\\\Rightarrow x\geq -2

Taking the intersection of the above values of x, we get

x\in [-2,-\dfrac{4}{3}]  

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