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3 years ago

Factor completely B. (x+5)²-2(x+5)-24 C. (x+2)²-8(x+2)+15 D. 2(2x-1)²-9(2x-1)+4

Mathematics

1 answer:

MatroZZZ [7]3 years ago

5 0

Ok I don’t use this to answer math questions
But you could use
Photomath in the AppStore

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Answer: Time taken by Ximena to paint the fence alone = 24 hours

Time taken by Candice to paint the fence alone = 12 hours

Step-by-step explanation:

Let x= Time taken by Ximena to paint the fence alone .

Time taken by Candice to paint the fence alone = x-12

As per given , we have

$\dfrac{1}{x}+\dfrac{1}{x-12}=\dfrac{1}{8}\\\\\Rightarrow\ \dfrac{x-12+x}{x(x-12)}=\dfrac{1}{8}\\\\\Rightarrow\ 8(2x-12)=x^2-12x\\\\\Rightarrow\ 16x-96=x^2-12x\\\\\Rightarrow\ x^2-12x-16x+96=0\\\\\Rightarrow\ x^2-28x+96=0\\\\\Rightarrow\ x^2-4x-24x+96=0\\\\\Rightarrow\ x(x-4)-24(x-4)=0\\\\\Rightarrow\ (x-4)(x-24)=0\\\\\Rightarrow x=4, 24$

if x= 4

Time taken by Ximena = 4 hours

Time taken by Candice = 4-12 hours =-8 hours which is not possible. (time cannot be negative)

Therefore, x= 24

Such that

Time taken by Ximena to paint the fence alone = 24 hours

Time taken by Candice to paint the fence alone = 24-12=12 hours

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