– Jack can paint a room in 9 hours alone. If Sara helps, they can do the job in 5 hours. How long

Mathematics

1 answer:

Dafna11 [192]3 years ago

8 0

Answer: 9

Step-by-step explanation:

If Jack can paint the room in 9 hours by his self she can only do the same

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When the sum of 5 and three times a positive number is subtracted from the square of the number, 0 results. Find the number.

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$x-the\ number\\\\x^2-(5+3x)=0\\\\x^2-5-3x=0\\\\x^2-3x-5=0$

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$x^2-3x-5=0\\\\a=1;\ b=-3;\ c=-5\\\\\Delta=(-3)^2-4\cdot1\cdot(-5)+3+20=29 \ \textgreater \ 0\\\\\sqrt\Delta=\sqrt{29}\\\\x_1=\dfrac{3-\sqrt{29}}{2\cdot1}=\dfrac{3-\sqrt{29}}{2} \ \textless \ 0\\\\x_2=\dfrac{3+\sqrt{29}}{2\cdot1}=\dfrac{3+\sqrt{29}}{2} \ \textgreater \ 0$

$Answer:\ \boxed{x=\dfrac{3+\sqrt{29}}{2}}$