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Bài 3:
Gọi số học sinh là x
Theo đề, ta có: \(x-5\in BC\left(8;12;15\right)\)
mà 300<=x<=400
nên x=365
a)\(-1,6:\left(1+\dfrac{2}{3}\right)=-1,6:\dfrac{5}{3}=-\dfrac{8}{5}.\dfrac{3}{5}=\dfrac{-24}{25}\)
b)\(\left(\dfrac{-2}{3}\right)+\dfrac{3}{4}-\left(-\dfrac{1}{6}\right)+\left(\dfrac{-2}{5}\right)=-\dfrac{2}{3}+\dfrac{3}{4}+\dfrac{1}{6}-\dfrac{2}{5}=\dfrac{-40+45+10-24}{60}=\dfrac{-9}{60}=\dfrac{-3}{20}\)
c)\(\left(\dfrac{-3}{7}:\dfrac{2}{11}+\dfrac{-4}{7}:\dfrac{2}{11}\right).\dfrac{7}{33}=\left(\dfrac{-3}{7}.\dfrac{11}{2}+\dfrac{-4}{7}.\dfrac{11}{2}\right).\dfrac{7}{33}=\left[\dfrac{11}{2}\left(\dfrac{-3}{7}+\dfrac{-4}{7}\right)\right].\dfrac{7}{33}=\dfrac{-11}{2}.\dfrac{7}{33}=\dfrac{-7}{6}\)
d)\(\dfrac{-5}{8}+\dfrac{4}{9}:\left(\dfrac{-2}{3}\right)-\dfrac{7}{20}.\left(\dfrac{-5}{14}\right)=\dfrac{-5}{8}-\dfrac{4}{9}.\dfrac{3}{2}+\dfrac{1}{8}=\dfrac{-5}{8}+\dfrac{1}{8}-\dfrac{2}{3}=-\dfrac{7}{6}\)
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Christmas is a magical and enchanting time of year. It is a joyous and festive occasion filled with love, happiness, and excitement. The air is filled with a warm and cozy atmosphere, as families come together to celebrate. The beautifully decorated Christmas tree sparkles with twinkling lights and shimmering ornaments. Delicious and indulgent feasts are prepared, filling the air with mouth-watering aromas. Generosity and kindness abound as people exchange thoughtful and heartfelt gifts. The joyful laughter of children fills the air, accompanied by the melodic sounds of Christmas carols. The winter scenery is breathtaking, with glistening snowflakes and frosty landscapes. The spirit of Christmas is truly magical, bringing warmth, joy, and togetherness to all.
Gọi số sản phẩm mỗi ngày phải sản xuất theo kế hoạch là x(sản phẩm)
(Điều kiện: \(x\in Z^+\))
Số ngày dự kiến sẽ hoàn thành là \(\dfrac{1100}{x}\left(ngày\right)\)
Số sản phẩm thực tế làm được trong 1 ngày là x+5(sản phẩm)
Số ngày thực tế hoàn thành là \(\dfrac{1100}{x+5}\left(ngày\right)\)
Theo đề, ta có phương trình:
\(\dfrac{1100}{x}-\dfrac{1100}{x+5}=2\)
=>\(\dfrac{550}{x}-\dfrac{550}{x+5}=1\)
=>\(\dfrac{550x+2750-550x}{x\left(x+5\right)}=1\)
=>\(x\left(x+5\right)=2750\)
=>\(x^2+5x-2750=0\)
=>(x+55)(x-50)=0
=>\(\left[{}\begin{matrix}x=-55\left(loại\right)\\x=50\left(nhận\right)\end{matrix}\right.\)
Vậy: Mỗi ngày theo kế hoạch phải làm được 50 sản phẩm