(3/4)*{(1/3)*[8^2+(24/6*4)+10]+[(2/5)*(10^2-12+3)]}

asked by guest
on Nov 15, 2024 at 3:51 am



You asked:

Evaluate the expression: 34(13(82+246⋅4+10)+25(102−12+3))\frac{3}{4} \left(\frac{1}{3} \left({8}^{2} + \frac{24}{6} \cdot 4 + 10\right) + \frac{2}{5} \left({10}^{2} - 12 + 3\right)\right)

MathBot Answer:

34(13(82+246⋅4+10)+25(102−12+3))=2495=49.8\frac{3}{4} \left(\frac{1}{3} \left({8}^{2} + \frac{24}{6} \cdot 4 + 10\right) + \frac{2}{5} \left({10}^{2} - 12 + 3\right)\right) = \frac{249}{5} = 49.8

34(13(82+246⋅4+10)+25(102−12+3))=34(13(64+246⋅4+10)+25(102−12+3))=34(13(64+4⋅4+10)+25(102−12+3))=34(13(64+16+10)+25(102−12+3))=34(13(80+10)+25(102−12+3))=34(13⋅90+25(102−12+3))=34(30+25(102−12+3))=34(30+25(100−12+3))=34(30+25(88+3))=34(30+25⋅91)=34(30+1825)=34⋅3325=2495\begin{aligned}\frac{3}{4} \left(\frac{1}{3} \left({8}^{2} + \frac{24}{6} \cdot 4 + 10\right) + \frac{2}{5} \left({10}^{2} - 12 + 3\right)\right)&=\frac{3}{4} \left(\frac{1}{3} \left(64 + \frac{24}{6} \cdot 4 + 10\right) + \frac{2}{5} \left({10}^{2} - 12 + 3\right)\right)\\&=\frac{3}{4} \left(\frac{1}{3} \left(64 + 4 \cdot 4 + 10\right) + \frac{2}{5} \left({10}^{2} - 12 + 3\right)\right)\\&=\frac{3}{4} \left(\frac{1}{3} \left(64 + 16 + 10\right) + \frac{2}{5} \left({10}^{2} - 12 + 3\right)\right)\\&=\frac{3}{4} \left(\frac{1}{3} \left(80 + 10\right) + \frac{2}{5} \left({10}^{2} - 12 + 3\right)\right)\\&=\frac{3}{4} \left(\frac{1}{3} \cdot 90 + \frac{2}{5} \left({10}^{2} - 12 + 3\right)\right)\\&=\frac{3}{4} \left(30 + \frac{2}{5} \left({10}^{2} - 12 + 3\right)\right)\\&=\frac{3}{4} \left(30 + \frac{2}{5} \left(100 - 12 + 3\right)\right)\\&=\frac{3}{4} \left(30 + \frac{2}{5} \left(88 + 3\right)\right)\\&=\frac{3}{4} \left(30 + \frac{2}{5} \cdot 91\right)\\&=\frac{3}{4} \left(30 + \frac{182}{5}\right)\\&=\frac{3}{4} \cdot \frac{332}{5}\\&=\frac{249}{5}\end{aligned}

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