A=1x2+2x3+...+98x99

=1x(1+1)+2x(1+2)+...+98x(1+98)

=(1+2+...+98)+(1²+2²+...+98²)

\(=\dfrac{98\times99}{2}+\dfrac{98\times\left(98+1\right)\left(2\times98+1\right)}{6}\)

\(=323400\)

B đúng, hệ đã cho có 1 nghiệm: \(\left\{{}\begin{matrix}x=\dfrac{2019m+7}{4}\\y=\dfrac{-6061m-1}{8}\end{matrix}\right.\)

Mặt có số chấm lẻ là: 1; 3; 5

Số lần xuất hiện mặt có số chấm lẻ:

\(5+3+2=10\) (lần)

Xác suất thực nghiệm xuất hiện mặt có số chấm lẻ:

\(P=\dfrac{10}{22}=\dfrac{5}{11}\)

Chọn A

A

Trong tam giác vuông BDE:

\(DE=\dfrac{BD}{sinE}=\dfrac{1,5}{sin30^0}=3\left(m\right)\)

Trong tam giác vuông ABC:

\(AC=\dfrac{AB}{sinC}=\dfrac{3}{sin60^0}=2\sqrt{3}\left(m\right)\)

Ta có:

\(CE=BE+BC=\dfrac{BD}{tanE}+\dfrac{AB}{tanC}=\dfrac{1,5}{tan30^0}+\dfrac{3}{tan60^0}=\dfrac{5\sqrt{3}}{2}\left(m\right)\)

\(A⋮B\)

=>\(x^4+3x^3-3x^2-ax+b⋮x^2+3x+1\)

=>\(x^4+3x^3+x^2-4x^2-12x-4+\left(12-a\right)x+b+4⋮x^2+3x+1\)

=>12-a=0 và b+4=0

=>\(\left\{{}\begin{matrix}a=12\\b=-4\end{matrix}\right.\)

5x3²=45(dm²)

a.

\(6,1.\left(-5,3\right)+6,1.\left(-4,7\right)=6,1.\left(-5,3-4,7\right)=6,1.\left(-10\right)=-61\)

b.

\(\dfrac{-5}{2}:\left(\dfrac{3}{4}-\dfrac{1}{2}\right)=\dfrac{-5}{2}:\left(\dfrac{3}{4}-\dfrac{2}{4}\right)=\dfrac{-5}{2}:\dfrac{1}{4}=-10\)

\(\dfrac{1}{1+2}+\dfrac{1}{1+2+3}+...+\dfrac{1}{1+2+...+99}\)

\(=\dfrac{1}{2\cdot\dfrac{3}{2}}+\dfrac{1}{3\cdot\dfrac{4}{2}}+...+\dfrac{1}{99\cdot\dfrac{100}{2}}\)

\(=\dfrac{2}{2\cdot3}+\dfrac{2}{3\cdot4}+...+\dfrac{2}{99\cdot100}\)

\(=2\left(\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+...+\dfrac{1}{99\cdot100}\right)\)

\(=2\left(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{99}-\dfrac{1}{100}\right)\)

\(=2\left(\dfrac{1}{2}-\dfrac{1}{100}\right)=1-\dfrac{1}{50}=\dfrac{49}{50}\)

1: \(\left(2,07-3,005\right)-\left(12,005-4,23\right)\)

\(=2,07-3,005-12,005+4,23\)

\(=6,3-15,01\)

=-8,71

2: \(\left(-0,4\right)\cdot\left(-0,5\right)\cdot\left(-0,8\right)\)

\(=-0,4\cdot0,5\cdot0,8\)

\(=-0,2\cdot0,8=-0,16\)

3: \(\left(-0,76\right)+6,72+0,76+\left(-2,72\right)\)

\(=\left(-0,76+0,76\right)+\left(6,72-2,72\right)\)

=0+4

=4