Cho tích 34x44x54x64x.....2024 có chữ số tận cùng là mấy?
Giúp m vơi
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
a: \(\left[\left(-21,8\right)+4,125\right]+\left[11,8+\left(-2,125\right)\right]\)
=-21,8+4,125+11,8-2,125
=(4,125-2,125)+(-21,8+11,8)
=2-10
=-8
b: \(\left(-124,5\right)+\left(-6,24+124,5\right)\)
\(=-124,5-6,24+124,5\)
=-6,24
\(a,\left[\left(-21,8\right)+4,125\right]+\left[11,8+\left(-2,125\right)\right]\)
\(=-21,8+4,125+11,8-2,125\)
\(=\left[\left(-21,8\right)+11,8\right]+\left(4,125-2,125\right)\)
\(=-10+2\)
\(=-8\)
\(b,\left(-124,5\right)+\left(-6,24+124,5\right)\)
\(=-124,5-6,24+124,5\)
\(=\left[\left(-124,5\right)+124,5\right]-6,24\)
\(=0-6,24\)
\(=-6,24\)
$\color{#90EE90}{\text{4}}$ $\color{#B0E0E6}{\text{56}}$
a: \(\left\{{}\begin{matrix}2\left(x+y\right)+3\left(x-y\right)=4\\\left(x+y\right)+2\left(x-y\right)=5\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}2x+2y+3x-3y=4\\x+y+2x-2y=5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}5x-y=4\\3x-y=5\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}5x-y-3x+y=4-5\\3x-y=5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x=-1\\y=3x-5\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=-\dfrac{1}{2}\\y=3x-5=-\dfrac{3}{2}-5=-\dfrac{13}{2}\end{matrix}\right.\)
b: \(\left\{{}\begin{matrix}\left(x+1\right)\left(y-1\right)=xy-1\\\left(x-3\right)\left(y+3\right)=xy-3\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}xy-x+y-1=xy-1\\xy+3x-3y-9=xy-3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}-x+y=0\\3x-3y=-3+9=6\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=y\\x-y=2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x-y=0\\x-y=2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}0=2\left(vôlý\right)\\x=y\end{matrix}\right.\)
vậy: Hệ vô nghiệm
a)
\(\left\{{}\begin{matrix}2\left(x+y\right)+3\left(x-y\right)=4\\\left(x+y\right)+2\left(x-y\right)=5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x+2y+3x-3y=4\\x+y+2x-2y=5\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}5x-y=4\\3x-y=5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x=-1\\3x-y=5\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x=-\dfrac{1}{2}\\-\dfrac{3}{2}-y=5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-\dfrac{1}{2}\\y=-\dfrac{3}{2}-5=-\dfrac{13}{2}\end{matrix}\right.\)
b)
\(\left\{{}\begin{matrix}\left(x+1\right)\left(y-1\right)=xy-1\\\left(x-3\right)\left(y+3\right)=xy-3\end{matrix}\right. \Leftrightarrow\left\{{}\begin{matrix}xy-x+y-1=xy-1\\xy+3x-3y-9=xy-3\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}-x+y=0\\3x-3y=6\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}-x+y=0\\x-y=2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x-y=0\\x-y=2\end{matrix}\right.\)
mà: 2 khác 0
=> Hpt vô nghiệm
Số phần quyển sách còn lại sau ngày thứ nhất là:
\(1-40\%=60\%=\dfrac{3}{5}\)
Số phần quyển sách còn lại sau ngày thứ hai là:
\(\dfrac{3}{5}\times\left(1-60\%\right)=\dfrac{3}{5}\times\dfrac{2}{5}=\dfrac{6}{25}\)
Số phần quyển sách còn lại sau ngày thứ ba là:
\(\dfrac{6}{25}\times\left(1-80\%\right)=\dfrac{6}{25}\times\dfrac{1}{5}=\dfrac{6}{125}\)
Số trang của quyển sách là:\(30:\dfrac{6}{125}=30\times\dfrac{125}{6}=625\left(trang\right)\)
a: ĐKXĐ: \(x\ne0;y\ne0\)
Đặt \(\dfrac{1}{x}=a;\dfrac{1}{y}=b\)
Hệ phương trình sẽ trở thành: \(\left\{{}\begin{matrix}a-2b=-1\\2a+b=3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}a-2b=-1\\4a+2b=6\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}a-2b+4a+2b=-1+6\\2a+b=3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}5a=5\\b=3-2a\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}a=1\\b=3-2=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\dfrac{1}{x}=1\\\dfrac{1}{y}=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=1\\y=1\end{matrix}\right.\left(nhận\right)\)
b: ĐKXĐ: \(\left\{{}\begin{matrix}x\ne y\\x\ne-\dfrac{y}{2}\end{matrix}\right.\)
Đặt \(\dfrac{1}{x-y}=a;\dfrac{1}{2x+y}=b\)
Hệ phương trình sẽ trở thành:
\(\left\{{}\begin{matrix}a+b=2\\3a-2b=-2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2a+2b=4\\3a-2b=-2\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}2a+2b+3a-2b=4-2\\a+b=2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}5a=2\\b=2-a\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}a=\dfrac{2}{5}\\b=2-\dfrac{2}{5}=\dfrac{10}{5}-\dfrac{2}{5}=\dfrac{8}{5}\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}\dfrac{1}{x-y}=\dfrac{2}{5}\\\dfrac{1}{2x+y}=\dfrac{8}{5}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x-y=\dfrac{5}{2}\\2x+y=\dfrac{5}{8}\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x-y+2x+y=\dfrac{5}{2}+\dfrac{5}{8}\\x-y=\dfrac{5}{2}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}3x=\dfrac{25}{8}\\y=x-\dfrac{5}{2}\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=\dfrac{25}{8}:3=\dfrac{25}{24}\\y=\dfrac{25}{24}-\dfrac{5}{2}=\dfrac{25}{24}-\dfrac{60}{24}=-\dfrac{35}{24}\end{matrix}\right.\left(nhận\right)\)
c: ĐKXĐ: \(x\ne1;y\ne-3\)
Đặt \(\dfrac{x}{x-1}=a;\dfrac{1}{y+3}=b\)
Hệ phương trình sẽ trở thành:
\(\left\{{}\begin{matrix}3a-2b=3\\4a+b=5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}3a-2b=3\\8a+2b=10\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}3a-2b+8a+2b=13\\4a+b=5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}11a=13\\b=5-4a\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}a=\dfrac{13}{11}\\b=5-4\cdot\dfrac{13}{11}=\dfrac{55}{11}-\dfrac{52}{11}=\dfrac{3}{11}\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}\dfrac{x}{x-1}=\dfrac{13}{11}\\\dfrac{1}{y+3}=\dfrac{3}{11}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}13\left(x-1\right)=11x\\y+3=\dfrac{11}{3}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}13x-13=11x\\y=\dfrac{11}{3}-3=\dfrac{2}{3}\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=\dfrac{13}{2}\\y=\dfrac{2}{3}\end{matrix}\right.\left(nhận\right)\)
a)
\(\left(-12,5\right)+3.4+12,5+\left(-3,4\right)\\ =\left(12,5-12,5\right)+\left(3,4-3,4\right)\\ =0+0=0\)
b)
\(32,8+4,2+\left(-4,3\right)+\left(-32,8\right)+4,3\\ =\left(32,8-32,8\right)+\left(4,3-4,3\right)+4,2\\ =0+0+4,2\\ =4,2\)
c)
\(-\left(42,5+150\right)\cdot2,5-7,5\cdot2,5\\ =2,5\left(-42,5-150-7,5\right)\\ =2,5\cdot\left(-50-150\right)\\ =2,5\cdot-200\\ =-500\)
d)
\(\left(-2,45\right)\cdot2,6+2,6\cdot\left(-7,55\right)\\ =2,6\cdot\left(-2,45-7,55\right)\\ =2,6\cdot-10\\ =-26\)
a: \(\left(-12,5\right)+3,4+12,5+\left(-3,4\right)\)
\(=\left(-12,5+12,5\right)+\left(3,4-3,4\right)\)
=0+0=0
b: \(32,8+4,2+\left(-4,3\right)+\left(-32,8\right)+4,3\)
\(=\left(32,8-32,8\right)+\left(4,3-4,3\right)+4,2\)
=0+0+4,2
=4,2
c: \(-\left(42,5+150\right)\cdot2,5-7,5\cdot2,5\)
\(=2,5\cdot\left(-42,5-150-7,5\right)\)
\(=2,5\cdot\left(-200\right)=-500\)
d: Sửa đề: \(\left(-2,45\right)\cdot2,6+2,6\cdot\left(-7,55\right)\)
\(=2,6\left(-2,45-7,55\right)\)
\(=2,6\cdot\left(-10\right)=-26\)
2:
a: \(x^2+4x+4=x^2+2\cdot x\cdot2+2^2=\left(x+2\right)^2\)
b: \(x^2+10x+25=x^2+2\cdot x\cdot5+5^2=\left(x+5\right)^2\)
c: \(x^2+12x+36=x^2+2\cdot x\cdot6+6^2=\left(x+6\right)^2\)
d: \(4x^2+4x+1=\left(2x\right)^2+2\cdot2x\cdot1+1^2=\left(2x+1\right)^2\)
e: \(9x^2+6x+1=\left(3x\right)^2+2\cdot3x\cdot1+1^2=\left(3x+1\right)^2\)
f: \(16x^2+24x+9=\left(4x\right)^2+2\cdot4x\cdot3+3^2=\left(4x+3\right)^2\)
3:
a: \(A=\left(x+2\right)^2-x\left(x+3\right)+4x-3\)
\(=x^2+4x+4-x^2-3x+4x-3\)
=5x+1
b: \(B=\left(x+3\right)^2-x\left(x-5\right)+7x-8\)
\(=x^2+6x+9-x^2+5x+7x-8\)
=18x+1
c: \(C=\left(2x+3\right)^2-x\left(x+4\right)-9x-3\)
\(=4x^2+12x+9-x^2-4x-9x-3\)
\(=3x^2-x+6\)
d: \(D=\left(2x+21\right)^2-2x\left(2x-4\right)-5x-21\)
\(=4x^2+84x+441-4x^2+8x-5x-21\)
=87x+420
2:
\(a.x^2+4x+4=x^2+2\cdot x\cdot2+2^2=\left(x+2\right)^2\\ b.x^2+10x+25=x^2+2\cdot x\cdot5+5^2=\left(x+5\right)^2\\ c.x^2+12x+36=x^2+2\cdot x\cdot6+6^2=\left(x+6\right)^2\\ d.4x^2+4x+1=\left(2x\right)^2+2\cdot2x\cdot1+1^2=\left(2x+1\right)^2\\ e.9x^2+6x+1=\left(3x\right)^2+2\cdot3x\cdot1+1^2=\left(3x+1\right)^2\\ f.16x^2+24x+9=\left(4x\right)^2+2\cdot4x\cdot3+3^2=\left(4x+3\right)^2\)
Bài 3:
a: \(\left\{{}\begin{matrix}\dfrac{x+y}{2}=\dfrac{x-y}{4}\\\dfrac{x}{3}=\dfrac{y}{5}+1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2\left(x+y\right)=x-y\\\dfrac{5x}{15}=\dfrac{3y}{15}+\dfrac{15}{15}\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}2x+2y=x-y\\5x=3y+15\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x+3y=0\\5x-3y=15\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x+3y+5x-3y=0+15\\x=-3y\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}6x=15\\x=-3y\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{15}{6}=\dfrac{5}{2}\\y=\dfrac{x}{-3}=\dfrac{5}{2}:\left(-3\right)=-\dfrac{5}{6}\end{matrix}\right.\)
b: \(\left\{{}\begin{matrix}\left(x-1\right)\left(y+3\right)=xy+27\\\left(x-2\right)\left(y+1\right)=xy+8\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}xy+3x-y-3=xy+27\\xy+x-2y-2=xy+8\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}3x-y=30\\x-2y=10\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}6x-2y=60\\x-2y=10\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}6x-2y-x+2y=60-10\\x-2y=10\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}5x=50\\2y=x-10\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=10\\2y=10-10=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=10\\y=0\end{matrix}\right.\)
Số số hạng trong tích này là:
(2024-34):10+1=200(số)
Vì 200 chia hết cho 4
nên \(4^{200}\) có chữ số tận cùng là 6
\(34\times44\times...\times2024\) sẽ có chữ số tận cùng giống với chữ số tận cùng của 4x4x4x...4x4(200 chữ số 4)
=>34x44x...x2024 có chữ số tận cùng là 6