Câu 158:

A(-1;1); B(3;1); C(2;4)

\(AB=\sqrt{\left(3+1\right)^2+\left(1-1\right)^2}=4\)

\(AC=\sqrt{\left(2+1\right)^2+\left(4-1\right)^2}=\sqrt{3^2+3^2}=3\sqrt{2}\)

\(BC=\sqrt{\left(2-3\right)^2+\left(4-1\right)^2}=\sqrt{3^2+1^2}=\sqrt{10}\)

Xét ΔABC có \(cosBAC=\dfrac{AB^2+AC^2-BC^2}{2\cdot AB\cdot AC}=\dfrac{16+18-10}{2\cdot4\cdot3\sqrt{2}}=\dfrac{\sqrt{2}}{2}\)

=>\(sinBAC=\sqrt{1-cos^2BAC}=\dfrac{\sqrt{2}}{2}\)

Diện tích tam giác ABC là:

\(S_{ABC}=\dfrac{1}{2}\cdot AB\cdot AC\cdot sinBAC\)

\(=\dfrac{1}{2}\cdot\dfrac{\sqrt{2}}{2}\cdot4\cdot3\sqrt{2}=6\)

=>Chọn B

Câu 143:

\(\overrightarrow{a}=\left(4;3\right);\overrightarrow{b}=\left(1;7\right)\)

\(\overrightarrow{a}\cdot\overrightarrow{b}=4\cdot1+3\cdot7=25\)

\(cos\left(\overrightarrow{a};\overrightarrow{b}\right)=\dfrac{\overrightarrow{a}\cdot\overrightarrow{b}}{\left|\overrightarrow{a}\right|\cdot\left|\overrightarrow{b}\right|}=\dfrac{25}{\sqrt{\left(4^2+3^2\right)}\cdot\sqrt{1^2+7^2}}=\dfrac{25}{5\cdot5\sqrt{2}}=\dfrac{1}{\sqrt{2}}\)=>\(\left(\overrightarrow{a};\overrightarrow{b}\right)=45^0\)

=>Chọn B

Câu 142:

\(\overrightarrow{a}=\left(6;0\right);\overrightarrow{b}=\left(3;1\right)\)

\(cos\left(\overrightarrow{a};\overrightarrow{b}\right)=\dfrac{\overrightarrow{a}\cdot\overrightarrow{b}}{\left|\overrightarrow{a}\right|\cdot\left|\overrightarrow{b}\right|}=\dfrac{6\cdot3+1\cdot0}{\sqrt{6^2+0^2}\cdot\sqrt{3^2+1^2}}=\dfrac{18}{6\cdot\sqrt{10}}=\dfrac{3}{\sqrt{10}}\)

=>Chọn A

Câu 131:

Đặt \(\overrightarrow{c}=x\cdot\overrightarrow{a}+y\cdot\overrightarrow{b}\)

=>\(\left\{{}\begin{matrix}2x+\left(-4\right)y=-6\\3x+3y=1\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}6x-12y=-18\\12x+12y=4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}18x=-14\\x+y=\dfrac{1}{3}\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}x=-\dfrac{7}{9}\\y=\dfrac{1}{3}-x=\dfrac{1}{3}+\dfrac{7}{9}=\dfrac{10}{9}\end{matrix}\right.\)

=>Chọn A

Xét tứ giác ABCD có:

A + B + C + D = 360 độ(theo định lý)

Suy ra C = 360 độ - ( A + B + D)

                360 độ - 240 độ

                 120 độ

Vậy...

Bạn thêm ký hiệu góc vào giúp mình.

\(\Leftrightarrow\left(3x+7\right)\left(2x-5\right)=0\)

=>x=-7/3 hoặc x=5/2

\(2x\left(3x+7\right)-15x-35=0\\ \Rightarrow2x\left(3x+7\right)-\left(15x+35\right)=0\\ \Rightarrow2x\left(3x+7\right)-5\left(3x+7\right)=0\\ \Rightarrow\left(2x-5\right)\left(3x+7\right)=0\\ \Rightarrow\left[{}\begin{matrix}x=\dfrac{5}{2}\\x=-\dfrac{7}{3}\end{matrix}\right.\)

\(a.253\\ b.123,5\)

\(\left\{{}\begin{matrix}u_3=13\\u_5=23\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}u_1+2d=13\\u_1+4d=23\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}u_1=3\\d=5\end{matrix}\right.\)

Hàm \(f\left(x\right)\) ko xác định khi \(x+4=0\Rightarrow x=-4\)

\(\Rightarrow\) Hàm gián đoạn tại \(x=-4\)

a)

-Phân số nhỏ nhất là 17/60

b) 

S= 8/3 + 32/15 + 72/35 + 128/63 + 200/99

  = ( 40+32/15 ) + (72/35 + 128/63 ) + 200/99

  = 24/5 + 184/45 + 200/99 

  = 80/9 + 200/99

  = 120/11

Chọn B