\(4\left(\dfrac{1}{2}-x\right)-5\left(x-\dfrac{3}{10}\right)=\dfrac{7}{4}\)

\(\Leftrightarrow2-4x-5x+\dfrac{3}{2}=\dfrac{7}{4}\)

\(\Leftrightarrow-9x+\dfrac{7}{2}=\dfrac{7}{4}\)

\(\Leftrightarrow-9x=-\dfrac{7}{4}\)

\(\Leftrightarrow x=\dfrac{7}{36}\)

1b 2a 3c 4a 5b 6b

5, I wish the food were good.

6, I wish she didn't tell lies.

7, I wish they joined us today.

8, I wish she could go abroad.

9, We used to go to school by bus.

\(a,\left(x+3\right)\left(x+4\right)-\left(x-3\right)\left(x-5\right)=2\)

\(\Leftrightarrow x^2+3x+4x+12-\left(x^2-3x-5x+15\right)=2\)

\(\Leftrightarrow x^2+7x+12-\left(x^2-8x+15\right)=2\)

\(\Leftrightarrow x^2+7x+12-x^2+8x-15=2\)

\(\Leftrightarrow15x-3=2\)

\(\Leftrightarrow15x=5\Leftrightarrow x=\dfrac{1}{3}\)

\(b,x^2\left(x-3\right)-4x+12=0\)

\(\Leftrightarrow x^2\left(x-3\right)-4\left(x-3\right)=0\)

\(\Leftrightarrow\left(x-3\right)\left(x^2-4\right)=0\)

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

\(\Leftrightarrow\left[{}\begin{matrix}x-3=0\\x-2=0\\x+2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\x=2\\x=-2\end{matrix}\right.\)

I.

1. D          2. B          3. D          4. C          5. A          6. B          7. C

II.

1. D          2. C          3. B          4. A          5. D          6. C          7. A

8. B          9. D          10. C

\(A=\left(x+\dfrac{1}{2}\right)^{2022}+0,5\)

\(\)Vì \(\left(x+\dfrac{1}{2}\right)^{2022}\ge0\forall x\in R\)\(\Rightarrow\left(x+\dfrac{1}{2}\right)^{2022}+0,5\ge0,5\forall x\in R\)

Dấu = xảy ra khi: \(\left(x+\dfrac{1}{2}\right)^{2022}=0\Leftrightarrow x=-\dfrac{1}{2}\)

Vậy GTNN của A = 0,5 khi x = -1/2

37a 38c 39c 40b

The children enjoy watching the performing lions.

a,

Vì \(\Delta ABC\perp A\Rightarrow\widehat{BAC}=90^0\Leftrightarrow\widehat{EAF}=90^0\)

\(HE\perp AB\Rightarrow\widehat{AEH}=90^0\)

\(HF\perp AC\Rightarrow\widehat{AFH}=90^0\)

Tứ giác AEHF có: \(\widehat{EAF}=\widehat{AEH}=\widehat{AFH}=90^0\)

\(\Rightarrow\) AEHF là hình chữ nhật.

\(\Rightarrow\) AH = EF (2 đường chéo trong hình chữ nhật bằng nhau)

Câu b hình như sai đề.

\(I_1=\dfrac{U_1}{R_1}=\dfrac{9}{2}=4,5A\)

Mà \(R_1ntR_2\Rightarrow I_1=I_2=4,5A\)

\(U_2=I_2.R_2=4,5.6=27V\)

\(U=U_1+U_2=9+27=36V\)