Câu 5:
a. $|x+\frac{4}{5}|-\frac{1}{7}=0$
$|x+\frac{4}{5}|=\frac{1}{7}$
$\Rightarrow x+\frac{4}{5}=\pm \frac{1}{7}$
$\Rightarrow x=\frac{-23}{35}$ hoặc $x=\frac{-33}{35}$
v.
$2x+5-(x-7)=18$
$2x+5-x+7=18$
$x+12=18$
$x=6$
c.
$2(x+1)+4^2=2^4$
$2(x+1)+16=16$
$2(x+1)=0$
$x+1=0$
$x=-1$
d.
$\frac{x-3}{x+5}=\frac{5}{7}$
$\Rightarrow 7(x-3)=5(x+5)$
$\Rightarrow 7x-21=5x+25$
$\Rightarrow 2x=46$
$\Rightarrow x=23$
Câu 5:
\(a,\left|x+\dfrac{4}{5}\right|-\dfrac{1}{7}=0\\ \Leftrightarrow\left|x+\dfrac{4}{5}\right|=\dfrac{1}{7}\\ \Leftrightarrow\left[{}\begin{matrix}x+\dfrac{4}{5}=\dfrac{1}{7}\\x+\dfrac{4}{5}=-\dfrac{1}{7}\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{7}-\dfrac{4}{5}\\x=-\dfrac{1}{7}-\dfrac{4}{5}\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{23}{35}\\x=-\dfrac{33}{35}\end{matrix}\right.\\ b,2x+5-\left(x-7\right)=18\\ \Leftrightarrow2x-x=18-5-7\\ \Leftrightarrow x=6\\ c,2\left(x+1\right)+4^2=2^4\\ \Leftrightarrow2\left(x+1\right)=2^4-4^2=16-16\\ \Leftrightarrow2\left(x+1\right)=0\\ \Rightarrow x+1=0\\ \Leftrightarrow x=0-1=-1\\ d,\dfrac{x-3}{x+5}=\dfrac{5}{7}\left(x\ne-5\right)\\ \Leftrightarrow7\left(x-3\right)=5\left(x+5\right)\\ \Leftrightarrow7x-21=5x+25\\ \Leftrightarrow7x-5x=25+21\\ \Leftrightarrow2x=46\\ \Leftrightarrow x=23\)
Câu 6:
Điểm số | 5 | 6 | 7 | 8 | 9 | 10 |
Tần số | 1 | 3 | 4 | 5 | 4 | 3 |
b. Trung bình cộng các điểm:
$\overline{x}=\frac{5.1+6.3+7.4+8.5+9.4+10.3}{20}=7,85$
Câu 7:
a.
$P(x)=5x^3-(3x+x)+7=5x^3-4x+7$
$Q(x)=-5x^3-x^2+(2x+2x)-(3+2)=-5x^3-x^2+4x-5$
b.
$P(x)+Q(x)=(5x^3-4x+7)+(-5x^3-x^2+4x-5)$
$=(5x^3-5x^3)-x^2+(-4x+4x)+(7-5)=-x^2+2$
$P(x)-Q(x)=(5x^3-4x+7)-(-5x^3-x^2+4x-5)$
$=(5x^3+5x^3)+x^2+(-4x-4x)+(7+5)$
$=10x^3+x^2-8x+12$
Câu 7:
\(a,P\left(x\right)=5x^3-3x+7-x=5x^3-4x+7\\ Q\left(x\right)=-5x^3+2x-3+2x-x^2-2=-5x^3-x^2+2x+2x-3-2=-5x^3-x^2+4x-5\\ b,P\left(x\right)+Q\left(x\right)=\left(5x^3-4x+7\right)+\left(-5x^3-x^2+4x-5\right)\\ =-5x^3+5x^3-x^2-4x+4x+7-5\\ =-x^2+2\\ P\left(x\right)-Q\left(x\right)=\left(5x^3-4x+7\right)-\left(-5x^3-x^2+4x-5\right)\\ =\left(5x^3+5x^3\right)+x^2-4x-4x+7+5\\ =10x^3+x^2-8x+12\)