matikkaeditori

1dia

$2+5+7+12=26$ $2\cdot5+7=17$
$\frac{1}{4}+\frac{2}{3}=\frac{3}{12}+\frac{8}{12}=\frac{11}{12}$
$\frac{1}{4}\cdot\frac{2}{3}=\frac{1\cdot2}{4\cdot3}=\frac{2}{12}=\frac{1}{6}$
$\frac{1}{4}:\frac{2}{3}=\frac{1}{4}\cdot\frac{3}{2}=\frac{3}{8}$
$\left(\frac{2}{3}\right)^2=\frac{2^2}{3^2}=\frac{4}{9}$

dia10

$k=\frac{5-1}{2-\left(-2\right)}=\frac{4}{4}=1$
$y-y_1=k\cdot\left(x-x_1\right):$
$y-5=1\cdot\left(x-2\right)$
$y-5=x-2$
$y=x-2+5$
$y=x+3$

dia2

$5^2\cdot5^3=5^5$ $5^{2=25}$ $\left(5^2\right)^4=5^8$
$\left(2x^2\right)^3=2^3\cdot\left(x^2\right)^3=8x^6$

dia3

$4x-5=-2x+7$
$4x-5=-2x+7$
$4x+2x=7+5$
$6x=12$
$x=\frac{12}{6}=2$

dia4

$a_n=a_1+\left(n-1\right)\cdot d$
$a_1=2$
$d=4$
$an=2+\left(n-1\right)\cdot4\ =2+4n-2$
$4n-2=506$
$4n=508$
$n=127$

dia5

$\frac{20}{16}=1,25=125\%$
$125\%-100\%=25\%$

dia6

$\sum_{k-1}^{15}2^k$
$a_1=2$
$q=2$
$n=15$
$S_{15}\frac{2\cdot\left(1-2^{15}\right)}{1-2}=\frac{2\cdot\left(-32767\right)}{-1}=65534$

dia7

$2^x=8\cdot16$
$2^x=\left(2^3\right)^7$
$2^x=8\cdot16$
$2^x=2^3\cdot2^4$
$2^x=2^{3+4}$
$2^x=2^7$
$X=7$
$2^x=\left(2^3\right)^7$
$2^x=2^{3\cdot7}$
$2^x=2^{21}$
$x=21$

dia8

$\frac{5}{3}=\frac{2}{x}$
$5\cdot x=3\cdot2$
$5x=6$
$x=\frac{6}{5}=1,20€$

dia9

$x^2+4,2^2=7,0^2$
$x^2+17,64=49$
$x^2=49-17,64$
$x^2=31,36$
$x=\sqrt{31,36}$
$x=5,6$
$\sin\alpha=\frac{18}{24}$
$\alpha=48,590...°$
$\alpha\approx49°$