I gimnazjum

Matematyka 1

Matematyka

Od 21 czerwca do 30 czerwca jest 9 dni (nie wliczamy 21 czerwca).&nbsp; Od 1 lipca do 31 lipca jest 31 dni.&nbsp;

a) 1513​=0,8(6) &nbsp; b) 94​=0,(4)

a) x=0,(3) &nbsp;    10x=3,(3) &nbsp; Okresy liczb x i 10x są takie same, więc: 10x−x=3,(3)−0,(3) &nbsp; 9x=3       ∣:9 &nbsp; x=93​=31​ &nbsp;                                              ​​ &nbsp; b) x=0,(1) &nbsp;    10x=1,(1) &nbsp; &nbsp; Okresy liczb x i 10x są takie same, więc: 10x−x=1,(1)−0,(1) &nbsp; 9x=1       ∣:9

a) 3125<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
c69,-144,104.5,-217.7,106.5,-221
l0 -0
c5.3,-9.3,12,-14,20,-14
H400000v40H845.2724
s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z'/></svg>​=5   bo 53=125 &nbsp; b) 31000<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
c69,-144,104.5,-217.7,106.5,-221
l0 -0
c5.3,-9.3,12,-14,20,-14
H400000v40H845.2724
s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z'/></svg>​=10   bo 103=1000

&nbsp;

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<td style="vertical-align: top; padding: 7px 7px 7px 7px; border: solid #000000 1px;">
<span style="font-size: 16px; font-family: 'Times New Roman'; color: #000000; background-color: transparent; font-weight: bold; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">XVII
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<span style="font-size: 16px; font-family: 'Times New Roman'; color: #000000; background-color: transparent; font-weight: bold; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">LV
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<span style="font-size: 16px; font-family: 'Times New Roman'; color: #000000; background-color: transparent; font-weight: bold; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">CXX
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<td style="vertical-align: top; padding: 7px 7px 7px 7px; border: solid #000000 1px;">
<span style="font-size: 16px; font-family: 'Times New Roman'; color: #000000; background-color: transparent; font-weight: bold; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">CXLVIII
</td>
<td style="vertical-align: top; padding: 7px 7px 7px 7px; border: solid #000000 1px;">
<span style="font-size: 16px; font-family: 'Times New Roman'; color: #000000; background-color: transparent; font-weight: bold; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">DCXI
</td>
<td style="vertical-align: top; padding: 7px 7px 7px 7px; border: solid #000000 1px;">
<span style="font-size: 16px; font-family: 'Times New Roman'; color: #000000; background-color: transparent; font-weight: bold; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">MMCCCLII
</td>
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<tr style="height: 0px;">
<td style="vertical-align: top; background-color: #f9cb9c; padding: 7px 7px 7px 7px; border: solid #000000 1px;">
<span style="font-size: 16px; font-family: 'Times New Roman'; color: #000000; background-color: transparent; font-weight: bold; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">System dziesiętny
</td>
<td style="vertical-align: top; background-color: #fce5cd; padding: 7px 7px 7px 7px; border: solid #000000 1px;">
<span style="font-size: 16px; font-family: 'Times New Roman'; color: #000000; background-color: transparent; font-weight: bold; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">17
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<td style="vertical-align: top; background-color: #fce5cd; padding: 7px 7px 7px 7px; border: solid #000000 1px;">
<span style="font-size: 16px; font-family: 'Times New Roman'; color: #000000; background-color: transparent; font-weight: bold; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">21
</td>
<td style="vertical-align: top; background-color: #fce5cd; padding: 7px 7px 7px 7px; border: solid #000000 1px;">
<span style="font-size: 16px; font-family: 'Times New Roman'; color: #000000; background-color: transparent; font-weight: bold; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">55
</td>
<td style="vertical-align: top; background-color: #fce5cd; padding: 7px 7px 7px 7px; border: solid #000000 1px;">
<span style="font-size: 16px; font-family: 'Times New Roman'; color: #000000; background-color: transparent; font-weight: bold; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">76
</td>
<td style="vertical-align: top; background-color: #fce5cd; padding: 7px 7px 7px 7px; border: solid #000000 1px;">
<span style="font-size: 16px; font-family: 'Times New Roman'; color: #000000; background-color: transparent; font-weight: bold; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">120
</td>
<td style="vertical-align: top; background-color: #fce5cd; padding: 7px 7px 7px 7px; border: solid #000000 1px;">
<span style="font-size: 16px; font-family: 'Times New Roman'; color: #000000; background-color: transparent; font-weight: bold; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">148
</td>
<td style="vertical-align: top; background-color: #fce5cd; padding: 7px 7px 7px 7px; border: solid #000000 1px;">
<span style="font-size: 16px; font-family: 'Times New Roman'; color: #000000; background-color: transparent; font-weight: bold; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">611
</td>
<td style="vertical-align: top; background-color: #fce5cd; padding: 7px 7px 7px 7px; border: solid #000000 1px;">
<span style="font-size: 16px; font-family: 'Times New Roman'; color: #000000; background-color: transparent; font-weight: bold; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">2352
</td>
</tr>
</tbody>
</table>

a) Liczba przeciwna to:&nbsp; −54​ &nbsp; Liczba odwrotna do liczby przeciwnej to: −45​=−141​ &nbsp;                                              ​ &nbsp; b) Liczba przeciwna to: 97​

System rzymski	XVII	XXI	LV	LXXVI	CXX	CXLVIII	DCXI	MMCCCLII
System dziesiętny	17	21	55	76	120	148	611	2352

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