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Matematyka 1

Matematyka

Liczy się matematyka 1

Matematyka 1. Ćwiczenia podstawowe

Matematyka 1. Zeszyt zadań

Matematyka 2001

Matematyka 2001. Zeszyt ćwiczeń cz. 1 

Matematyka 2001. Zeszyt ćwiczeń cz. 2

Matematyka na czasie! 1

Matematyka wokół nas 1

Matematyka wokół nas 1. Zeszyt ćwiczeń cz. 2 - ukr

Matematyka z plusem 1

Matematyka z plusem 1. Podręcznik

Matematyka z plusem 1. Zbiór zadań

Matematyka z plusem 1. Zeszyt ćwiczeń

Policzmy to razem 1

a) 0,012=0,01⋅0,01=0,0001

Podstawą każdej z potęg jest liczba mieszana, więc najpierw należy zamienić ją na ułamek niewłaściwy (włączyć całości).&nbsp; a) (−421​)2=(−29​)2=481​=2041​ &nbsp; b) (251​)2=(511​)2=25121​=42521​

a) 0<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
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c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z'/></svg>​=0   bo 02=0 &nbsp; b) 1<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
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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>​=1   bo 12=1

a) 0,01<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.28em' viewBox='0 0 400000 1296' preserveAspectRatio='xMinYMin slice'><path d='M263,681c0.7,0,18,39.7,52,119
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c340,-704.7,510.7,-1060.3,512,-1067
l0 -0
c4.7,-7.3,11,-11,19,-11
H40000v40H1012.3
s-271.3,567,-271.3,567c-38.7,80.7,-84,175,-136,283c-52,108,-89.167,185.3,-111.5,232
c-22.3,46.7,-33.8,70.3,-34.5,71c-4.7,4.7,-12.3,7,-23,7s-12,-1,-12,-1
s-109,-253,-109,-253c-72.7,-168,-109.3,-252,-110,-252c-10.7,8,-22,16.7,-34,26
c-22,17.3,-33.3,26,-34,26s-26,-26,-26,-26s76,-59,76,-59s76,-60,76,-60z
M1001 80h400000v40h-400000z'/></svg>​=0,1   bo 0,12=0,01 &nbsp; b) 0,16<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.28em' viewBox='0 0 400000 1296' preserveAspectRatio='xMinYMin slice'><path d='M263,681c0.7,0,18,39.7,52,119
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c340,-704.7,510.7,-1060.3,512,-1067
l0 -0
c4.7,-7.3,11,-11,19,-11
H40000v40H1012.3
s-271.3,567,-271.3,567c-38.7,80.7,-84,175,-136,283c-52,108,-89.167,185.3,-111.5,232
c-22.3,46.7,-33.8,70.3,-34.5,71c-4.7,4.7,-12.3,7,-23,7s-12,-1,-12,-1
s-109,-253,-109,-253c-72.7,-168,-109.3,-252,-110,-252c-10.7,8,-22,16.7,-34,26
c-22,17.3,-33.3,26,-34,26s-26,-26,-26,-26s76,-59,76,-59s76,-60,76,-60z
M1001 80h400000v40h-400000z'/></svg>​=0,4   bo 0,42=0,16

Liczby podpierwiastkowe to liczby mieszane. Aby obliczyć wartość pierwiastka należy zapisane podane liczby w postaci ułamków niewłaściwych (włączyć całości).&nbsp; a) 241​<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='2.48em' viewBox='0 0 400000 2592' preserveAspectRatio='xMinYMin slice'><path d='M424,2478
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c0,-2,-10.7,14.3,-32,49c-4.7,7.3,-9.8,15.7,-15.5,25c-5.7,9.3,-9.8,16,-12.5,20
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c-2,6,-10,9,-24,9
c-8,0,-12,-0.7,-12,-2z M1001 80
h400000v40h-400000z'/></svg>​=49​<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='2.48em' viewBox='0 0 400000 2592' preserveAspectRatio='xMinYMin slice'><path d='M424,2478
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l0 -0c4,-6.7,10,-10,18,-10 H400000
v40H1014.6
s-87.3,378.7,-272.6,1166c-185.3,787.3,-279.3,1182.3,-282,1185
c-2,6,-10,9,-24,9
c-8,0,-12,-0.7,-12,-2z M1001 80
h400000v40h-400000z'/></svg>​=23​=121​ &nbsp; &nbsp; b) 197​<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='2.48em' viewBox='0 0 400000 2592' preserveAspectRatio='xMinYMin slice'><path d='M424,2478
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v40H1014.6
s-87.3,378.7,-272.6,1166c-185.3,787.3,-279.3,1182.3,-282,1185
c-2,6,-10,9,-24,9
c-8,0,-12,-0.7,-12,-2z M1001 80
h400000v40h-400000z'/></svg>​=916​<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='2.48em' viewBox='0 0 400000 2592' preserveAspectRatio='xMinYMin slice'><path d='M424,2478
c-1.3,-0.7,-38.5,-172,-111.5,-514c-73,-342,-109.8,-513.3,-110.5,-514
c0,-2,-10.7,14.3,-32,49c-4.7,7.3,-9.8,15.7,-15.5,25c-5.7,9.3,-9.8,16,-12.5,20
s-5,7,-5,7c-4,-3.3,-8.3,-7.7,-13,-13s-13,-13,-13,-13s76,-122,76,-122s77,-121,77,-121
s209,968,209,968c0,-2,84.7,-361.7,254,-1079c169.3,-717.3,254.7,-1077.7,256,-1081
l0 -0c4,-6.7,10,-10,18,-10 H400000
v40H1014.6
s-87.3,378.7,-272.6,1166c-185.3,787.3,-279.3,1182.3,-282,1185
c-2,6,-10,9,-24,9
c-8,0,-12,-0.7,-12,-2z M1001 80
h400000v40h-400000z'/></svg>​=34​=131​

Dziewczęta stanowią 1/6 klasy, czyli 1/6 z 30.&nbsp;&nbsp; Obliczamy ile dziewcząt liczy ta klasa.&nbsp; 611​⋅305=5

Obliczamy ile wynosi 3/7 liczby 1,05, czyli 3/7 z 1,05.&nbsp;

Kasia wypiła już&nbsp;2/5 z 2,5 l soku, czyli w butelce pozostało jeszcze&nbsp;3/5&nbsp;(1-2/5)&nbsp;&nbsp;z 2,5 l soku.&nbsp;

Podstawą każdej z potęg jest liczba mieszana, więc najpierw należy zamienić ją na ułamek niewłaściwy (włączyć całości).&nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/75f84bdd68c1ab7593343244a465b3f39c6a208e11832ee01a7acd35fa3a6518_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/75f84bdd68c1ab7593343244a465b3f39c6a208e11832ee01a7acd35fa3a6518_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/237016eb8513b261c325e992f46309489abba6fdd13d949cb73082b189410066_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/237016eb8513b261c325e992f46309489abba6fdd13d949cb73082b189410066_big.svg" type="image/svg+xml"></object>

Liczby podpierwiastkowe to liczby mieszane. Aby obliczyć wartość pierwiastka należy zapisane podane liczby w postaci ułamków niewłaściwych (włączyć całości).&nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/10b1b26fcdf9e9dd53736d4aff0df3516c61ff084138e9e15c61106274af0971_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/10b1b26fcdf9e9dd53736d4aff0df3516c61ff084138e9e15c61106274af0971_big.svg" type="image/svg+xml"></object> &nbsp; &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/c815efaa135119d1590e7e381bc3ff1be16a2751e384659f8099db7cd698fc59_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/c815efaa135119d1590e7e381bc3ff1be16a2751e384659f8099db7cd698fc59_big.svg" type="image/svg+xml"></object>

Dziewczęta stanowią 1/6 klasy, czyli 1/6 z 30.&nbsp;&nbsp; Obliczamy ile dziewcząt liczy ta klasa.&nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/2c586389f65e9958294ced6bcfaf5292a02ee3920443a8bc3d9c7a2e2ce35ced_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/2c586389f65e9958294ced6bcfaf5292a02ee3920443a8bc3d9c7a2e2ce35ced_big.svg" type="image/svg+xml"></object>

Średnia arytmetyczna liczb to iloraz ich sumy i ich ilości.&nbsp; Średnia arytmetyczna podanych liczb to: <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/2fac24215ef9c16ef9d6574b168795afaff343b1bf0419bbf657f3cd1e4bd701_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/2fac24215ef9c16ef9d6574b168795afaff343b1bf0419bbf657f3cd1e4bd701_big.svg" type="image/svg+xml"></object> <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/2fac24215ef9c16ef9d6574b168795afaff343b1bf0419bbf657f3cd1e4bd701_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/2fac24215ef9c16ef9d6574b168795afaff343b1bf0419bbf657f3cd1e4bd701_big.svg" type="image/svg+xml"></object> &nbsp;&nbsp; &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/0ea9912b2014feafbb7512409e5786fdd07380167d12df390a518b19a9f5c99f_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/0ea9912b2014feafbb7512409e5786fdd07380167d12df390a518b19a9f5c99f_big.svg" type="image/svg+xml"></object> &nbsp; Średnia arytmetyczna podanych liczb jest równa -&nbsp;53/240. &nbsp;

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