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ola737626
October 2020 | 0 Replies
BŁAGAM POMÓŻCIE PLIIIISSSSSSSS ❤️❤️❤️ DAJE ❤️ I NAJ!!!!!! BĘDĘ WDZIĘCZNA PLISSSSSSSSS...W tabeli (w załączniku) podano wyniki zakończonego sezonu szkolnej ligi piłkarskiej każda z drużyn rozegrała 10 meczów. Za wygrany mecz otrzymywała 3 punkty za remis 1 punkt a za porażkę 0 punktówWykonaj polecenie i napisz działanie Niebiescy w 10 meczach zdobyli 26 punktów. Ile razy odnieśli zwycięstwo A ile razy zremisowali
zadanie 3.1
4³*4⁴:4²=4⁷:4²=4⁵
zadanie 3.2
a)
5³*5⁻¹:5⁴=5²:5⁴=5⁻²
b)
4²*8³*(0,25)²*32=(2²)²*(2³)³*(2⁻²)²*2⁵=2⁴*2⁹*2⁻⁴*2⁵=2¹⁴
c)
(-3/4)⁻¹*(-1 i 1/3)⁻¹*(-2)⁻¹=(-3/4)⁻¹*(-4/3)⁻¹*(-2)⁻¹=(-4/3)¹*(-4/3)⁻¹*(-2)⁻¹=
(-4/3)⁰*(-2)⁻¹=1*(-2)⁻¹=(-2)⁻¹
d)
2⁷*3⁷ 6⁷
____ =____=6²
6³ 6⁵
zadanie 3.3
a)
[a⁸:(a*a⁵)]:[a*(a⁷:a⁶)]=[a⁸:a⁶]:[a*a]=a²:a²=a⁰=1
b)
[x³*(x²)³]:[(x³)⁴:x⁵]=[x³*x⁶]:[x¹²:x⁵]=x⁹:x⁷=x²
zadanie 3.5
a)
[(-3)²+2³]*(-5)=[9+8]*(-5)=17*(-5)= -85
b)
(-6)²:(1+2³)=36:(1+8)=36:9=4
c)
12²:2⁴-(-1)⁹*0⁷*10³=144:16-(-1)*0*1000=144:16-0=9-0=9
zadanie 3.6
a) 2,5+(2/3-1,8*5/6):(-1/3)³=2,5+(2/3-9/5*5/6):(-1/27)=2,5+(2/3-3/2)*(-27)=
2,5+(-5/6)*(27)=2,5+135/6=2,5+22,5=25
b)
[(6 3/8)+(1/3)⁻²*(4*3⁻¹-√9⁻¹)]⁻¹=[(6 3/8)+9*(4*1/3-1/3)]⁻¹=
[(6 3/8)+9*3/3)]⁻¹=[(6 3/8)+9)]⁻¹=[51/8+9]⁻¹=[123/8]⁻¹=8/123
zadanie 3.7
a)
10⁵ 10⁰
___ = ___
10⁷ 10²
b)
2³*2⁶
_______ =
2⁷*3²*5²
2⁹
_______ =
2⁷*3²*5²
2²
_______
3²*5²
c)
2²⁰+2²⁰+2²⁰
___________ =
4¹⁰+4¹⁰+4¹⁰
2²⁰+2²⁰+2²⁰
_________________ =
(2²)¹⁰+(2²)¹⁰+(2²)¹⁰
2²⁰+2²⁰+2²⁰
__________ =1
2²⁰+2²⁰+2²⁰
zadanie 3.8-nie całe zadanie jest widoczne
a)
4-2⁻¹*(3/5)⁰=2²-2⁻¹*1=4-1/2=3,5
b)
1/2*2⁰-3⁻²=1/2*1-3⁻²=1/3-1/9=3/9-1/9=2/9
c)
[2/3+(2/3)⁻²]⁻¹=[2/3+9/4]⁻¹=[8/12+27/12]⁻¹=[35/12]⁻¹=12/35
zadanie 3.44
a)
-3²*(-6)⁻¹
________ =
√1-16/25
-9*(-1/6)
________ =
√9/25
3/2
____ =3/2*5/3=5/2=2,5
3/5
b)
√1 9/16 -(-2)²: 1 1/3
__________________ =
-5
√25/16-4:4/3
____________=
-5
5/4-4*3/4
_________=
-5
5/4-3
______ =
-5
-1,75
_____ = 0,35
-5
c)
∛27/8*√4/9
___________ =
5⁻²*125
3/2*2/3
_______ = 1/5
5⁻²*5³
zadanie 3.45
a)
√49+3√16-(√25)²=7+3*4-5=7+12-5=14
b)
6*√121-(√7)²=6*11-7=66-7=59
c)
√25-9 *(-2)=√16 *(-2)=4*(-2)= -8
zadanie 3.46
a)
√12:√6*√2=√2*√2=√4=2
b)
√40*√5:√8=√200:√8=√25=5
c)
√27:(√6:√2)=√27:√3=√9=3
d)
√3:(√2*√6)=√3:√12=√3/12=√1/4=1/2
zadanie 3.47
a)
√12=√4*3=2√3
b)
√75=√25*3=5√3
c)
∛250=∛125*2=5∛2
d)
∛81=∛27*3=3∛3
zadanie 3.48
a)
(5-√8)-(7+2√8)=5-√8-7-2√8= -2-3√8
b)
(8-3√2)*√18=8√18-3√36=8√9*2-3*6=24√2-18=6(4√2-3)
c)
(3√8-√32):√2=(3√4*2-√16*2):√2=(6√2-4√2):√2=2√2:√2=2
zadanie 3.50
a)
∛1000-∛-343
______________ =
∛0,001+(√0,9)²
10-(-7)
_______ =17/1=17
0,1+0,9
b)
∛3 3/8-√10²
_______________=
(√0,5)²-∛(-0,5)³
∛27/8-√100
__________ =
0,5-(-0,5)
3/2-10
_______ = -8,5
0,5+0,5
zadanie 3.56
a)
∛131-√36=∛131-6=∛125=5
b)
√38-∛8=√38-2=√36=6
d)
√270*√225*√16=√270*√225*4=√270*√900=√270*30=√8100=90
e)
√110+√121=√110+11=√121=11
Własności działań na potęgach:
====================================================================
zad 3.1
4³ * 4⁴ : 4²=4³⁺⁴⁻²=4⁵
4⁵=(2²)⁵=2¹⁰
======================
zad 3.2
a) 5³ * 5⁻¹ : 5⁴=5³⁻¹⁻⁴=5⁻²
------------------------------
b) 4² * 8³ * (0,25)² * 32=
=(2²)² * (2³)³ * (1/4)² * 2⁵=
=2⁴ * 2⁹ * (2⁻²)² * 2⁵=
=2⁴ * 2⁹ * 2⁻⁴ * 2⁵=
=2⁴⁺⁹⁻⁴⁺⁵=
=2¹⁴
------------------------------
c)
------------------------------
d)![></span></p><p><span>======================</span></p><p><span>zad 3.3</span></p><p><span>a) [a⁸ : (a * a⁵)]:[a * (a⁷ : a⁶)]=</span></p><p><span>=[a⁸ : a¹⁺⁵]:[a * a⁷⁻⁶]=</span></p><p><span>=[a⁸ : a⁶]:[a * a]=</span></p><p><span>=a⁸⁻⁶ : a¹⁺¹=</span></p><p><span>=a² : a²=</span></p><p><span>=a²⁻²=</span></p><p><span>=a⁰=</span></p><p><span>=1</span></p><p><span>------------------------------</span></p><p><span>b) [x³ * (x²)³]:[(x³)⁴ : x⁵]=</span></p><p><span>=[x³ * x⁶]:[x¹² : x⁵]=</span></p><p><span>=x³⁺⁶ : x¹²⁻⁵=</span></p><p><span>=x⁹ : x⁷=</span></p><p><span>=x⁹⁻⁷=</span></p><p><span>=x²</span></p><p><span>======================</span></p><p><span>zad 3.4</span></p><p><span>Połowa liczby 2⁴⁰:</span></p><p><span>2²⁰ : 2=20²⁰⁻¹=2¹⁹</span></p><p><span>Czwatrta część liczby 4²⁰:</span></p><p><span>4²⁰ : 4=4²⁰⁻¹=4¹⁹</span></p><p><span>4¹⁹=(2²)¹⁹=2³⁸</span></p><p><span>Odp. 2³⁸ > 2¹⁹</span></p><p><span>======================</span></p><p><span>zad 3.5</span></p><p><span>a) [(-3)²+2³]*(-5)=</span></p><p><span>=[9+8]*(-5)=</span></p><p><span>=17*(-5)=</span></p><p>=-85</p><p><span>------------------------------</span></p><p><span>b) (-6)²:[1+2³]=</span></p><p><span>=36:[1+8]=</span></p><p><span>=36:9=</span></p><p><span>=4</span></p><p><span>------------------------------</span></p><p><span>c) 12²:2⁴-(-1)⁹ * 0⁷ * 10³=</span></p><p><span>=144:16-0=</span></p><p><span>=9</span></p><p><span>======================</span></p><p><span>zad 3.6</span></p><p><span>a) <img src=](https://tex.z-dn.net/?f=%5Cfrac%7B2%5E%7B7%7D%2A3%5E%7B7%7D%7D%7B6%5E%7B3%7D%7D%3D%5Cfrac%7B%282%2A3%29%5E%7B7%7D%7D%7B6%5E%7B3%7D%7D%3D%5Cfrac%7B6%5E%7B7%7D%7D%7B6%5E%7B3%7D%7D%3D6%5E%7B4%7D%5C%5C+%5Cfrac%7B2%5E%7B7%7D%2A3%5E%7B7%7D%7D%7B6%5E%7B5%7D%7D%3D%5Cfrac%7B%282%2A3%29%5E%7B7%7D%7D%7B6%5E%7B5%7D%7D%3D%5Cfrac%7B6%5E%7B7%7D%7D%7B6%5E%7B5%7D%7D%3D6%5E%7B2%7D%5C%5C "\frac{2^{7}*3^{7}}{6^{3}}=\frac{(2*3)^{7}}{6^{3}}=\frac{6^{7}}{6^{3}}=6^{4}\\ \frac{2^{7}*3^{7}}{6^{5}}=\frac{(2*3)^{7}}{6^{5}}=\frac{6^{7}}{6^{5}}=6^{2}\\")
------------------------------
b)![[(6\frac{3}{8}+(\frac{1}{3})^{-2})*(4*3^{-1}-\sqrt{9^{-1}})]^{-1}=\\ =[(\frac{51}{8}+9)*(4*\frac{1}{3}-\sqrt{\frac{1}{9}})]^{-1}=\\ =[(\frac{51}{8}+\frac{72}{8})*(\frac{4}{3}-\frac{1}{3})]^{-1}=\\ =[\frac{123}{8}*1]^{-1}=\\ =\frac{8}{123}](https://tex.z-dn.net/?f=%5B%286%5Cfrac%7B3%7D%7B8%7D%2B%28%5Cfrac%7B1%7D%7B3%7D%29%5E%7B-2%7D%29%2A%284%2A3%5E%7B-1%7D-%5Csqrt%7B9%5E%7B-1%7D%7D%29%5D%5E%7B-1%7D%3D%5C%5C+%3D%5B%28%5Cfrac%7B51%7D%7B8%7D%2B9%29%2A%284%2A%5Cfrac%7B1%7D%7B3%7D-%5Csqrt%7B%5Cfrac%7B1%7D%7B9%7D%7D%29%5D%5E%7B-1%7D%3D%5C%5C+%3D%5B%28%5Cfrac%7B51%7D%7B8%7D%2B%5Cfrac%7B72%7D%7B8%7D%29%2A%28%5Cfrac%7B4%7D%7B3%7D-%5Cfrac%7B1%7D%7B3%7D%29%5D%5E%7B-1%7D%3D%5C%5C+%3D%5B%5Cfrac%7B123%7D%7B8%7D%2A1%5D%5E%7B-1%7D%3D%5C%5C+%3D%5Cfrac%7B8%7D%7B123%7D "[(6\frac{3}{8}+(\frac{1}{3})^{-2})*(4*3^{-1}-\sqrt{9^{-1}})]^{-1}=\\ =[(\frac{51}{8}+9)*(4*\frac{1}{3}-\sqrt{\frac{1}{9}})]^{-1}=\\ =[(\frac{51}{8}+\frac{72}{8})*(\frac{4}{3}-\frac{1}{3})]^{-1}=\\ =[\frac{123}{8}*1]^{-1}=\\ =\frac{8}{123}")
======================
zad 3.7
a) 10⁵/10⁷=1/10²=10⁻²
------------------------------
b) (2³ * 3⁶)/(2⁷ * 3² * 5²)=
=3⁴/(2⁴ * 5²)
------------------------------
c) [2²⁰+2²⁰+2²⁰]/[4¹⁰+4¹⁰+4¹⁰]=
=[2²⁰+2²⁰+2²⁰]/[(2²)¹⁰+(2²)¹⁰+(2²)¹⁰]=
=[2²⁰+2²⁰+2²⁰]/[2²⁰+2²⁰+2²⁰]=
=1
======================
zad 3.8
a)
------------------------------
b)
------------------------------
c)![[\frac{2}{3}+(\frac{2}{3})^{-2}]^{-1}=[\frac{2}{3}+\frac{9}{4}]^{-1}=[\frac{8}{12}+\frac{27}{12}]^{-1}=(\frac{35}{12})^{-1}=\frac{12}{35}](https://tex.z-dn.net/?f=%5B%5Cfrac%7B2%7D%7B3%7D%2B%28%5Cfrac%7B2%7D%7B3%7D%29%5E%7B-2%7D%5D%5E%7B-1%7D%3D%5B%5Cfrac%7B2%7D%7B3%7D%2B%5Cfrac%7B9%7D%7B4%7D%5D%5E%7B-1%7D%3D%5B%5Cfrac%7B8%7D%7B12%7D%2B%5Cfrac%7B27%7D%7B12%7D%5D%5E%7B-1%7D%3D%28%5Cfrac%7B35%7D%7B12%7D%29%5E%7B-1%7D%3D%5Cfrac%7B12%7D%7B35%7D "[\frac{2}{3}+(\frac{2}{3})^{-2}]^{-1}=[\frac{2}{3}+\frac{9}{4}]^{-1}=[\frac{8}{12}+\frac{27}{12}]^{-1}=(\frac{35}{12})^{-1}=\frac{12}{35}")
======================
zad 3.44
a)
------------------------------
b)
------------------------------
c)![\frac{\sqrt[3]{\frac{8}{27}}*\sqrt{\frac{4}{9}}}{5^{-2}*125}=\frac{\frac{2}{3}*\frac{2}{3}}{\frac{1}{25}*125}=\frac{4}{9}*\frac{1}{5}=\frac{4}{45}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%5B3%5D%7B%5Cfrac%7B8%7D%7B27%7D%7D%2A%5Csqrt%7B%5Cfrac%7B4%7D%7B9%7D%7D%7D%7B5%5E%7B-2%7D%2A125%7D%3D%5Cfrac%7B%5Cfrac%7B2%7D%7B3%7D%2A%5Cfrac%7B2%7D%7B3%7D%7D%7B%5Cfrac%7B1%7D%7B25%7D%2A125%7D%3D%5Cfrac%7B4%7D%7B9%7D%2A%5Cfrac%7B1%7D%7B5%7D%3D%5Cfrac%7B4%7D%7B45%7D "\frac{\sqrt[3]{\frac{8}{27}}*\sqrt{\frac{4}{9}}}{5^{-2}*125}=\frac{\frac{2}{3}*\frac{2}{3}}{\frac{1}{25}*125}=\frac{4}{9}*\frac{1}{5}=\frac{4}{45}")
======================
zad 3.45
a) √49+3√16-(√25)²=
=7+3*4-25=
=7+12-25=
=-6
------------------------------
b) 6*√121-(√7)²=
=6*11-7=
=66-7=
=59
------------------------------
c) √[25-9]*(-2)=
=√16* (-2)=
=4*(-2)=
=-8
======================
zad 3.46
a) √12:√6*√2=√[12:6]*√2=√2*√2=2
------------------------------
b) √40*√5:√8=√[40*5]:√8=√200:√8=√[200:8]=√25=5
------------------------------
c) √27:(√6:√2)=√27:(√[6:2])=√27:√3=√[27:3]=√9=3
------------------------------
d) √3:(√2*√6)=√3:(√[2*6])=√3:√12=√3/√[4*3]=√3/2√3=1/2
======================
zad 3.47
a) √12=√[4*3]=√4*√3=2√3
------------------------------
b) √75=√[25*3]=√25*√3=5√3
------------------------------
c) ∛250=∛[125*2]=∛125*∛2=5∛2
------------------------------
d) ∛81=∛[27*3]=∛27*∛3=3∛3
======================
zad 3.48
a) 5-√8-(7+2√8)=
=5-√8-7-2√8=
=-2-3√8
------------------------------
b) (8-3√2)*√18=
=8√18-3√[2*18]=
=8√18-3√36=
=8√18-3*6=
=8√18-18
------------------------------
c) (3√8-√32):√2=
=3√[8:2]-√[32:2]=
=3√4-√16=
=3*2-4=
=6-4=
=2
======================
zad 3.50
a)![\frac{\sqrt[3]{1000}-\sqrt[3]{-343}}{\sqrt[3]{0,001}+\sqrt{0,9}^{2}}=\frac{10-(-7)}{0,1+0,9}=\frac{10+7}{1}=17](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%5B3%5D%7B1000%7D-%5Csqrt%5B3%5D%7B-343%7D%7D%7B%5Csqrt%5B3%5D%7B0%2C001%7D%2B%5Csqrt%7B0%2C9%7D%5E%7B2%7D%7D%3D%5Cfrac%7B10-%28-7%29%7D%7B0%2C1%2B0%2C9%7D%3D%5Cfrac%7B10%2B7%7D%7B1%7D%3D17 "\frac{\sqrt[3]{1000}-\sqrt[3]{-343}}{\sqrt[3]{0,001}+\sqrt{0,9}^{2}}=\frac{10-(-7)}{0,1+0,9}=\frac{10+7}{1}=17")
------------------------------
b)![\frac{\sqrt[3]{\frac{27}{8}}-\sqrt{10^{2}}}{\sqrt{0,5}^{2}-{\sqrt[3]{(-0,5)^{3}}}}=\frac{\frac{3}{2}-10}{0,5-(-0,5)}=\frac{1,5-10}{1}=0,5](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%5B3%5D%7B%5Cfrac%7B27%7D%7B8%7D%7D-%5Csqrt%7B10%5E%7B2%7D%7D%7D%7B%5Csqrt%7B0%2C5%7D%5E%7B2%7D-%7B%5Csqrt%5B3%5D%7B%28-0%2C5%29%5E%7B3%7D%7D%7D%7D%3D%5Cfrac%7B%5Cfrac%7B3%7D%7B2%7D-10%7D%7B0%2C5-%28-0%2C5%29%7D%3D%5Cfrac%7B1%2C5-10%7D%7B1%7D%3D0%2C5 "\frac{\sqrt[3]{\frac{27}{8}}-\sqrt{10^{2}}}{\sqrt{0,5}^{2}-{\sqrt[3]{(-0,5)^{3}}}}=\frac{\frac{3}{2}-10}{0,5-(-0,5)}=\frac{1,5-10}{1}=0,5")
======================
zad
a)![\sqrt[3]{131-\sqrt{36}}=\sqrt[3]{131-6}=\sqrt[3]{125}=5](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B131-%5Csqrt%7B36%7D%7D%3D%5Csqrt%5B3%5D%7B131-6%7D%3D%5Csqrt%5B3%5D%7B125%7D%3D5 "\sqrt[3]{131-\sqrt{36}}=\sqrt[3]{131-6}=\sqrt[3]{125}=5")
------------------------------
b)![\sqrt{38-\sqrt[3]{8}}=\sqrt{38-2}=\sqrt{36}=6](https://tex.z-dn.net/?f=%5Csqrt%7B38-%5Csqrt%5B3%5D%7B8%7D%7D%3D%5Csqrt%7B38-2%7D%3D%5Csqrt%7B36%7D%3D6 "\sqrt{38-\sqrt[3]{8}}=\sqrt{38-2}=\sqrt{36}=6")
------------------------------
d)
------------------------------
e)