2.5E: Mazoezi
- Page ID
- 177627
Mazoezi hufanya kamili
Tatua equations na Coefficients Fraction
Katika mazoezi yafuatayo, tatua kila equation na coefficients sehemu.
\(\frac{1}{4} x-\frac{1}{2}=-\frac{3}{4}\)
\(\frac{3}{4} x-\frac{1}{2}=\frac{1}{4}\)
- Jibu
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x=1
\(\frac{5}{6} y-\frac{2}{3}=-\frac{3}{2}\)
\(\frac{5}{6} y-\frac{1}{3}=-\frac{7}{6}\)
- Jibu
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\(y=-1\)
\(\frac{1}{2} a+\frac{3}{8}=\frac{3}{4}\)
\(\frac{5}{8} b+\frac{1}{2}=-\frac{3}{4}\)
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\(b=-2\)
\(2=\frac{1}{3} x-\frac{1}{2} x+\frac{2}{3} x\)
\(2=\frac{3}{5} x-\frac{1}{3} x+\frac{2}{5} x\)
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\(x=3\)
\(\frac{1}{4} m-\frac{4}{5} m+\frac{1}{2} m=-1\)
\(\frac{5}{6} n-\frac{1}{4} n-\frac{1}{2} n=-2\)
- Jibu
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\(n=-24\)
\(x+\frac{1}{2}=\frac{2}{3} x-\frac{1}{2}\)
\(x+\frac{3}{4}=\frac{1}{2} x-\frac{5}{4}\)
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\(x=-4\)
\(\frac{1}{3} w+\frac{5}{4}=w-\frac{1}{4}\)
\(\frac{3}{2} z+\frac{1}{3}=z-\frac{2}{3}\)
- Jibu
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\(z=-2\)
\(\frac{1}{2} x-\frac{1}{4}=\frac{1}{12} x+\frac{1}{6}\)
\(\frac{1}{2} a-\frac{1}{4}=\frac{1}{6} a+\frac{1}{12}\)
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\(a=1\)
\(\frac{1}{3} b+\frac{1}{5}=\frac{2}{5} b-\frac{3}{5}\)
\(\frac{1}{3} x+\frac{2}{5}=\frac{1}{5} x-\frac{2}{5}\)
- Jibu
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\(x=-6\)
\(1=\frac{1}{6}(12 x-6)\)
\(1=\frac{1}{5}(15 x-10)\)
- Jibu
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\(x=1\)
\(\frac{1}{4}(p-7)=\frac{1}{3}(p+5)\)
\(\frac{1}{5}(q+3)=\frac{1}{2}(q-3)\)
- Jibu
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\(q=7\)
\(\frac{1}{2}(x+4)=\frac{3}{4}\)
\(\frac{1}{3}(x+5)=\frac{5}{6}\)
- Jibu
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\(x=-\frac{5}{2}\)
\(\frac{5 q-8}{5}=\frac{2 q}{10}\)
\(\frac{4 m+2}{6}=\frac{m}{3}\)
- Jibu
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\(m=-1\)
\(\frac{4 n+8}{4}=\frac{n}{3}\)
\(\frac{3 p+6}{3}=\frac{p}{2}\)
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\(p=-4\)
\(\frac{u}{3}-4=\frac{u}{2}-3\)
\(\frac{v}{10}+1=\frac{v}{4}-2\)
- Jibu
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\(v=20\)
\(\frac{c}{15}+1=\frac{c}{10}-1\)
\(\frac{d}{6}+3=\frac{d}{8}+2\)
- Jibu
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\(d=-24\)
\(\frac{3 x+4}{2}+1=\frac{5 x+10}{8}\)
\(\frac{10 y-2}{3}+3=\frac{10 y+1}{9}\)
- Jibu
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\(y=-1\)
\(\frac{7 u-1}{4}-1=\frac{4 u+8}{5}\)
\(\frac{3 v-6}{2}+5=\frac{11 v-4}{5}\)
- Jibu
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\(v=4\)
Tatua equations na Coefficients ya Decimal
Katika mazoezi yafuatayo, tatua kila equation na coefficients decimal.
\(0.6 y+3=9\)
\(0.4 y-4=2\)
- Jibu
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\(y=15\)
\(3.6 j-2=5.2\)
\(2.1 k+3=7.2\)
- Jibu
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\(k=2\)
\(0.4 x+0.6=0.5 x-1.2\)
\(0.7 x+0.4=0.6 x+2.4\)
- Jibu
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\(x=20\)
\(0.23 x+1.47=0.37 x-1.05\)
\(0.48 x+1.56=0.58 x-0.64\)
- Jibu
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\(x=22\)
\(0.9 x-1.25=0.75 x+1.75\)
\(1.2 x-0.91=0.8 x+2.29\)
- Jibu
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\(x=8\)
\(0.05 n+0.10(n+8)=2.15\)
\(0.05 n+0.10(n+7)=3.55\)
- Jibu
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\(n=19\)
\(0.10 d+0.25(d+5)=4.05\)
\(0.10 d+0.25(d+7)=5.25\)
- Jibu
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\(d=10\)
\(0.05(q-5)+0.25 q=3.05\)
\(0.05(q-8)+0.25 q=4.10\)
- Jibu
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\(q=15\)
kila siku Math
Sarafu Taylor ina\(\$ 200\) katika dimes na pennies. Idadi ya pennies ni 2 zaidi ya idadi ya dimes. Kutatua equation\(0.10 d+0.01(d+2)=2\) kwa\(d\), idadi ya dimes.
Mihuri Paula kununuliwa $22.82 yenye thamani ya mihuri 49-asilimia na mihuri 21 asilimia. Idadi ya mihuri ya asilimia 21 ilikuwa 8 chini ya idadi ya mihuri ya asilimia 49. Kutatua equation\(0.49 s+0.21(s-8)=22.82\) kwa s, kupata idadi ya 49-asilimia mihuri Paula kununuliwa.
- Jibu
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\(s=35\)
Mazoezi ya kuandika
Eleza jinsi ya kupata denominator angalau ya kawaida ya\(\frac{3}{8}, \frac{1}{6},\) na\(\frac{2}{3}\)
Ikiwa equation ina sehemu ndogo, kuzidisha pande zote mbili na LCD hufanya iwe rahisi kutatua?
- Jibu
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Majibu yatatofautiana.
Ikiwa equation ina sehemu ndogo tu upande mmoja, kwa nini unapaswa kuzidisha pande zote mbili za equation na LCD?
Katika equation ni\(0.35 x+2.1=3.85\) nini LCD? Unajuaje?
- Jibu
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100. Haki zitatofautiana.
Self Check
ⓐ Baada ya kukamilisha mazoezi, tumia orodha hii ili kutathmini ujuzi wako wa malengo ya sehemu hii.
ⓑ Kwa ujumla, baada ya kuangalia orodha, unafikiri umeandaliwa vizuri kwa sehemu inayofuata? Kwa nini au kwa nini?