8.6E: Mazoezi
- Page ID
- 177685
Mazoezi hufanya kamili
Kutatua milinganyo ya busara
Katika mazoezi yafuatayo, tatua.
\(\frac{1}{a}+\frac{2}{5}=\frac{1}{2}\)
- Jibu
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10
\(\frac{5}{6}+\frac{3}{b}=\frac{1}{3}\)
\(\frac{5}{2}−\frac{1}{c}=\frac{3}{4}\)
- Jibu
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\(\frac{4}{7}\)
\(\frac{6}{3}−\frac{2}{d}=\frac{4}{9}\)
\(\frac{4}{5}+\frac{1}{4}=\frac{2}{v}\)
- Jibu
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\(\frac{40}{21}\)
\(\frac{3}{7}+\frac{2}{3}=\frac{1}{w}\)
\(\frac{7}{9}+\frac{1}{x}=\frac{2}{3}\)
- Jibu
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-9
\(\frac{3}{8}+\frac{2}{y}=\frac{1}{4}\)
\(1−\frac{2}{m}=\frac{8}{m^2}\)
- Jibu
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-2, 4
\(1+\frac{4}{n}=\frac{21}{n^2}\)
\(1+\frac{9}{p}=−\frac{20}{p^2}\)
- Jibu
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-5, -4
\(1−\frac{7}{q}=−\frac{6}{q^2}\)
\(\frac{1}{r+3}=\frac{4}{2r}\)
- Jibu
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-6
\(\frac{3}{t−6}=\frac{1}{t}\)
\(\frac{5}{3v−2}=\frac{7}{4v}\)
- Jibu
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14
\(\frac{8}{2w+1}=\frac{3}{w}\)
\(\frac{3}{x+4}+\frac{7}{x−4}=\frac{8}{x^2−16}\)
- Jibu
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\(-\frac{4}{5}\)
\(\frac{5}{y−9}+\frac{1}{y+9}=\frac{18}{y^2−81}\)
\(\frac{8}{z−10}+\frac{7}{z+10}=\frac{5}{z^2−100}\)
- Jibu
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-13
\(\frac{9}{a+11}+\frac{6}{a−11}=\frac{7}{a^2−121}\)
\(\frac{1}{q+4}−\frac{7}{q−2}=1\)
- Jibu
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hakuna suluhisho
\(\frac{3}{r+10}−\frac{4}{r−4}=1\)
\(\frac{1}{t+7}−\frac{5}{t−5}=1\)
- Jibu
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-5, -1
\(\frac{2}{s+7}−\frac{3}{s−3}=1\)
\(\frac{v−10}{v^2−5v+4}=\frac{3}{v−1}−\frac{6}{v−4}\)
- Jibu
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hakuna suluhisho
\(\frac{w+8}{w^2−11w+28}=\frac{5}{w−7}+\frac{2}{w−4}\)
\(\frac{x−10}{x^2+8x+12}=\frac{3}{x+2}+\frac{4}{x+6}\)
- Jibu
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hakuna suluhisho
\(\frac{y−3}{y^2−4y−5}=\frac{1}{y+1}+\frac{8}{y−5}\)
\(\frac{z}{16}+\frac{z+2}{4z}=\frac{1}{2z}\)
- Jibu
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-4
\(\frac{a}{9}+\frac{a+3}{3a}=\frac{1}{a}\)
\(\frac{b+3}{3b}+\frac{b}{24}=\frac{1}{b}\)
- Jibu
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-8
\(\frac{c+3}{12c}+\frac{c}{36}=\frac{1}{4c}\)
\(\frac{d}{d+3}=\frac{18}{d^2−9}+4\)
- Jibu
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2
\(\frac{m}{m+5}=\frac{50}{m^2−25}+6\)
\(\frac{n}{n+2}=\frac{8}{n^2−4}+3\)
- Jibu
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1
\(\frac{p}{p+7}=\frac{98}{p^2−49}+8\)
\(\frac{q}{3q−9}−\frac{3}{4q+12}=\frac{7q^2+6q+63}{24q^2−216}\)
- Jibu
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hakuna suluhisho
\(\frac{r}{3r−15}−\frac{1}{4r+20}=\frac{3r^2+17r+40}{12r^2−300}\)
\(\frac{s}{2s+6}−\frac{2}{5s+5}=\frac{5s^2−3s−7}{10s^2+40s+30}\)
- Jibu
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hakuna suluhisho
\(\frac{t}{6t−12}−\frac{5}{2t+10}=\frac{t^2−23t+70}{12t^2+36t−120}\)
Tatua Equation ya Mantiki kwa Variable Maalum
Katika mazoezi yafuatayo, tatua.
\(\frac{C}{r}=2π\)kwa r
- Jibu
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\(r=\frac{C}{2π}\)
\(\frac{I}{r}=P\)kwa r
\(\frac{V}{h}=lw\)kwa h
- Jibu
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\(h=\frac{v}{lw}\)
\(\frac{2A}{b}=h\)kwa b
\(\frac{v+3}{w−1}=\frac{1}{2}\)kwa w
- Jibu
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w=2v+7
\(\frac{x+5}{2−y}=\frac{4}{3}\)kwa y
\(a=\frac{b+3}{c−2}\)kwa c
- Jibu
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\(c=\frac{b+3+2a}{a}\)
\(m=\frac{n}{2−n}\)kwa n
\(\frac{1}{p}+\frac{2}{q}=4\)kwa p
- Jibu
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\(p=\frac{q}{4q−2}\)
\(\frac{3}{s}+\frac{1}{t}=2\)kwa s
\(\frac{2}{v}+\frac{1}{5}=\frac{1}{2}\)kwa w
- Jibu
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\(w=\frac{15v}{10+v}\)
\(\frac{6}{x}+\frac{2}{3}=\frac{1}{y}\)kwa y
\(\frac{m+3}{n−2}=\frac{4}{5}\)kwa n
- Jibu
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\(n=\frac{5m+23}{m}\)
\(\frac{E}{c}=m^2\)kwa c
\(\frac{3}{x}−\frac{5}{y}=\frac{1}{4}\)kwa y
- Jibu
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\(y=\frac{20x}{12−x}\)
\(\frac{R}{T}=W\)kwa T
\(r=\frac{s}{3−t}\)kwa t
- Jibu
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\(t=\frac{3r−s}{r}\)
\(c=\frac{2}{a}+\frac{b}{5}\)kwa
kila siku Math
Uchoraji wa Nyumba Alain anaweza kuchora nyumba katika siku 4. Spiro itachukua siku 7 kuchora nyumba moja. Kutatua equation\(\frac{1}{4}+\frac{1}{7}=\frac{1}{t}\) kwa t kupata idadi ya siku ingekuwa kuchukua yao kwa rangi ya nyumba kama kazi pamoja.
- Jibu
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\(2\frac{6}{11}\)siku
Boating Ari anaweza kuendesha mashua yake 18 maili na sasa katika kiasi hicho cha muda inachukua kuendesha 10 maili dhidi ya sasa. Ikiwa kasi ya mashua ni ncha 7, tatua equation\(\frac{18}{7+c}=\frac{10}{7−c}\) kwa c ili kupata kasi ya sasa.
Mazoezi ya kuandika
Kwa nini hakuna suluhisho la equation\(\frac{3}{x−2}=\frac{5}{x−2}\)
- Jibu
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Majibu yatatofautiana.
Pete anadhani equation\(\frac{y}{y+6}=\frac{72}{y^2−36}+4\) ina ufumbuzi mbili, y=-6 na y=4. Eleza kwa nini Pete ni makosa.
Self Check
ⓐ Baada ya kukamilisha mazoezi, tumia orodha hii ili kutathmini ujuzi wako wa malengo ya sehemu hii.
ⓑ Baada ya kuchunguza orodha hii, utafanya nini ili uwe na ujasiri kwa malengo yote?