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Sagot :
Claro, vamos a resolver cada proporción una a una detalladamente:
1. [tex]\(\frac{3}{4} = \frac{x}{8}\)[/tex]
[tex]\[ x = \frac{3}{4} \times 8 = 6.0 \][/tex]
Entonces, [tex]\(x = 6.0\)[/tex].
2. [tex]\(\frac{2}{n} = \frac{8}{32}\)[/tex]
[tex]\[ n = \frac{2}{\frac{8}{32}} = 8.0 \][/tex]
Entonces, [tex]\(n = 8.0\)[/tex].
3. [tex]\(\frac{4}{5} = \frac{12}{m}\)[/tex]
[tex]\[ m = \frac{12}{\frac{4}{5}} = 15.0 \][/tex]
Entonces, [tex]\(m = 15.0\)[/tex].
4. [tex]\(\frac{a}{5} = \frac{6}{15}\)[/tex]
[tex]\[ a = \frac{6}{15} \times 5 = 2.0 \][/tex]
Entonces, [tex]\(a = 2.0\)[/tex].
5. [tex]\(\frac{20}{x} = \frac{6}{15}\)[/tex]
[tex]\[ x = \frac{20}{\frac{6}{15}} = 50.0 \][/tex]
Entonces, [tex]\(x = 50.0\)[/tex].
6. [tex]\(\frac{7}{14} = \frac{y}{10}\)[/tex]
[tex]\[ y = \frac{7}{14} \times 10 = 5.0 \][/tex]
Entonces, [tex]\(y = 5.0\)[/tex].
7. [tex]\(\frac{x}{4} = \frac{6}{2}\)[/tex]
[tex]\[ x = \frac{6}{2} \times 4 = 12.0 \][/tex]
Entonces, [tex]\(x = 12.0\)[/tex].
8. [tex]\(\frac{2}{3} = \frac{12}{n}\)[/tex]
[tex]\[ n = \frac{12}{\frac{2}{3}} = 18.0 \][/tex]
Entonces, [tex]\(n = 18.0\)[/tex].
9. [tex]\(\frac{7}{8} = \frac{56}{p}\)[/tex]
[tex]\[ p = \frac{56}{\frac{7}{8}} = 64.0 \][/tex]
Entonces, [tex]\(p = 64.0\)[/tex].
10. [tex]\(\frac{x}{8} = \frac{9}{12}\)[/tex]
[tex]\[ x = \frac{9}{12} \times 8 = 6.0 \][/tex]
Entonces, [tex]\(x = 6.0\)[/tex].
11. [tex]\(\frac{3}{7} = \frac{z}{28}\)[/tex]
[tex]\[ z = \frac{3}{7} \times 28 = 12.0 \][/tex]
Entonces, [tex]\(z = 12.0\)[/tex].
12. [tex]\(\frac{y}{5} = \frac{8}{20}\)[/tex]
[tex]\[ y = \frac{8}{20} \times 5 = 2.0 \][/tex]
Entonces, [tex]\(y = 2.0\)[/tex].
13. [tex]\(\frac{3}{9} = \frac{x}{27}\)[/tex]
[tex]\[ x = \frac{3}{9} \times 27 = 9.0 \][/tex]
Entonces, [tex]\(x = 9.0\)[/tex].
14. [tex]\(\frac{x}{100} = \frac{150}{75}\)[/tex]
[tex]\[ x = \frac{150}{75} \times 100 = 200.0 \][/tex]
Entonces, [tex]\(x = 200.0\)[/tex].
15. [tex]\(\frac{15}{70} = \frac{30}{x}\)[/tex]
[tex]\[ x = \frac{30}{\frac{15}{70}} = 140.0 \][/tex]
Entonces, [tex]\(x = 140.0\)[/tex].
Resumiendo los valores encontrados:
1. [tex]\( x = 6.0 \)[/tex]
2. [tex]\( n = 8.0 \)[/tex]
3. [tex]\( m = 15.0 \)[/tex]
4. [tex]\( a = 2.0 \)[/tex]
5. [tex]\( x = 50.0 \)[/tex]
6. [tex]\( y = 5.0 \)[/tex]
7. [tex]\( x = 12.0 \)[/tex]
8. [tex]\( n = 18.0 \)[/tex]
9. [tex]\( p = 64.0 \)[/tex]
10. [tex]\( x = 6.0 \)[/tex]
11. [tex]\( z = 12.0 \)[/tex]
12. [tex]\( y = 2.0 \)[/tex]
13. [tex]\( x = 9.0 \)[/tex]
14. [tex]\( x = 200.0 \)[/tex]
15. [tex]\( x = 140.0 \)[/tex]
1. [tex]\(\frac{3}{4} = \frac{x}{8}\)[/tex]
[tex]\[ x = \frac{3}{4} \times 8 = 6.0 \][/tex]
Entonces, [tex]\(x = 6.0\)[/tex].
2. [tex]\(\frac{2}{n} = \frac{8}{32}\)[/tex]
[tex]\[ n = \frac{2}{\frac{8}{32}} = 8.0 \][/tex]
Entonces, [tex]\(n = 8.0\)[/tex].
3. [tex]\(\frac{4}{5} = \frac{12}{m}\)[/tex]
[tex]\[ m = \frac{12}{\frac{4}{5}} = 15.0 \][/tex]
Entonces, [tex]\(m = 15.0\)[/tex].
4. [tex]\(\frac{a}{5} = \frac{6}{15}\)[/tex]
[tex]\[ a = \frac{6}{15} \times 5 = 2.0 \][/tex]
Entonces, [tex]\(a = 2.0\)[/tex].
5. [tex]\(\frac{20}{x} = \frac{6}{15}\)[/tex]
[tex]\[ x = \frac{20}{\frac{6}{15}} = 50.0 \][/tex]
Entonces, [tex]\(x = 50.0\)[/tex].
6. [tex]\(\frac{7}{14} = \frac{y}{10}\)[/tex]
[tex]\[ y = \frac{7}{14} \times 10 = 5.0 \][/tex]
Entonces, [tex]\(y = 5.0\)[/tex].
7. [tex]\(\frac{x}{4} = \frac{6}{2}\)[/tex]
[tex]\[ x = \frac{6}{2} \times 4 = 12.0 \][/tex]
Entonces, [tex]\(x = 12.0\)[/tex].
8. [tex]\(\frac{2}{3} = \frac{12}{n}\)[/tex]
[tex]\[ n = \frac{12}{\frac{2}{3}} = 18.0 \][/tex]
Entonces, [tex]\(n = 18.0\)[/tex].
9. [tex]\(\frac{7}{8} = \frac{56}{p}\)[/tex]
[tex]\[ p = \frac{56}{\frac{7}{8}} = 64.0 \][/tex]
Entonces, [tex]\(p = 64.0\)[/tex].
10. [tex]\(\frac{x}{8} = \frac{9}{12}\)[/tex]
[tex]\[ x = \frac{9}{12} \times 8 = 6.0 \][/tex]
Entonces, [tex]\(x = 6.0\)[/tex].
11. [tex]\(\frac{3}{7} = \frac{z}{28}\)[/tex]
[tex]\[ z = \frac{3}{7} \times 28 = 12.0 \][/tex]
Entonces, [tex]\(z = 12.0\)[/tex].
12. [tex]\(\frac{y}{5} = \frac{8}{20}\)[/tex]
[tex]\[ y = \frac{8}{20} \times 5 = 2.0 \][/tex]
Entonces, [tex]\(y = 2.0\)[/tex].
13. [tex]\(\frac{3}{9} = \frac{x}{27}\)[/tex]
[tex]\[ x = \frac{3}{9} \times 27 = 9.0 \][/tex]
Entonces, [tex]\(x = 9.0\)[/tex].
14. [tex]\(\frac{x}{100} = \frac{150}{75}\)[/tex]
[tex]\[ x = \frac{150}{75} \times 100 = 200.0 \][/tex]
Entonces, [tex]\(x = 200.0\)[/tex].
15. [tex]\(\frac{15}{70} = \frac{30}{x}\)[/tex]
[tex]\[ x = \frac{30}{\frac{15}{70}} = 140.0 \][/tex]
Entonces, [tex]\(x = 140.0\)[/tex].
Resumiendo los valores encontrados:
1. [tex]\( x = 6.0 \)[/tex]
2. [tex]\( n = 8.0 \)[/tex]
3. [tex]\( m = 15.0 \)[/tex]
4. [tex]\( a = 2.0 \)[/tex]
5. [tex]\( x = 50.0 \)[/tex]
6. [tex]\( y = 5.0 \)[/tex]
7. [tex]\( x = 12.0 \)[/tex]
8. [tex]\( n = 18.0 \)[/tex]
9. [tex]\( p = 64.0 \)[/tex]
10. [tex]\( x = 6.0 \)[/tex]
11. [tex]\( z = 12.0 \)[/tex]
12. [tex]\( y = 2.0 \)[/tex]
13. [tex]\( x = 9.0 \)[/tex]
14. [tex]\( x = 200.0 \)[/tex]
15. [tex]\( x = 140.0 \)[/tex]
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