Answer :
Claro, vamos a resolver la tabla de conversiones y las ecuaciones paso a paso.
### Tabla de Conversiones
#### Convertir las unidades de medida
1. [tex]$7.95 \, hm$[/tex] a [tex]$Mm$[/tex]:
[tex]\[ 1 \, hm = 0.1 \, Mm \][/tex]
[tex]\[ 7.95 \, hm \times 0.1 \, Mm/hm = 0.795 \, Mm \][/tex]
Entonces, [tex]\( 7.95 \, hm = 0.795 \, Mm \)[/tex].
2. [tex]$95 \, dm$[/tex] a [tex]$dam$[/tex]:
[tex]\[ 1 \, dm = 0.01 \, dam \][/tex]
[tex]\[ 95 \, dm \times 0.01 \, dam/dm = 0.95 \, dam \][/tex]
Entonces, [tex]\( 95 \, dm = 0.95 \, dam \)[/tex].
3. [tex]$0.9 \, mam$[/tex] a [tex]$mm$[/tex]:
[tex]\[ 1 \, mam = 1000 \, mm \][/tex]
[tex]\[ 0.9 \, mam \times 1000 \, mm/mam = 900 \, mm \][/tex]
Entonces, [tex]\( 0.9 \, mam = 900 \, mm \)[/tex].
4. [tex]$954 \, mm$[/tex] a [tex]$Dam$[/tex]:
[tex]\[ 1 \, mm = 0.0001 \, Dam \][/tex]
[tex]\[ 954 \, mm \times 0.0001 \, Dam/mm = 0.0954 \, Dam \][/tex]
Entonces, [tex]\( 954 \, mm = 0.0954 \, Dam \)[/tex].
5. [tex]$12 \, km$[/tex] a [tex]$dm$[/tex]:
[tex]\[ 1 \, km = 10000 \, dm \][/tex]
[tex]\[ 12 \, km \times 10000 \, dm/km = 120,000 \, dm \][/tex]
Entonces, [tex]\( 12 \, km = 120,000 \, dm \)[/tex].
6. [tex]$96 \, m$[/tex] a [tex]$dn$[/tex]:
[tex]\[ 1 \, m = 0.1 \, dn \][/tex]
[tex]\[ 96 \, m \times 0.1 \, dn/m = 9.6 \, dn \][/tex]
Entonces, [tex]\( 96 \, m = 9.6 \, dn \)[/tex].
7. [tex]$9.45 \, ham$[/tex] a [tex]$Mm$[/tex]:
[tex]\[ 1 \, ham = 0.01 \, Mm \][/tex]
[tex]\[ 9.45 \, ham \times 0.01 \, Mm/ham = 0.0945 \, Mm \][/tex]
Entonces, [tex]\( 9.45 \, ham = 0.0945 \, Mm \)[/tex].
8. [tex]$34 \, cm$[/tex] a [tex]$m$[/tex]:
[tex]\[ 1 \, cm = 0.01 \, m \][/tex]
[tex]\[ 34 \, cm \times 0.01 \, m/cm = 0.34 \, m \][/tex]
Entonces, [tex]\( 34 \, cm = 0.34 \, m \)[/tex].
### Tabla Completa
[tex]\[ \begin{array}{|l|l|} \hline 7.95 \, hm & 0.795 \, Mm \\ \hline 95 \, dm & 0.95 \, dam \\ \hline 0.9 \, mam & 900 \, mm \\ \hline 954 \, mm & 0.0954 \, Dam \\ \hline 12 \, km & 120,000 \, dm \\ \hline 96 \, m & 9.6 \, dn \\ \hline 9.45 \, ham & 0.0945 \, Mm \\ \hline 34 \, cm & 0.34 \, m \\ \hline \end{array} \][/tex]
### Resolución de Ecuaciones
1. Ecuación A:
[tex]\[ x - (2x + 1) = 8 - (3x + 3) \][/tex]
Simplificando:
[tex]\[ x - 2x - 1 = 8 - 3x - 3 \][/tex]
[tex]\[ -x - 1 = 5 - 3x \][/tex]
[tex]\[ -x + 3x = 5 + 1 \][/tex]
[tex]\[ 2x = 6 \][/tex]
[tex]\[ x = 3 \][/tex]
2. Ecuación B:
[tex]\[ 15x - 10 = 6x - (x + 2) + (-x + 3) \][/tex]
Simplificando:
[tex]\[ 15x - 10 = 6x - x - 2 - x + 3 \][/tex]
[tex]\[ 15x - 10 = 4x + 1 \][/tex]
[tex]\[ 15x - 4x = 11 \][/tex]
[tex]\[ 11x = 11 \][/tex]
[tex]\[ x = 1 \][/tex]
3. Ecuación C:
[tex]\[ (5 - 3x) - (-4x + 6) = (8x + 11) - (3x - 6) \][/tex]
Simplificando:
[tex]\[ 5 - 3x + 4x - 6 = 8x + 11 - 3x + 6 \][/tex]
[tex]\[ 5 - 6 + x = 8x + 11 - 3x + 6 \][/tex]
[tex]\[ x - 1 = 5x + 17 \][/tex]
[tex]\[ x - 5x = 17 + 1 \][/tex]
[tex]\[ -4x = 18 \][/tex]
[tex]\[ x = -\frac{18}{4} \][/tex]
[tex]\[ x = -4.5 \][/tex]
4. Ecuación D:
[tex]\[ 3x + [-5x - (x + 3)] = 8x + (-5x - 9) \][/tex]
Simplificando:
[tex]\[ 3x + [-5x - x - 3] = 8x - 5x - 9 \][/tex]
[tex]\[ 3x - 6x - 3 = 3x - 9 \][/tex]
[tex]\[ -3x - 3 = 3x - 9 \][/tex]
[tex]\[ -3x - 3x = -9 + 3 \][/tex]
[tex]\[ -6x = -6 \][/tex]
[tex]\[ x = 1 \][/tex]
5. Ecuación E:
[tex]\[ 5x = 8x - 15 \][/tex]
Simplificando:
[tex]\[ 5x - 8x = -15 \][/tex]
[tex]\[ -3x = -15 \][/tex]
[tex]\[ x = 5 \][/tex]
Entonces, las soluciones son las siguientes:
- A) [tex]\( x = 3 \)[/tex]
- B) [tex]\( x = 1 \)[/tex]
- C) [tex]\( x = -4.5 \)[/tex]
- D) [tex]\( x = 1 \)[/tex]
- E) [tex]\( x = 5 \)[/tex]
### Tabla de Conversiones
#### Convertir las unidades de medida
1. [tex]$7.95 \, hm$[/tex] a [tex]$Mm$[/tex]:
[tex]\[ 1 \, hm = 0.1 \, Mm \][/tex]
[tex]\[ 7.95 \, hm \times 0.1 \, Mm/hm = 0.795 \, Mm \][/tex]
Entonces, [tex]\( 7.95 \, hm = 0.795 \, Mm \)[/tex].
2. [tex]$95 \, dm$[/tex] a [tex]$dam$[/tex]:
[tex]\[ 1 \, dm = 0.01 \, dam \][/tex]
[tex]\[ 95 \, dm \times 0.01 \, dam/dm = 0.95 \, dam \][/tex]
Entonces, [tex]\( 95 \, dm = 0.95 \, dam \)[/tex].
3. [tex]$0.9 \, mam$[/tex] a [tex]$mm$[/tex]:
[tex]\[ 1 \, mam = 1000 \, mm \][/tex]
[tex]\[ 0.9 \, mam \times 1000 \, mm/mam = 900 \, mm \][/tex]
Entonces, [tex]\( 0.9 \, mam = 900 \, mm \)[/tex].
4. [tex]$954 \, mm$[/tex] a [tex]$Dam$[/tex]:
[tex]\[ 1 \, mm = 0.0001 \, Dam \][/tex]
[tex]\[ 954 \, mm \times 0.0001 \, Dam/mm = 0.0954 \, Dam \][/tex]
Entonces, [tex]\( 954 \, mm = 0.0954 \, Dam \)[/tex].
5. [tex]$12 \, km$[/tex] a [tex]$dm$[/tex]:
[tex]\[ 1 \, km = 10000 \, dm \][/tex]
[tex]\[ 12 \, km \times 10000 \, dm/km = 120,000 \, dm \][/tex]
Entonces, [tex]\( 12 \, km = 120,000 \, dm \)[/tex].
6. [tex]$96 \, m$[/tex] a [tex]$dn$[/tex]:
[tex]\[ 1 \, m = 0.1 \, dn \][/tex]
[tex]\[ 96 \, m \times 0.1 \, dn/m = 9.6 \, dn \][/tex]
Entonces, [tex]\( 96 \, m = 9.6 \, dn \)[/tex].
7. [tex]$9.45 \, ham$[/tex] a [tex]$Mm$[/tex]:
[tex]\[ 1 \, ham = 0.01 \, Mm \][/tex]
[tex]\[ 9.45 \, ham \times 0.01 \, Mm/ham = 0.0945 \, Mm \][/tex]
Entonces, [tex]\( 9.45 \, ham = 0.0945 \, Mm \)[/tex].
8. [tex]$34 \, cm$[/tex] a [tex]$m$[/tex]:
[tex]\[ 1 \, cm = 0.01 \, m \][/tex]
[tex]\[ 34 \, cm \times 0.01 \, m/cm = 0.34 \, m \][/tex]
Entonces, [tex]\( 34 \, cm = 0.34 \, m \)[/tex].
### Tabla Completa
[tex]\[ \begin{array}{|l|l|} \hline 7.95 \, hm & 0.795 \, Mm \\ \hline 95 \, dm & 0.95 \, dam \\ \hline 0.9 \, mam & 900 \, mm \\ \hline 954 \, mm & 0.0954 \, Dam \\ \hline 12 \, km & 120,000 \, dm \\ \hline 96 \, m & 9.6 \, dn \\ \hline 9.45 \, ham & 0.0945 \, Mm \\ \hline 34 \, cm & 0.34 \, m \\ \hline \end{array} \][/tex]
### Resolución de Ecuaciones
1. Ecuación A:
[tex]\[ x - (2x + 1) = 8 - (3x + 3) \][/tex]
Simplificando:
[tex]\[ x - 2x - 1 = 8 - 3x - 3 \][/tex]
[tex]\[ -x - 1 = 5 - 3x \][/tex]
[tex]\[ -x + 3x = 5 + 1 \][/tex]
[tex]\[ 2x = 6 \][/tex]
[tex]\[ x = 3 \][/tex]
2. Ecuación B:
[tex]\[ 15x - 10 = 6x - (x + 2) + (-x + 3) \][/tex]
Simplificando:
[tex]\[ 15x - 10 = 6x - x - 2 - x + 3 \][/tex]
[tex]\[ 15x - 10 = 4x + 1 \][/tex]
[tex]\[ 15x - 4x = 11 \][/tex]
[tex]\[ 11x = 11 \][/tex]
[tex]\[ x = 1 \][/tex]
3. Ecuación C:
[tex]\[ (5 - 3x) - (-4x + 6) = (8x + 11) - (3x - 6) \][/tex]
Simplificando:
[tex]\[ 5 - 3x + 4x - 6 = 8x + 11 - 3x + 6 \][/tex]
[tex]\[ 5 - 6 + x = 8x + 11 - 3x + 6 \][/tex]
[tex]\[ x - 1 = 5x + 17 \][/tex]
[tex]\[ x - 5x = 17 + 1 \][/tex]
[tex]\[ -4x = 18 \][/tex]
[tex]\[ x = -\frac{18}{4} \][/tex]
[tex]\[ x = -4.5 \][/tex]
4. Ecuación D:
[tex]\[ 3x + [-5x - (x + 3)] = 8x + (-5x - 9) \][/tex]
Simplificando:
[tex]\[ 3x + [-5x - x - 3] = 8x - 5x - 9 \][/tex]
[tex]\[ 3x - 6x - 3 = 3x - 9 \][/tex]
[tex]\[ -3x - 3 = 3x - 9 \][/tex]
[tex]\[ -3x - 3x = -9 + 3 \][/tex]
[tex]\[ -6x = -6 \][/tex]
[tex]\[ x = 1 \][/tex]
5. Ecuación E:
[tex]\[ 5x = 8x - 15 \][/tex]
Simplificando:
[tex]\[ 5x - 8x = -15 \][/tex]
[tex]\[ -3x = -15 \][/tex]
[tex]\[ x = 5 \][/tex]
Entonces, las soluciones son las siguientes:
- A) [tex]\( x = 3 \)[/tex]
- B) [tex]\( x = 1 \)[/tex]
- C) [tex]\( x = -4.5 \)[/tex]
- D) [tex]\( x = 1 \)[/tex]
- E) [tex]\( x = 5 \)[/tex]
