me podrían ayudar con esto intente tomar una foto mejor pero no pude...por favor y gracias

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CallahanW295737 CallahanW295737

29-10-2022
Mathematics

contestada

me podrían ayudar con esto intente tomar una foto mejor pero no pude...por favor y gracias

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BrayliS357947 BrayliS357947 · Answer 1 · 2022-10-29T22:07:45+02:00

we have the following:

1.

[tex]\begin{gathered} AB=x,BC=4x,AC=35 \\ AC=AB+BC \\ 35=x+4x \\ 35=5x \\ x=\frac{35}{5}=7 \\ AB=7,BC=7\cdot4=28 \end{gathered}[/tex]

2.

[tex]\begin{gathered} AB=5,BC=6x+1,AC=42 \\ AC=AB+BC \\ 42=5+6x+1 \\ 6x=36 \\ x=\frac{36}{6}=6 \\ BC=6\cdot6+1=37 \end{gathered}[/tex]

3.

[tex]\begin{gathered} AB=x+4,BC=8x-4,AC=63 \\ AC=AB+BC \\ 63=x+4+8x-4 \\ 9x=63 \\ x=\frac{63}{9}=7 \\ AB=7+4=11,BC=8\cdot7-4=52,AC=63 \end{gathered}[/tex]

4.

[tex]\begin{gathered} AB=2x+4,BC=6x+15,AC=91 \\ AC=AB+BC \\ 91=2x+4+6x+15 \\ 8x=72 \\ x=\frac{72}{8}=9 \\ AB=2\cdot9+4=22,BC=6\cdot9+15=69,AC=91 \end{gathered}[/tex]

5.

[tex]\begin{gathered} AB=3x-1,BC=6x+5,AC=3x+22 \\ AC=AB+BC \\ 3x+22=3x-1+6x+5 \\ 6x=18 \\ x=\frac{18}{6}=3 \\ AB=3\cdot3-1=8,BC=6\cdot3+5=23,AC=3\cdot3+22=31 \end{gathered}[/tex]

6.

[tex]\begin{gathered} AB=2x-3,BC=8x-7,AC=9x+14 \\ 9x+14=2x-3+8x-7 \\ x=24 \\ AB=2\cdot24-3=45,BC=8\cdot24-7=185,AC=9\cdot24+14=230 \\ \end{gathered}[/tex][tex]\begin{gathered} AB=3x+6,BC=5x+8,AC=15x \\ AC=AB+BC \\ 15x=3x+6+5x+8 \\ 7x=14 \\ x=\frac{14}{7}=2 \\ AB=3\cdot2+6=12,BC=5\cdot2+8=18,AC=15\cdot2=30 \end{gathered}[/tex]