Pregunta
11. If \( D F=78, D E=5 x-9 \), and \( E F=2 x+10 \), find \( E F \)
Ask by Salinas George. in the United States
Feb 03,2025
Solución de tutoría real
Respuesta verificada por el tutor
Responder
\( E F = 32 \)
Solución
To find \( EF \), we can use the fact that \( D F = D E + E F \). Given:
\[
D F = 78 \\
D E = 5x - 9 \\
E F = 2x + 10
\]
Substitute \( D E \) and \( E F \) into the equation for \( D F \):
\[
78 = (5x - 9) + (2x + 10)
\]
Combine like terms:
\[
78 = 7x + 1
\]
Subtract 1 from both sides:
\[
77 = 7x
\]
Divide both sides by 7:
\[
x = 11
\]
Now, substitute \( x = 11 \) back into the expression for \( E F \):
\[
E F = 2(11) + 10 = 22 + 10 = 32
\]
**Answer:** \( E F = 32 \)
Revisado y aprobado por el equipo de tutoría de UpStudy
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Simplifique esta solución The Deep Dive
To solve for \( E F \), we start with the equation \( D F = D E + E F \). Given \( D F = 78 \), \( D E = 5x - 9 \), and \( E F = 2x + 10 \), we can set up the equation: \[ 78 = (5x - 9) + (2x + 10) \] Now, simplify the right side: \[ 78 = 5x - 9 + 2x + 10 \] \[ 78 = 7x + 1 \] Next, isolate \( x \) by subtracting 1 from both sides: \[ 77 = 7x \] Now, divide by 7: \[ x = 11 \] With \( x \) known, substitute it back into the equation for \( E F \): \[ E F = 2x + 10 = 2(11) + 10 = 22 + 10 = 32 \] Thus, the value of \( E F \) is \( \boxed{32} \).
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