Respuesta :
The measure of side BC is 30 units.
Given:
Points A, B, and C are collinear and B lies between A and C.
[tex]AC=48[/tex]
[tex]AB=2x+2[/tex]
[tex]BC=3x+6[/tex]
To find:
The value of BC.
Solution:
Points A, B, and C are collinear and B lies between A and C. So,
[tex]AB+BC=AC[/tex] [Segment addition postulate]
[tex](2x+2)+(3x+6)=48[/tex]
[tex]5x+8=48[/tex]
Subtract 8 from both sides.
[tex]5x=48-8[/tex]
[tex]5x=40[/tex]
Divide both sides by 5.
[tex]\dfrac{5x}{5}=\dfrac{40}{5}[/tex]
[tex]x=8[/tex]
Now,
[tex]BC=3(8)+6[/tex]
[tex]BC=24+6[/tex]
[tex]BC=30[/tex]
Therefore, the value of BC is 30.
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The possible coordinates for G are -11 and 5.
Given:
On a number line, suppose point E has a coordinate of [tex]-3[/tex], and [tex]EG=8[/tex].
To find:
The possible coordinates of point G.
Solution:
Either point G lies 8 units left of point E or 8 units right of point E.
[tex]G=-3-8[/tex]
[tex]G=-11[/tex]
And
[tex]G=-3+8[/tex]
[tex]G=5[/tex]
Therefore, the possible coordinates for G are -11 and 5.
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