Question

find xy.
1.
2.
3.
4.
find the value x.
5.
6.
7.
8.
point c is between a and b on ab. use the given information to write an equation in terms of x. then s equation to find x, ac, cb, and ab.
9.
ac = 3x + 16
bc = 10
ab = 16x
10.
ac = 2x + 5
cb = 5x + 15
ab = 27x

Explanation:

Step1: Use segment addition postulate

For problem 1: By segment addition postulate \(XY = XZ+ZY\). Given \(XZ = 7\) and \(ZY=9\).

Step2: Calculate \(XY\)

\(XY=7 + 9\)
For problem 2: By segment addition postulate \(ZY=XY - XZ\). Given \(XY = 12\) and \(XZ = 5\)
\(ZY=12-5\)
For problem 3: By segment addition postulate \(XY=XZ - YZ\). Given \(XZ = 24\) and \(YZ = 8\)
\(XY=24 - 8\)
For problem 4: By segment addition postulate \(XY=XZ - ZY\). Given \(XZ = 12\) and \(ZY = 3\)
\(XY=12-3\)
For problem 5: By segment addition postulate \(AC+CB=AB\). Given \(AC = 6\), \(CB=2x + 10\) and \(AB = 36\)
\(6+(2x + 10)=36\)
\(2x+16 = 36\)
\(2x=36 - 16\)
\(2x=20\)
\(x = 10\)
For problem 6: By segment addition postulate \(DE+EF=DF\). Given \(DE = 22\), \(EF=3x - 6\) and \(DF = 40\)
\(22+(3x - 6)=40\)
\(3x+16 = 40\)
\(3x=40 - 16\)
\(3x=24\)
\(x = 8\)
For problem 7: By segment addition postulate \(JK+KL=JL\). Given \(JK = 20\), \(KL = 4\) and \(JL = 8x\)
\(20 + 4=8x\)
\(24=8x\)
\(x = 3\)
For problem 8: By segment addition postulate \(GH+HI=GI\). Given \(GH = 8\), \(HI=5x - 3\) and \(GI=- 10+20x\)
\(8+(5x - 3)=-10 + 20x\)
\(5x+5=-10 + 20x\)
\(20x-5x=5 + 10\)
\(15x=15\)
\(x = 1\)
For problem 9: By segment addition postulate \(AC+BC=AB\). Given \(AC = 3x + 16\), \(BC = 10\) and \(AB = 16x\)
\((3x + 16)+10=16x\)
\(3x+26=16x\)
\(16x-3x=26\)
\(13x=26\)
\(x = 2\)
\(AC=3\times2+16=6 + 16=22\)
\(CB = 10\)
\(AB=16\times2=32\)
For problem 10: By segment addition postulate \(AC+CB=AB\). Given \(AC = 2x + 5\), \(CB=5x + 15\) and \(AB = 27x\)
\((2x + 5)+(5x + 15)=27x\)
\(7x+20=27x\)
\(27x-7x=20\)
\(20x=20\)
\(x = 1\)
\(AC=2\times1+5=7\)
\(CB=5\times1+15=20\)
\(AB=27\times1=27\)

Answer:

1. \(XY = 16\)
2. \(ZY = 7\)
3. \(XY = 16\)
4. \(XY = 9\)
5. \(x = 10\)
6. \(x = 8\)
7. \(x = 3\)
8. \(x = 1\)
9. \(x = 2\), \(AC = 22\), \(CB = 10\), \(AB = 32\)
10. \(x = 1\), \(AC = 7\), \(CB = 20\), \(AB = 27\)