Question

suppose s is between r and t. draw and label the diagram then use the segment addition postulate to solve for each variable.
6)
a. rs = 7y - 4
st = y + 5
rt = 28
b. rs = 3x + 1
st = 1/2x + 3
rt = 18
c. rs = 2z + 6
st = 4z - 3
rt = 5z + 12

Explanation:

Step1: Apply Segment Addition Postulate

According to the Segment Addition Postulate, $RS + ST=RT$.

Step2: Solve for y in part a

Substitute the given expressions into the postulate: $(7y - 4)+(y + 5)=28$.
Combine like - terms: $7y+y-4 + 5=28$, which simplifies to $8y+1 = 28$.
Subtract 1 from both sides: $8y=28 - 1=27$.
Divide both sides by 8: $y=\frac{27}{8}=3.375$.

Step3: Solve for x in part b

Substitute the given expressions into the postulate: $(3x + 1)+(\frac{1}{2}x+3)=18$.
Combine like - terms: $3x+\frac{1}{2}x+1 + 3=18$, which is $\frac{6x + x}{2}+4=18$, or $\frac{7x}{2}+4=18$.
Subtract 4 from both sides: $\frac{7x}{2}=18 - 4 = 14$.
Multiply both sides by $\frac{2}{7}$: $x=\frac{14\times2}{7}=4$.

Step4: Solve for z in part c

Substitute the given expressions into the postulate: $(2z + 6)+(4z-3)=5z + 12$.
Combine like - terms: $2z+4z+6 - 3=5z + 12$, which is $6z + 3=5z + 12$.
Subtract $5z$ from both sides: $6z-5z+3=12$, so $z+3=12$.
Subtract 3 from both sides: $z=12 - 3=9$.

Answer:

a. $y = 3.375$
b. $x = 4$
c. $z = 9$