Question

let c be between d and e. use the segment addition postulate to solve for y. dc = 3y - 30, ce = 6y - 15, de = 27. a. y = 3 b. y = 11 c. y = -5 d. y = 7

Explanation:

Step1: Apply Segment - Addition Postulate

According to the Segment - Addition Postulate, if C is between D and E, then \(DC + CE=DE\). Given \(DC = 3y - 30\), \(CE = 6y - 15\), and \(DE = 27\), we substitute these values into the equation: \((3y - 30)+(6y - 15)=27\).

Step2: Combine like - terms

Combine the y - terms and the constant terms on the left - hand side: \(3y+6y-30 - 15 = 27\), which simplifies to \(9y-45 = 27\).

Step3: Isolate the variable term

Add 45 to both sides of the equation: \(9y-45 + 45=27 + 45\), resulting in \(9y=72\).

Step4: Solve for y

Divide both sides of the equation by 9: \(\frac{9y}{9}=\frac{72}{9}\), so \(y = 8\). But this is not in the given options. Let's re - check our work.

Let's correct the substitution and combination of terms again.
\((3y - 30)+(6y - 15)=27\)
\(3y+6y-30 - 15=27\)
\(9y-45 = 27\)
Add 45 to both sides: \(9y=27 + 45=72\)
Divide by 9: \(y = 8\) (There seems to be a misprint in the problem or options)

If we assume there is an error and we work with the correct method:

Answer:

None of the given options (a. \(y = 3\), b. \(y = 11\), c. \(y=-5\), d. Not clear from the image but assuming it's a non - relevant option) are correct. If we follow the Segment - Addition Postulate correctly, \(y = 8\).