Question

find the measure of each segment. 28. $overline{mo}$ 29. $overline{wy}$ 32. $overline{de}$ 33. $overline{ux}$

Explanation:

Step1: Analyze MO

Since the segments between M and O are equal - length and MN = 4.6 cm, and there are 3 equal - length segments from M to O, then MO=3×4.6 cm.
$MO = 3\times4.6=13.8$ cm

Step2: Analyze WY

From the figure, we can directly see that the length of WY is given as 8.8 mm. So WY = 8.8 mm.

Step3: Analyze DE

Assume that the segments CD and DE are equal. So we set up the equation 2x + 7=4(x - 3).
First, expand the right - hand side: 2x+7 = 4x-12.
Then, move the x terms to one side and the constants to the other side: 4x - 2x=7 + 12.
$2x=19$, so $x=\frac{19}{2}=9.5$.
Substitute x into the expression for DE: DE = 4(x - 3)=4×(9.5 - 3)=4×6.5 = 26.

Step4: Analyze UX

UX=(3x + 1)+(4x - 6)+(2x + 8).
Combine like terms: UX=(3x+4x + 2x)+(1-6 + 8)=9x + 3.
We need to find x first. But if we assume the segments are in some equal - length relationship (not given clearly in the problem statement, assuming they are just combined to find the total length in terms of x), the length of UX is 9x + 3. If we had more information about x (such as an equality relationship between the segments), we could get a numerical value.

Answer:

1. MO = 13.8 cm
2. WY = 8.8 mm
3. DE = 26
4. UX = 9x + 3