34. find the length of $overline{uw}$ if $w$ is between $u$ and $v$, $uv = 16.8$ centimeters, and $vw = 7.9$ centimeters.
35. find the value of $x$ if $rs = 24$ centimeters.
36. find the length of $overline{lo}$ if $m$ is between $l$ and $o$, $lm = 7x - 9$, $mo = 14$ inches, and $lo = 10x - 7$.
37. find the value of $x$ if $overline{pq}congoverline{rs}$, $pq = 9x - 7$, and $rs = 29$.
38. find the measure of $overline{nl}$.
39. precision if point $p$ is between $a$ and $m$, write a true statement.
40. hiking a hiking trail is 20 kilometers long. park organizers want to build 5 rest stops for hikers with one on each end of the trail and the other 3 spaced evenly between. how much distance will separate successive rest stops?
41. race the map shows the route of a race. you are at $y$, 6000 feet from the first checkpoint $a$. the second checkpoint $b$ is located at the mid - point between $a$ and the end of the race $z$. the total race is 3.1 miles. how far apart are the two checkpoints?
42. field trip the marching band at jefferson high school is taking a field trip from lansing, michigan, to detroit, michigan. the bus driver was told to stop 53 miles into the trip. if the rest of the trip is 41 miles and the entire journey can be represented by the expression $3x + 16$, find the value of $x$.

Question

Accepted Answer

### 34.
# Explanation:
## Step1: Use segment - addition postulate
Since $UW + VW=UV$, then $UW = UV - VW$.
## Step2: Substitute given values
Given $UV = 16.8$ cm and $VW = 7.9$ cm, so $UW=16.8 - 7.9$.
## Step3: Calculate the result
$UW = 8.9$ cm.
# Answer:
$8.9$ cm

### 35.
# Explanation:
## Step1: Use segment - addition postulate
Since $RS=RT + TS$, and $RS = 24$ cm, $RT = 6x - 4$, $TS = 10$ cm, we have the equation $6x-4 + 10=24$.
## Step2: Simplify the left - hand side
$6x+6 = 24$.
## Step3: Isolate the variable term
Subtract 6 from both sides: $6x=24 - 6=18$.
## Step4: Solve for $x$
Divide both sides by 6: $x=\frac{18}{6}=3$.
# Answer:
$x = 3$

### 36.
# Explanation:
## Step1: Use segment - addition postulate
Since $LO=LM + MO$, and $LO = 10x - 7$, $LM = 7x - 9$, $MO = 14$ inches, we get the equation $10x-7=(7x - 9)+14$.
## Step2: Simplify the right - hand side
$10x-7=7x + 5$.
## Step3: Isolate the variable terms
Subtract $7x$ from both sides: $10x-7x-7=7x-7x + 5$, $3x-7 = 5$.
## Step4: Isolate the variable
Add 7 to both sides: $3x=5 + 7 = 12$.
## Step5: Solve for $x$
Divide both sides by 3: $x = 4$.
## Step6: Find the length of $LO$
Substitute $x = 4$ into $LO = 10x - 7$, $LO=10\times4-7=40 - 7 = 33$ inches.
# Answer:
$33$ inches

### 37.
# Explanation:
## Step1: Use congruent - segment property
Since $\overline{PQ}\cong\overline{RS}$, then $PQ = RS$. Given $PQ = 9x - 7$ and $RS = 29$, we have the equation $9x-7=29$.
## Step2: Isolate the variable term
Add 7 to both sides: $9x=29 + 7=36$.
## Step3: Solve for $x$
Divide both sides by 9: $x=\frac{36}{9}=4$.
# Answer:
$x = 4$

### 38.
# Explanation:
## Step1: Use segment - addition postulate
Since $NL=MN+ML$, and $MN = 2.1$ cm, $ML = 5.8$ cm, then $NL=2.1 + 5.8$.
## Step2: Calculate the result
$NL = 7.9$ cm.
# Answer:
$7.9$ cm

### 40.
# Explanation:
## Step1: Determine the number of intervals
There are 5 rest - stops, so there are 6 intervals (including the intervals from the start and end of the trail to the first and last rest - stops).
## Step2: Calculate the length of each interval
The length of the trail is 20 km. Let $d$ be the distance between successive rest - stops. Then $d=\frac{20}{6}=\frac{10}{3}\approx3.33$ km.
# Answer:
$\frac{10}{3}$ km or approximately $3.33$ km

### 41.
# Explanation:
## Step1: Convert miles to feet
Since 1 mile = 5280 feet, the total length of the race $Z$ in feet is $3.1\times5280 = 16368$ feet.
## Step2: Find the distance from $A$ to $Z$
You are at $Y$, 6000 feet from $A$. Let the distance from $A$ to $Z$ be $d_{AZ}$. Then $d_{AZ}=16368 - 6000=10368$ feet.
## Step3: Find the distance from $A$ to $B$
Since $B$ is the mid - point between $A$ and $Z$, the distance from $A$ to $B$ is $\frac{d_{AZ}}{2}=\frac{10368}{2}=5184$ feet.
# Answer:
$5184$ feet

### 42.
# Explanation:
## Step1: Find the total distance of the trip
The total distance of the trip is the sum of the distance already traveled and the remaining distance. So the total distance is $53 + 41=94$ miles.
## Step2: Set up an equation
Since the total distance is represented by $3x + 16$, we have the equation $3x+16 = 94$.
## Step3: Isolate the variable term
Subtract 16 from both sides: $3x=94 - 16=78$.
## Step4: Solve for $x$
Divide both sides by 3: $x=\frac{78}{3}=26$.
# Answer:
$x = 26$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

34.

Step1: Use segment - addition postulate

Step2: Substitute given values

Step3: Calculate the result

Step1: Use segment - addition postulate

Step2: Simplify the left - hand side

Step3: Isolate the variable term

Step4: Solve for \(x\)

Step1: Use segment - addition postulate

Step2: Simplify the right - hand side

Step3: Isolate the variable terms

Step4: Isolate the variable

Step5: Solve for \(x\)

Step6: Find the length of \(LO\)

Answer:

35.