Question

1. find the length of uw if w is between u and v, uv = 16.8 centimeters, and vw = 7.9 centimeters. 35. find the value of x if m is between l and q, lm = 7x - 9, mq = 14 inches, and lq = 10x - 7. 36. find the length of qr if pq ≅ rs, pq = 9x - 7, and rs = 29. 37. find the value of x if ∠lom is between ∠l and ∠o, ∠lom = 6x - 4, ∠moq = 10 cm. 38. find the measure of nl if point p is between a and m, ap = 2.1 cm, pm = 5.8 cm. 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 at 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, 600 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.

Explanation:

Step1: Set up the equation for problem 35

Since $LM$ is between $L$ and $O$, we have $LO = LM+MO$. Given $LO = 10x - 7$, $LM=7x - 9$, and $MO = 14$ inches. So the equation is $10x-7=(7x - 9)+14$.

Step2: Simplify the right - hand side of the equation

$(7x - 9)+14=7x+(-9 + 14)=7x + 5$. So the equation becomes $10x-7=7x + 5$.

Step3: Isolate the variable terms

Subtract $7x$ from both sides: $10x-7x-7=7x-7x + 5$, which simplifies to $3x-7 = 5$.

Step4: Isolate the variable

Add 7 to both sides: $3x-7 + 7=5 + 7$, so $3x=12$.

Step5: Solve for x

Divide both sides by 3: $\frac{3x}{3}=\frac{12}{3}$, so $x = 4$.

Answer:

$x = 4$