Question

1. a farmer plants trees in a straight row that is 21 feet long. the trees must be 7 feet from each other. how many trees can be planted in this row? draw a sketch to explain your answer.
2. the segment jl has midpoint m. jm = 3x + 2 and ml = 14 - x. what is the value of x?

a 6
b 3
c 16
d 12

Explanation:

7 feet apart. The number of 7 - foot intervals is $21\div7 = 3$.

Step2: Determine number of trees

The number of trees is one more than the number of intervals. So the number of trees is $3 + 1=4$.

Step3: Solve for x in segment problem

Since M is the mid - point of segment JL, then $JM = ML$. So we set up the equation $3x + 2=14 - x$.

Step4: Combine like terms

Add x to both sides: $3x+x + 2=14 - x+x$, which simplifies to $4x+2 = 14$.

Step5: Isolate x

Subtract 2 from both sides: $4x+2 - 2=14 - 2$, getting $4x = 12$. Then divide both sides by 4: $x=\frac{12}{4}=3$.

Answer:

For question 21: 4 trees
For question 22: B. 3