Question

question 4
if $ef = 2x - 12$, $fg = 3x - 15$, and $eg = 23$, find the values of $x$, $ef$, and $fg$. the drawing is not to scale.
question 5
are $m$, $n$, and $o$ collinear? if so, name the line on which they lie

Explanation:

Question 4

Step1: Use segment - addition postulate

Since $EG = EF+FG$, we substitute the given expressions: $(2x - 12)+(3x - 15)=23$.

Step2: Combine like - terms

$2x+3x-12 - 15 = 23$, which simplifies to $5x-27 = 23$.

Step3: Solve for x

Add 27 to both sides: $5x=23 + 27$, so $5x=50$. Then divide both sides by 5, getting $x = 10$.

Step4: Find EF

Substitute $x = 10$ into the expression for $EF$: $EF=2x-12=2\times10 - 12=8$.

Step5: Find FG

Substitute $x = 10$ into the expression for $FG$: $FG=3x-15=3\times10 - 15=15$.

Collinear points lie on the same straight - line. From the diagram, points $M$, $N$, and $O$ do not lie on the same line. Point $N$ is the intersection of two lines, but $M$, $N$, and $O$ are not all on one of those lines.

Answer:

D. $x = 10, EF = 8, FG = 15$

Question 5