Question

refer to the figure and the given information to find each measure.

1. given: ac = 39 m

a 2x - 8 b x + 17 c
x =
ab =
bc =

1. given the figure and dg = 60 ft.

d o g
4x - 3 2x + 21
x =
do =
og =

Explanation:

Step1: Set up equation for problem 9

Since $AC = AB + BC$, we have $(2x - 8)+(x + 17)=39$.
Combining like - terms gives $3x+9 = 39$.
Subtract 9 from both sides: $3x=39 - 9=30$.
Divide both sides by 3: $x = 10$.

Step2: Find $AB$ for problem 9

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

Step3: Find $BC$ for problem 9

Substitute $x = 10$ into the expression for $BC$: $BC=x + 17=10 + 17=27$ m.

Step4: Set up equation for problem 10

Since $DG=DO + OG$, we have $(4x - 3)+(2x + 21)=60$.
Combining like - terms gives $6x+18 = 60$.
Subtract 18 from both sides: $6x=60 - 18 = 42$.
Divide both sides by 6: $x = 7$.

Step5: Find $DO$ for problem 10

Substitute $x = 7$ into the expression for $DO$: $DO=4x - 3=4\times7 - 3=25$ ft.

Step6: Find $OG$ for problem 10

Substitute $x = 7$ into the expression for $OG$: $OG=2x + 21=2\times7+21=35$ ft.

Answer:

For problem 9:
$x = 10$
$AB = 12$ m
$BC = 27$ m
For problem 10:
$x = 7$
$DO = 25$ ft
$OG = 35$ ft