Question

1. what is pr? pr = 11

points a, b, c, and d on the figure below are collinear. use the figure for exercises 8 and 9.
a b c d
x 3x 4x - 13

1. if ac = 24, what is ab?
2. if bc = 15, what is bd?

Explanation:

Step1: Find the value of x for question 8

Since $AC=AB + BC$ and $AB = x$, $BC=3x$, $AC = 24$, we have $x + 3x=24$.
Combining like - terms gives $4x=24$.
Dividing both sides by 4, we get $x = 6$.

Step2: Calculate AB for question 8

Since $AB=x$ and $x = 6$, then $AB = 6$.

Step3: Find the value of x for question 9

Since $BC = 3x$ and $BC = 15$, we have the equation $3x=15$.
Dividing both sides by 3 gives $x = 5$.

Step4: Calculate BD for question 9

Since $BD=BC + CD$, $BC = 3x$, $CD=4x - 13$, and $x = 5$.
First, find $CD$: $CD=4\times5-13=20 - 13 = 7$.
Then $BD=3x+(4x - 13)=3\times5+7=15 + 7=22$.

Answer:

1. $AB = 6$
2. $BD = 22$