Question

question 6
1 pts
m is the mid - point of ab.
$am = 2x + 3$, $mb = 13$
what is the value of x?

question 7
1 pts
a 21x - 12 m 7x + 44 b
if m is the mid - point of ab, what is the length of ab?

Explanation:

Question 6

Step1: Use mid - point property

Since M is the mid - point of AB, $AM = MB$. So we set up the equation $2x+3 = 13$.

Step2: Solve the equation for x

Subtract 3 from both sides: $2x=13 - 3$, so $2x = 10$. Then divide both sides by 2: $x=\frac{10}{2}=5$.

Step1: Use mid - point property

Since M is the mid - point of AB, $AM = MB$. So we set up the equation $21x-12=7x + 44$.

Step2: Solve the equation for x

Subtract $7x$ from both sides: $21x-7x-12=7x-7x + 44$, which gives $14x-12 = 44$. Then add 12 to both sides: $14x=44 + 12=56$. Divide both sides by 14: $x = 4$.

Step3: Find the length of AM or MB

Substitute $x = 4$ into the expression for AM: $AM=21x-12=21\times4-12=84 - 12=72$.

Step4: Find the length of AB

Since $AB=2AM$ (because M is the mid - point), $AB = 2\times72=144$.

Answer:

5

Question 7