Ab = 10x + 4 bc = 4x - 3 ac = 12x + 16 what is x, ab, and bc?

We know that

AB = 10x + 4

BC = 4x - 3

AC = 12x + 16

We need to find x, AB and BC.

The solution of the question is based on the assumption that the point A, B and C are col-linear, i.e. they lie on the same line, and B lies between A and C

⇒ AB + BC = AC

Substituting the values of AB, BC and AC in terms of x in the above equation, and solving the linear equation.

⇒ 10x+4 + 4x-3 = 12x+16

⇒ 14x+1 = 12x+16

⇒ 2x = 15

⇒ x = 7.5

Substituting the value of x in 10x+4 to determine the length of AB

AB = 10x+4

⇒ AB = (10×7.5)+4

⇒ AB = 75+4

⇒ AB = 79

Hence, AB is 79 units

Substituting the value of x in 4x-3 to determine the length of BC

BC = 4x-3

⇒ BC = (4×7.5)-3

⇒ BC = 30-3

⇒ BC = 27

Hence, BC is 27 units

7.9m and 4.3°

step-by-step explanation:

let east be +x and north be +y, x = distance * cos θ, y = distance * sin θ  

for 3.5 south, y = -3.5  

for 8.2, x = 8.2 * cos 30 and y = 8.2 * sin 30  

for 15 west, x = -15  

total x = 8.2 * cos 30 – 15 ≈ -7.9  

total y = -3.5 + 8.2 * sin 30 = 0.6  

magnitude = [(8.2 * cos 30 – 15)^2 + 0.6^2)]^0.5  

the magnitude is approximately 7.9 m  

tan θ = y/x = 0.6/-7.9  

the angle is approximately 4.3˚ north of west