Find the value of each variable in the parallelogram.

u = 4

v = 18

Step-by-step explanation:

The diagonals of a parallelogram bisect each other (bisect means to divide into two equal parts).

   2u + 2 = 5u - 10

Add 10 to both sides:

⇒ 2u + 12 = 5u

Subtract 2u from both sides:

⇒ 12 = 3u

⇒ 3u = 12

Divide both sides by 3:

⇒ u = 4

Multiply both sides by 3:

⇒ v = 18

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