Theorem: A line parallel to one side of a triangle divides the other two proportionately. In the figure below, segment DE is parallel to segment BC and segment EF is parallel to AB:

The figure shows triangle ABC with segments DE and EF. Point D is on side AB, point E is on side AC, and point F is on side BC. Segment AD is 6, segment AE is 12, segment EC is 18, and segment FC is 24.

Which statement can be proved true using the given theorem?

Segment BD = 12
Segment BD = 4
Segment BF = 16
Segment BF = 9

Segment BD = 12

Step-by-step explanation:

should have been evaluated with one odd value and one even value. the expressions have equivalent values when . when , the first expression has a value of 3 and the second

step-by-step explanation:

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