Find the angle between the pair of vector to the nearest tenth of degree (4,5),(-4,-1)

Step-by-step explanation:

Given the pair vector

U = (4, 5) = 4•i + 5•j

V = (-4, -1) = -4•i - 1•j

Then,

The angle between two vectors can be determined using

U•V = |U||V| Cosθ

|U| = √(4²+5²) = √(16 + 25) = √41

|V| = √(-4)²+(-1)² =√(16 + 1) = √17

U•V = |U||V| Cosθ

(4•i + 5•j)•(-4•i - 1•j) = √41 × √17 Cosθ

-16 - 5 = √(41×17) Cosθ

-21 = √697 Cosθ

Cosθ = -21 / √697

Cosθ = -0.7954

θ = Arccos(-0.7954)

θ = 142.7°.

38.5

step-by-step explanation:

lets say, first number = r

second number = 3r+7

total = 49

(r)+(3r+7)= 49

4r+7 = 49

4r = 42

r = 42/4

r= 10.5

3r+7 = 3(10.5)+7 = 38.5

hope this

answer

d. 10

explanation

the distance from point y to wx is the height of the triangle.

using pythagoras theorem,

group similar terms to get,

this implies that,

take positive square root of both sides to get,

this implies that,