What equation results from completing the square and then factoring? X^2 + 10x= 15
A. (x + 10)^2 = 40
B. (x + 5)^2 = 40
C. (x+ 5)^2 = 15
D. (x+ 10)^2 = 15

B

Step-by-step explanation:

Given

x² + 10x = 15

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(5)x + 25 = 15 + 25, that is

(x + 5)² = 40 → B

Step-by-step explanation:

Add on both sides.

Factor left side of the equation.

13

step-by-step explanation:

distance formula is d=√(x2-x1)^2   +   (y2-y1)^2

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