Mrs. archangel deposited two checks, valued at $27.45 and $122.90, into her checking account last week. then, she wrote three checks for $14.99, $32.49, and $43.85 out of this account to pay her monthly bills. what is the total change of mrs. archangel’s checking account after all checks are processed? question 5 options: +241.68 +59.02 -59.02 -241.68

d. corresponding side lengths in similar triangles are proportional in length.

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