Fatima earned an 85 average in her science class. The average is based on 6 tests that she takes over the span of the marking period. On her first four tests she earned an 83, a 78, an 87, and an 80. On her sixth test she scored 8 points more than on her fifth test. Let x be the score Fatima received on her fifth test. Set up an equation using x that models this scenario. Solve the equation and state what Fatima earned on her fifth and sixth tests.

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

perimeter of the base times height

step-by-step explanation: