You need to show the rest of the functions
Answer:
3x - 6 = x + 9
2x - 6 = 9
2x = 15
x = 7.5
Step-by-step explanation:
Let x be the speed of the motorboat and y be the speed of the current.
Then, for downstream, the speed is x + y.
Now, speed = distance/time.
Distance = 80 miles.
Time for downstream = 4 hours.
So, x + y = 80/4 = 20 (1)
Against the current, that is for upstream, the speed is x - y.
Time for upstream = 5 hours.
x - y = 80/5 = 16 (2)
Adding (1) and (2), we get,
2x = 36
x = 18
Hence, rate of the motorboat in calm water = 18 miles/hour.
Answer:
C. 40.2°
Step-by-step explanation:
Cosine rule (real handy to remember): c² = a² + b² - 2·a·b·cos(γ)
If you don't know this yet, look it up but in short: c, a and b are the lengths of the sides of the triangle, the angle opposite side a is called α, for b it is β and for c it is γ. That's the convention I've always used anyway, you can call them whatever of course. Anyhow:
c² = a² + b² - 2·a·b·cos(γ)
⇒ |AC|² = |AB|²+|BC|²-2·|AB|·|BC|·cos(∠B)
⇒ |AC|²-|AB|²-|BC|² = -2·|AB|·|BC|·cos(∠B)
⇒ ( |AC|²-|AB|²-|BC|² ) / ( -2·|AB|·|BC| ) = cos(∠B)
⇒ ∠B = arccos( ( |AC|²-|AB|²-|BC|² ) / ( -2·|AB|·|BC| ) )
= arccos( ( 11²-16²-16² ) / ( -2·16·16 ) )
= 40.21101958°
≈ 40.2°
Answer:
The height is 17 ft
Step-by-step explanation:
The surface area of a rectangular prism is
SA = 2(LW +WH + LH)
where L = length, W = width, and H = height
We know SA = 930, L = 12, and W = 9
930 = 2(12*9 +9H + 12H)
Divide each side by 2
930/2 = 2/2(12*9 +9H + 12H)
465 = (12*9 +9H + 12H)
Combine like terms
465 = 84+21H
Subtract 84 from each side
465-84 = 84-84+21H
357 = 21H
Divide by 21
357/21=21H/21
17 = H
The height is 17 ft
