Answer:
a. 8,953.5 seconds
b. 14,400 seconds (check note)
Step-by-step explanation:
a.
y=-4x
y=-35814 (negative because this is underwater)
-35814=-4x
8953.5
The model suggests it would take 8,953.5 seconds for DeepSea Challenger to reach the bottom (2.487083333 hours, or about 2 hours and 30 minutes).
b.
y=4x
x=3600 (positive because the vessel is rising)
4(3600)
14400
It took 14,400 seconds for the DeepSea Challenger to ascend to the surface.
[also note: I'm not sure if the second question is asking for how many seconds it takes to ascend to the surface with reference to the 4 seconds in the previous question (which is how I answered part b) or if it's asking how many seconds 1 hour is, and in that case. the answer is 3,600 seconds. I hope this helps and sorry if it's unclear!]
Answer:
t=1.06x+10 where x=The amount of tickets bought
Step-by-step explanation:
you multiply x by 1.06 to add the extra tax onto it.
You add the 10 to add the $10 booking fee
Answer:
x = 85°
Step-by-step explanation:
As noticed this is a Pentagon (5 sided polygon); therefore to find x, first we have to find the sum of it's interior angles;
Sum of interior angles of a pentagon = (n - 2) * 180°
=> Sum of interior angles of a pentagon = (5 - 2) * 180°
=> Sum of interior angles of a pentagon = 3 * 180
=> Sum of interior angles of a pentagon = 540
Now that we know the sum of interior angles, we can set up the equation and solve for x;
115 + 95 + 115 + 130 + x = 540
455 + x = 540
x = 540 - 455
x = 85
Hope this helps!
Answer as a fraction: 17/6
Answer in decimal form: 2.8333 (approximate)
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Work Shown:
Let's use the two black points to determine the equation of the red f(x) line.
Use the slope formula to get...
m = slope
m = (y2-y1)/(x2-x1)
m = (4-0.5)/(2-(-1))
m = (4-0.5)/(2+1)
m = 3.5/3
m = 35/30
m = (5*7)/(5*6)
m = 7/6
Now use the point slope form
y - y1 = m(x - x1)
y - 0.5 = (7/6)(x - (-1))
y - 0.5 = (7/6)(x + 1)
y - 0.5 = (7/6)x + 7/6
y = (7/6)x + 7/6 + 0.5
y = (7/6)x + 7/6 + 1/2
y = (7/6)x + 7/6 + 3/6
y = (7/6)x + 10/6
y = (7/6)x + 5/3
So,
f(x) = (7/6)x + 5/3
We'll use this later.
---------------------
We ultimately want to compute f(g(0))
Let's find g(0) first.
g(0) = 1 since the point (0,1) is on the g(x) graph
We then go from f(g(0)) to f(1). We replace g(0) with 1 since they are the same value.
We now use the f(x) function we computed earlier
f(x) = (7/6)x + 5/3
f(1) = (7/6)(1) + 5/3
f(1) = 7/6 + 5/3
f(1) = 7/6 + 10/6
f(1) = 17/6
f(1) = 2.8333 (approximate)
This ultimately means,
f(g(0)) = 17/6 as a fraction
f(g(0)) = 2.8333 as a decimal approximation
