Answer:
- rate of the boat in still water = 6.5 miles / hour
- rate of the current = 2.5 miles / hour.
Explanation:
<u>1) Name the two variables:</u>
- b: rate of the boat in still water:
With that, the net rates of the boat down the river and upstrean are:
<u>2) Now set the equations for the distance as a function of the times and the rates:</u>
- downstream: 18 miles = (b + c) × 2 hours
- upstream: 18 miles = (b - c) × 4.5 hours
<u>3) Set the system of equations:</u>
- 18 = 2(b + c) ⇒ 9 = b + c . . . Equation (1)
- 18 = 4.5 (b - c) ⇒ 4 = b - c . . . Equation (2)
<u>4) Solve the system by </u><u>elimination</u><u>:</u>
- Add equations (1) and (2): 9 + 4 = 2b
- Divide both sides by 2: 13/2 = b
- Replace b with 6.5 in equation (2) and solve:
4 = 6.5 - c ⇒ c = 6.5 - 4 = 2.5
<u>5) Results:</u>
- b = rate of the boat in still water = 6.5 miles / hour
- c = rate of the current = 2.5 miles / hour.
Answer:
8$
Step-by-step explanation:
Because the first car wash does not cause the price to to down, but the ones after it do, you need onltake away 7 dollars of the price because it has only been discounted 7 times. Therefore 15-7=8 so 8 dollars is the answer.
Answer:
x + 3y > 6
Step-by-step explanation:
Find two points that satisfy x + 3y = 6 and draw a DASHED line through them.
It is greater than so shade the section ABOVE that line.
Using the intercept method, the two points I chose are: (0, 2) & (6, 0)
y ≥ 2x + 4
Find two points that satisfy y = 2x + 4 and draw a SOLID line through them.
It is greater than so shade the section ABOVE that line.
The two points I chose are: (0, 4) & (1, 6)
The solution is where the shaded sections overlap.
Steps?
A graph shows zeros to be ±3. Factoring those out leaves the quadratic
(x-2)² +1
which has complex roots 2±i.
The function has roots -3, 3, 2-i, 2+i.