Answer:
0 < k < 2
Step-by-step explanation:
<u>In the first quadrant both of x and y get positive values, so </u>
<u>And replacing x with 2k in the second equation:</u>
- 3x + 2y = 12
- 3*2k + 2y = 12
- 2y= 12 - 6k
- y = 6 - 3k
<u>Since y > 0:</u>
<u>Combining both k > 0 and k < 2, we get:</u>
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.
The artistic crop isn't helpful; it cuts off some vertex names.
The circumcenter H is the meet of the perpendicular bisectors of the sides, helpfully drawn. We have right triangle ELH, right angle L, so
EH² = HL² + EL²
EL = √(EH² - HL²) = √(5.06²-2.74²) ≈ 4.2539393507665339
Since HL is a perpendicular bisector of EF, we get congruent segments FL=EL.
Answer: 4.25
To find the answer you would multiply 1,300 by .06, which gives you a commission of $78.
Hope this helps!
Answer:
17mL
Step-by-step explanation:
Convert 0.85 gr to miligrams
If 100 mg is 1 gr. Then, 0.85 gr is 850 mg
So, 850 multiply for 5ml and divide for 250 ml
or 
So all mg is gone and the amount of mililiters is 17
