Let V, be the rate in still water and let C = rate river current
If the boat is going :
upstream, its rate is V-C and if going
downstream, its rate is V+C,
But V = 5C, then
Upstream Rate: 5C - C = 4 C
Downstream rate: 5C+C = 6C
Time = distance/Rate, (or time = distance/speed) , then:
Upstream time 12/4C and
Downstream time: 12/.6C
Upstream time +downstream time:= 2h30 ' then:
12/4C + 12/.6C = 2.5 hours
3/C + 2/C = 5/2 (2.5 h = 5/2)
Reduce to same denominator :
5C = 10 and Rate of the current = 2 mi/h
You can identify the lines and their colour either by
1. the y-intercepts.
First equation has a y-intercept of 3 and second has a y-intercept of 2.
So first equation is blue, and second is red.
2. the slopes
First equation has a negative slope (so blue), and second has a positive slope (so red).
Now work on each of the equations.
1. first equation (blue)
If we put x=0, we end up with the equation y≤3, the ≤ sign indicates that the region is BELOW the BLUE line.
2. second equation (red).
If we put x=0, we end up with the equation y>2, the > sign indicates that the region is ABOVE the RED line AND the red line should be dotted (full line if ≥).
So at the point, it won't be too hard to find the correct region.
To confirm, take a point definitely in the region, such as (-6,0) and substitute in each equation to make sure that both conditions are satisfied.
The figure below shows a parallelogram PQRS:
A parallelogram PQRS is shown with the diagonal SQ.
The flowchart shown below shows the sequence of steps to prove the theorem: Opposite angles of a parallelogram are equal:
Which is the missing statement?
Answer - Triangle PQS is congruent to triangle RSQ
Answer:
8) No solution
9) n > -5 <em>(View explanation for info on how to graph)</em>
Step-by-step explanation:
<em><u>Question 8</u></em>
<em><u /></em>
<u>24+6k < -6(-4-k)</u> - Solve and graph
1) Distribute -6 to -4 and -k:
24+6k < 24+6k
2) Subtract 6k from both sides:
24<24
^ We know the following is false, therefore there is no solution to question 8.
<em><u>Question 9</u></em>
<em><u /></em>
<u>-2n-40 < 5(6+n)+7n</u> - Solve and graph
1) Distribute 5 to 6 and n:
-2n-40 < 30+5n+7n
2) Combine alike terms:
-2n-40 < 30+12n
3) Add 2n to both sides:
-40 < 30+14n
4) Subtract 30 from both sides:
-70 < 14n
5) Divide both sides by 14:
n > -5
6) To graph, plot an OPEN CIRCLE (<em>don't fill in the circle)</em> at point -5 and then draw an arrow pointing to the right!
Let me know if you need any help with the others :)
