Answer:
I'm going to paint you a picture in words of what this looks like on paper. We have a train leaving from a point on your paper heading straight west. We have another train leaving from the same point on your paper heading straight east. This is the "opposite directions" that your problem gives you.
Now let's make a table:
distance = rate * time
Train 1
Train 2
We will fill in this table from the info in the problem then refer back to our drawing. It says that one train is traveling 12 mph faster than the other train. We don't know how fast "the other train" is going, so let's call that rate r. If the first train is travelin 12 mph faster, that rate is r + 12. Let's put that into the table
distance = rate * time
Train 1 r
Train 2 (r + 12)
Then it says "after 2 hours", so the time for both trains is 2 hours:
distance = rate * time
Train 1 r * 2
Train 2 (r + 12) * 2
Since distance = rate * time, the distance (or length of the arrow pointing straight west) for Train 1 is 2r. The distance (or length of the arrow pointing straight east) for Train 2 is 2(r + 12) which is 2r + 24. The distance between them (which is also the length of the whole entire arrow) is 232. Thus:
2r + 2r + 24 = 232 and
4r = 208 so
r = 52
This means that Train 1 is traveling 52 mph and Train 2 is traveling 12 miles per hour faster than that at 64 mph
Step-by-step explanation:
Answer:
Yuri read 12 more books than Hiro.
Step-by-step explanation:
17-5=12
Answer: See explanation
Step-by-step explanation:
Let the cost for insuring the applicant = a.
Let the cost for insuring the spouse = b
Let the cost for insuring the first child= c
Let the cost for insuring the second child = d
A 35-year-old health insurance plan and that of his or her spouse costs $301 per month. This means that:
a + b = $301.
That rate increased to $430 per month if a child were included. This means the cost of a child will be:
= $430 - $301
= $129
The rate increased to $538 per month if two children were included. This means the cost for the second child will be:
= $538 - $430
= $108
The rate dropped to $269 per month for just the applicant and one child. His will be the cost of the applicant and a single child. This can be written as:
a + $129 = $269
a = $269 - $129
a = $140
Since a + b = $301
$140 + b = $301
b = $301 - $140
b = $161
Applicant = $140
The spouse = $161
The first child = $129
The second child = $108
Take half of the coefficient of x (which is 2/5) and square it:
[ (1/2)(2/5) ]^2 = (1/5)^2 = 1/25, or 0.04
Thus, to rewrite x^2 + (2/5)x to include a perfect square trinomial,
x^2 + (2/5)x = x^2 + (2/5)x + (1/5)^2 - (1/5)^2, or
(x+1/5)^2 - (1/5)^2, or (x + 1/5)^2 - 1/25
