Answer:
A. (3, 10)
Step-by-step explanation:
You are told that ...
(x, y) = (number of accessories, dollars)
and you are told that ...
number of accessories = 3
dollars = 10
so the ordered pair is ...
(x, y) = (3, 10) . . . . Point A
180 because you multiply the 12 packs by 10 to get 120. Then you subtract 120 from 300
No, Leo's answer is not a product of prime polynomials because x2 – 1 can be factored. This is a difference of squares. He should continue factoring to get
(x – 1)(x + 1)(3x + 5).
Original position: P1=(0,0)
<span>You drive 30 miles due east in a half hour: x=+30 miles, t1=1/2 hour=0.5 hours
</span><span>Then, you turn left and drive 30 miles north in 1 hour: y=+30 miles, t2=1 hour
Rectangular coordinates of final position: P2=(x,y)→P2=(30,30)
Total time: t=t1+t2=0.5 hours+1 hour→t=1.5 hours
Average speed: S ave=d/t
Total distance: d=x+y=30 miles+30 miles→d=60 miles
S ave = 60 miles / (1.5 hours)
S ave = 40 miles/hour
Velocity is a vector, the magnitude of this vector is the magnitude of the vector of change of position dividing by the total time t
The vector of change of position: s=P1-P2=(30,30)-(0,0)=(30-0,30-0)→
s=(30,30)
Magnitude of vector s=sqrt[30^2+30^2]=sqrt[30^2*2]=sqrt[30^2]*sqrt(2)
Magnitude of vector s=30*sqrt(2) miles
Magnitude of velocity vector = Magnitud of vector s / t
Magnitude of velocity vector = [30*sqrt(2) miles] / (1.5 hours)
Magnitude of velocity vector = 20*sqrt(2) miles / hour
Magnitude of velocity vector=20*1.4142 miles / hour
Magnitude of velocity vector=28.284 miles/hour
Polar coordinates of your position=(r, theta)
r=Magnitude of vector s=30*sqrt(2) miles
theta=tan^(-1) (y/x) = tan^(-1) [(30 miles) / (30 miles)]
theta=tan^(-1) (1)→theta=45°=Pi/4 (Pi=3.1416)
Polar coordinates of your position: ( 30*sqrt(2) miles, 45°)
Polar coordinate of your position: ( 30*sqrt(2) miles, Pi/4 )
Answers:
Average speed: 40 miles / hour
Velocity: 20*sqrt(2) miles / hour = 28.284 miles / hour
Rectangular coordinates of your position = (30,30)
Polar coordinates of your position=(30*sqrt(2) miles,45°)
Polar coordinates of your position=(30*sqrt(2) miles,Pi/4)</span>
General Idea:
The relationship between rate(R), distance(D) and time(T) given below:
Applying the concept:
We need to make use of the formula to find Kelly's walking rate before and after her snack
Option A isn't correct because before snack Kelly walking rate is not 4/14 miles per hour.
Option B is <u>Correct,</u> Kelly walking rate after snack is 2 2/3 miles per hour.
Option C isn't correct because it doesn't took Kelly 2 hours longer to walk 1/6 mile than it did for her to walk 1/4 mile. It took 1/112 hour longer.
Option D isn't correct because 2 2/3 miles per hour is slower than 3 1/2 miles per hour.
Conclusion:
Option B is <u>Correct,</u> Kelly walking rate after snack is 2 2/3 miles per hour.
