The path is the hypotenuse of a right triangle with legs 30 and 120.
30² + 120² = c²
900 + 14400 = c²
15300 = c²
c=√15300 ≈123.7'
instead of walking 30+120=150 feet they save 26.3 feet by taking the shortcut
The triangle ABC is similar to triangle LMP. The order here is very important. The letters correspond to one another
A corresponds to L (first letters of each sequence)
B corresponds to M (second letters of each sequence)
C corresponds to P (third letters of each sequence)
In a similar fashion, the segments also correspond to one another.
AB corresponds to LM (first two letters of each sequence)
AC corresponds to LP (first and last letters of each sequence)
BC corresponds to MP (last two letters of each sequence)
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AB corresponds to LM. AB is 4 units long. LM is 2 units long. So AB is twice as long as LM. This ratio (of 2:1) will be applied to every paired corresponding value.
Also, the right angle is at angle M for triangle LMP. The right angle will be at angle B for triangle ABC (since B corresponds to M). The answer will have an x coordinate of 7. So the answer is either choice B or choice C.
If we move 4 units down from point B, we land on (7,-10). That isn't listed as an answer choice. Let's try moving 4 units up from point B. We land on (7,-2). This is an answer choice
So the final answer is choice C) (7,-2)
If you drive 1000 miles, then you would multiply $0.05 * 1000 miles =$50.
Answer:
55 mph
Step-by-step explanation:
Speed = Distance/Time so Time = Distance / Speed.
If the first speed is x mph, the first trip will take 660/x hours.
The second trip will take 660/(x+5) hours.
We want to find x such that (660/x) - 660/(x+5) = 1 (i.e. solving this equation for x).
Multiply both sides by x*(x+5):
660*(x+5) - 660x = x*(x+5)
660x + 3300 - 660x = x2 + 5x
x2 + 5x - 3300 = 0
(x - 55)*(x + 60) = 0
So either x = 55 or x = -60. Since x > 0, x = 55mph.
Answer: option 4 is the correct answer.
Step-by-step explanation:
The graphs shown in the photo are plots of distance versus time.
Distance travelled = speed × time
On a run, Natasha ran for 1 1/4 hours at a speed of 6 miles per hour. The distance that she covered would be
6 × 1.25 = 7.5 miles
She then rested for 1/4 hour. This means that her speed is 0 and the distance covered is also 0 miles.
She then ran for another hour at a speed of 5 miles per hour. Distance covered would be
5 × 1 = 5 miles
Total time spent would be
1.25 + 0.25 + 1 = 2.5 hours
Total distance covered would be
7.5 + 5 = 12.5 miles
Therefore, the 4th graph best represents the distance she traveled
