In ΔMNO, the measure of ∠O=90°, the measure of ∠M=11°, and NO = 80 feet. Find the length of OM to the nearest tenth of a foot. Please show work.

Final answer:

To convert from miles per hour to miles per minute, we divide by 60. Therefore, a speed of 21 miles per hour is equivalent to 0.35 miles per minute. If the cyclist rides for 15 minutes at this speed, they will travel approximately 5.25 miles.

Explanation:

The subject of this question is Mathematics, and it concerns converting units of speed from miles per hour to miles per minute, and then using this information to solve a problem. If a cyclist rides his bike at a speed of 21 miles per hour, to convert this to miles per minute you'd divide by 60, as there are 60 minutes in an hour. This gives approximately 0.35 miles per minute.

Then, to calculate how many miles the cyclist will travel in 15 minutes, you multiply the speed in miles per minute (0.35) by the number of minutes (15 minutes). So, 0.35 miles per minute times 15 minutes equals 5.25 miles. Therefore, the cyclist will travel 5.25 miles in 15 minutes provided they maintain the same speed.

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Answer:

1. 0.35 miles per minute

2. 5.25 miles

Step-by-step explanation:

1. speed is 21 miles per hour

speed per minute = 21/60 = 0.35 miles per minute

2. distance covered in 15 minutes = 15*0.35

= 5.25miles

olume = length * height * width  

Therefore 280 = 4 * (n + 2) * (n + 5)  

Divide both sides of the equation by 4  

70 = (n + 2)(n +5)  

Expand  

70 = n^2 + 5n + 2n + 10  

Subtract 70 from both sides and simplify  

0 = n^2 + 7n -60  

Factor  

(n +12)(n -5) = 0  

Therefore n = -12 or + 5  

As n cannot be less than -2 as you cannot have a negative dimension, it means that n = 5 and the sides are 4, (5 + 2), (5 + 5) = 4, 7 and 10 inches respectively  

Volume is therefore  

4*7*10 = 280 = correct  

Hope this helped!