Answer:
10 miles.
Step-by-step explanation:
Let x be the number of miles on Henry's longest race.
We have been given that Henry ran five races, each of which was a different positive integer number of miles.
We can set an equation for the average of races as:

As distance covered in each race is a different positive integer, so let his first four races be 1, 2, 3, 4.
Now let us substitute the distances of 5 races as:


Let us multiply both sides of our equation by 5.


Let us subtract 10 from both sides of our equation.


Therefore, the maximum possible distance of Henry's longest race is 10 miles.
Answer: 127 11/12
Step-by-step explanation:
1. 1/2 + 3/4 = 2/3
Change 1/2 by by multiplying by 2 to get a common denominator of fourths.
2/4 + 3/4 = 2/3?
5/4 = 2/3?
no
2. 5/8 - 1/4
Change 1/4 by by multiplying by 2 to get a common denominator of eighths.
5/8 - 2/8 = 3/8?
3/8 = 3/8 ?
yes
3/8 x 10 = 30/8
3. 4/5 +7/10 = 1 1/2
Change 4/5 by multiplying by 2 to get a common denominator tenths.
8/10 + 7/10 = 1 1/2?
15 /10 = 1 1/2?
yes
1 1/2 x 10 = 25
4. 2 1/3 - 1 5/6 = 1/6
Change 1/3 by multiplying by 2 to get a common denominator sixths.
2 2/6 - 1 5/6 = 1/6?
3/6 = 1/6
no
100 -2/3 - 1/6 + 30/8 + 25
multiply the thirds by 8. Sixths by 4. Eighths by 3 to get a common denomonator of 24ths.
100 - 16/24 - 4/24 + 90/ 24 + 25 = 125 70/24
create mixed number
127 22/24
reduce
127 11/12
C because it is and I am in 12 grade I no this
Answer: The mat is 4.33 ft high off the ground.
Step-by-step explanation:
Since we have given that
Angle of elevation with the first triangle = 30°
Angle of elevation with the second triangle = 60°
Length at which gymnastics mat extends across the floor = 5 feet
so, As shown in the figure:
We need to find the height of the mat off the ground.
If CD = 5 ft,
Let, AB = y, DC = x.
In Δ ABC,

Similarly, in Δ ACD,

Hence, the mat is 4.33 ft high off the ground.