Hi there
So, if the track is 1/8 of a mile, let's call every lap a "one-eighth mile" run. We know John ran 24 laps, or that he ran 24 "one-eighth miles," just consecutive, one right after another. Let's stop worrying about rates or tricks or math for a second, and just ask: how many real miles is 24 "one-eighth" miles? We know it's less than 24---a lot less, since you have to go around 8 times just to get to 1 mile. Well wait, if we go around 8 times, we get 1 mile. That means if we go around 28, or 16 times, we get 2 miles; And let's just think to the next full mile---if we go 38, or 24 times, we get 3 miles. He did go around 24 times, so he must have run 3 miles on a 1/8 track.
Division and multiplication are inverses of each other. So we solved this by looking for an intuition for how many full miles corresponded to how many laps, with a bunch of steps of multiplication. But you can cut right to the chase and solve it faster with division---24 laps * 1 mile per 8 laps, means:
total distance = 24 Lap (1 mi / 8 Lap) total distance = 24/8 total distance = 3
Answer:
Step-by-step explanation: Simplifying
2(3y + -5) + -2 = 3(y + -3)
Reorder the terms:
2(-5 + 3y) + -2 = 3(y + -3)
(-5 * 2 + 3y * 2) + -2 = 3(y + -3)
(-10 + 6y) + -2 = 3(y + -3)
Reorder the terms:
-10 + -2 + 6y = 3(y + -3)
Combine like terms: -10 + -2 = -12
-12 + 6y = 3(y + -3)
Reorder the terms:
-12 + 6y = 3(-3 + y)
-12 + 6y = (-3 * 3 + y * 3)
-12 + 6y = (-9 + 3y)
Solving
-12 + 6y = -9 + 3y
Solving for variable 'y'.
Move all terms containing y to the left, all other terms to the right.
Add '-3y' to each side of the equation.
-12 + 6y + -3y = -9 + 3y + -3y
Combine like terms: 6y + -3y = 3y
-12 + 3y = -9 + 3y + -3y
Combine like terms: 3y + -3y = 0
-12 + 3y = -9 + 0
-12 + 3y = -9
Add '12' to each side of the equation.
-12 + 12 + 3y = -9 + 12
Combine like terms: -12 + 12 = 0
0 + 3y = -9 + 12
3y = -9 + 12
Combine like terms: -9 + 12 = 3
3y = 3
Divide each side by '3'.
y = 1
Simplifying
y = 1
Answer:
Step-by-step explanation:
Hope this helps :)
Answer:
1/52
Step-by-step explanation:
52/4=13 theirs only 4 5s in a deck of cards so 13*4 is 52
Answer:
You can multiply the brackets to make sure you get 4x² + 4x + 1. Since the numbers in the brackets are the same, we can just use one of them and let it equal to 0. Then solve it. ∴ The answer is x = -1/2.
Step-by-step explanation:
4x2+4x+1=(2x+1)2 or (2x+1)(2x+1)