68 degrees because they’re vertical angles
Answer:
The answer to your question is there were 88 children
Step-by-step explanation:
Data
Total number of people = 188
total cost = $5040
12 more adults than seniors
number of children = ?
adults = a
children = c
Process
1.- Write equations that help to solve this problem
a + c = 188 Equation l
a = c + 12 Equation ll
2.- Solve by substitution. Substitute equation equation ll in equation l
(c + 12) + c = 188
-Solve for c
c + 12 + c = 188
2c + 12 = 188
2c = 188 - 12
2c = 176
c = 176 / 2
c = 88
3.- Conclusion
There were 88 children
Answer:
<u>It</u><u> </u><u>is</u><u> </u><u>(</u><u>x</u><u> </u><u>-</u><u> </u><u>3</u><u>)</u><u>³</u><u> </u><u>-</u><u> </u><u>9</u><u>x</u><u>(</u><u>3</u><u> </u><u>-</u><u> </u><u>x</u><u>)</u>
Step-by-step explanation:
Express 27 in terms of cubes, 27 = 3³:
![= {x}^{3} - {3}^{3}](https://tex.z-dn.net/?f=%20%3D%20%20%7Bx%7D%5E%7B3%7D%20%20-%20%20%7B3%7D%5E%7B3%7D%20)
From trinomial expansion:
![{(x - y)}^{3} = (x - y)(x - y)(x - y) \\](https://tex.z-dn.net/?f=%20%7B%28x%20-%20y%29%7D%5E%7B3%7D%20%20%3D%20%28x%20-%20y%29%28x%20-%20y%29%28x%20-%20y%29%20%5C%5C%20%20)
open first two brackets to get a quadratic equation:
![{(x - y)}^{3} = ( {x}^{2} - 2xy + {y}^{2} )(x - y)](https://tex.z-dn.net/?f=%20%7B%28x%20-%20y%29%7D%5E%7B3%7D%20%20%3D%20%28%20%7Bx%7D%5E%7B2%7D%20%20-%202xy%20%2B%20%20%7By%7D%5E%7B2%7D%20%29%28x%20-%20y%29)
expand further:
![{(x - y)}^{3} = {x}^{3} - y {x}^{2} - 2y {x}^{2} + 2x {y}^{2} + x {y}^{2} - {y}^{3} \\ {(x - y)}^{3} = {x}^{3} - {y}^{3} + 3x {y}^{2} - 3y {x}^{2} \\ {(x - y)}^{3} = {x}^{3} - {y}^{3} + 3xy(y - x) \\ \\ { \boxed{( {x}^{3} - {y}^{3} ) = {(x - y)}^{3} - 3xy(y - x)}}](https://tex.z-dn.net/?f=%20%7B%28x%20-%20y%29%7D%5E%7B3%7D%20%20%3D%20%20%7Bx%7D%5E%7B3%7D%20%20%20-%20y%20%7Bx%7D%5E%7B2%7D%20%20-%202y%20%7Bx%7D%5E%7B2%7D%20%20%2B%202x%20%7By%7D%5E%7B2%7D%20%20%2B%20x%20%7By%7D%5E%7B2%7D%20%20-%20%20%7By%7D%5E%7B3%7D%20%20%5C%5C%20%20%7B%28x%20-%20y%29%7D%5E%7B3%7D%20%20%3D%20%20%7Bx%7D%5E%7B3%7D%20%20-%20%20%7By%7D%5E%7B3%7D%20%20%2B%203x%20%7By%7D%5E%7B2%7D%20%20-%203y%20%7Bx%7D%5E%7B2%7D%20%20%5C%5C%20%20%7B%28x%20-%20y%29%7D%5E%7B3%7D%20%20%3D%20%20%7Bx%7D%5E%7B3%7D%20%20-%20%20%7By%7D%5E%7B3%7D%20%20%2B%203xy%28y%20-%20x%29%20%5C%5C%20%20%5C%5C%20%7B%20%5Cboxed%7B%28%20%7Bx%7D%5E%7B3%7D%20-%20%20%7By%7D%5E%7B3%7D%20%29%20%3D%20%20%7B%28x%20-%20y%29%7D%5E%7B3%7D%20%20%20-%203xy%28y%20-%20x%29%7D%7D)
take y to be 3, then substitute:
![( {x}^{3} - 3^3) = {(x - 3)}^{3} - 9x(3 - x)](https://tex.z-dn.net/?f=%28%20%7Bx%7D%5E%7B3%7D%20%20-%203%5E3%29%20%3D%20%20%7B%28x%20-%203%29%7D%5E%7B3%7D%20%20-%209x%283%20-%20x%29)
Answer:
29
Step-by-step explanation:
anythin0.5 or higher you round up so for 28.5 you round up to 29.
hope this helps. :)