9514 1404 393
Answer:
- Tigers: 8 coaches, 72 players
- Eagles: 16 coaches, 136 players
Step-by-step explanation:
We can define a "basic unit" of each team to be the minimum number of players and coaches that can have the given ratio. For the Tigers, that is 1 coach and 9 players, for a total of 10 team members. For the Eagles, that is 2 coaches and 17 players, for a total of 19 team members. If we have t basic units of Tigers and e basic units of Eagles, then we want ...
10t +19e = 232 . . . . . the total of players and coaches in the two clubs
We want t and e to be integers, so this is a Diophantine equation. It can be solved any of several ways, including use of the Extended Euclidean Algorithm. Here, we'll make some observations based on "number sense."
The value of e must be an even number between 0 and 232/19 = 12. The product of e and 19 must be a number that ends in 2, because 10t will end in 0, and the sum with 19e must end in 2.
The only multiple of 9 that ends in 2 is 9×8 = 72, so the value of e must be a positive number less than 12 that ends in 8. We must have e=8.
Then t=(232 -8×19)/10 = 8. This tells us there are 8 "basic units" of each team.
The Tigers have 8 coaches and 72 players.
The Eagles have 16 coaches and 136 players.
Answer: -1 ± <em>i</em>√35
⁻⁻⁻⁻⁻⁻⁻⁻
6
Step-by-step explanation:
From the quadratic equation,
X = -b ±√b² - 4ac
⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻
2a
From the given equation, -3x² - x - 3 = 0
where a = -3, b = -1, c = -3
Now substitute for the values in the formula above
x = -(-1) ± √(-1)² - 4(-3)(-3)
⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻
2(-3)
x = 1 ± √ 1 - 36
⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻
-6
x = 1 ± √ -35
⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻
-6
x = -1 ± <em>i√35 this is because it has a negative root.</em>
<em> ⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻</em>
<em> 6</em>
<em> The answer is b</em>
Answer:
105
Step-by-step explanation:
105
9 times 5 equals 45 so yes
