<span>Each team in the softball league plays each of the other teams exactly once. For every game, there is 2 team playing. The order is not important because A vs B is same as B vs A
So you just need to makes a combination of 2 that have a result of 21. If there is t number of teams, the number of matches would be:
tC2 = t!/2!(t-2)! = 21
</span>t! / (t-2)! = 21 *2
(t)(t-1)= 42
t^2 -t -42=0
(t-7)(t+6)
t=7 ; t=-6
Excluding the minus result, you got 7 teams.
Step-by-step explanation:
step 1. if k is a zero then (x - 1) is a factor of 4x^3 + 23x^2 - 34x + 7.
step 2. we "can" use long division but synthetic division is easier!
step 3. 1 4 23 -34 7
4. 4. 27. -7.
4 27. -7. 0 (must get 0)
step 4. so the factors are (x - 1)(4x^2 + 27x - 7).
step 5. please note if you multiply these factors together you will get the original polynomial!
Answer:
31.76 ft and 58.64 ft
Step-by-step explanation:
The radius measures between 13 feet and 24 feet.
The wheel is able to turn 7π/9 radians before getting stuck.
We need to find the range of distances that the wheel could spin before getting stuck. That is, the length of arc.
Length of an arc is given as:
where θ = central angle = 7π/9 radians
r = radius of the circle
Therefore, for 13 feet:
For 24 feet:
The wheel could spin between 31.76 ft and 58.64 ft before getting stuck.
--8+4+6=2
Hope it helps :-)
The unit rate is found by dividing the amount earned by the number of hours worked. So
unit rate = amount earned / number of hours worked = 51 / 6 = $8.5 / hour
