Answer:
<h2>
3,654 different ways.</h2>
Step-by-step explanation:
If there are 30 students in a class with natasha in the class and natasha is to select four leaders in the class of which she is already part of the selection, this means there are 3 more leaders needed to be selected among the remaining 29 students (natasha being an exception).
Using the combination formula since we are selecting and combination has to do with selection, If r object are to selected from n pool of objects, this can be done in nCr number of ways.
nCr = n!/(n-r)!r!
Sinca natasha is to select 3 more leaders from the remaining 29students, this can be done in 29C3 number of ways.
29C3 = 29!/(29-3)!3!
29C3 = 29!/(26!)!3!
29C3 = 29*28*27*26!/26!3*2
29C3 = 29*28*27/6
29C3 = 3,654 different ways.
This means that there are 3,654 different ways to select the 4 leaders so that natasha is one of the leaders
When a quadratic equation ax^2+bx+c has a double root, the discriminant,
D=b^2-4ac=0
Here
a=2,
b=b,
c=18
and
D=b^2-4ac=b^2-4*2*18=0
solve for b
b^2-144=0
=> b= ± sqrt(144)= ± 12
So in order that the given equation has double roots, the possible values of b are ± 12.
Answer:
a.) f(x) = -⅙(x+3)²+6
Step-by-step explanation:
The maximum value, our vertex, is at point (-3,6).
We can insert this value into the vertex form of a quadratic function and then solve for a as follows...
a equals -1/6... We can input this into the original equation we used...
f(x) = -1/6(x+3)^2+6
Good luck on the bellwork ;)
Answer:
Step-by-step explanation:
Linear equation:
A linear equation has the following format:
In which m is the slope and b is the y-intercept.
Finding the slope:
We have two points: (110, 73.5) and (760, 301).
The slope is given by the change in y divided by the change in x. So
Change in y: 301 - 73.5 = 227.5
Change in x: 760 - 110 = 650
Slope: 
So
Finding the y-intercept:
(760, 301) means that when 
. So
So
