Ways to arrange the math books
1x1xxx 4 ways x 2 =8
1xx1xx 3 ways x2 6
1xxx1x 2 ways x 2 =4
1xxxx1 2 ways
total 20 ways
the other three slots can be arranged amonsth the remaining 4 books in 4 * 3 * 2 *1 = 24 ways for each math book arrangement
20 * 24 = 480 ways
There is only one x = -2. sum = -2
f = 9s
In three years :
f+3 = 6 (s+3) Sub in the red equation
9s +3 = 6 (s+3)
9s + 3 = 6s + 18
3s = 15
s = 5 y/o then f = 9s = 45 y/o
The sum of the squares of the diagonal = sum of sides squared
40^2 +d^2 = 30^2 + 30^2 + 20^2 + 20^2
d^2 = 1000
d = sqrt (1000) simplify as needed ...... ~EP
Using OJ start:
30 cans in total. 60% coke, 40% pepsi.
that means 18 cans is coke and 12 cans is pepsi.
75% of x is now Pepsi .75x = 12
x = 16 cans total
there WAS 30 30 -16 = 14 cans of Coke were consumed by diabeticNoah !
Correct...... what do YOU find for that answer? I'll let you answer that...... Thanx ! ~EP
Verical asymptopes occur when the denominator would be = 0
x^2 + 5x + 2 = 0 Quadratic formula shows x = - 5/2 +- sqrt (17)/2 sum = -5
bbggg
gbbgg
ggbbg
gggbb four ways for the two boys......but the two boys could switch places making 8 ways for the boys to be in line
then the other three spots can be filled by the girls 3 x 2 x 1 6 ways
8 x 6 = 48 ways (this assumes the boys and girls are distiguishable)
x =3 is one of the zeroes....this would be one of the legs of the triangle....the other would occur on the y axis and needs to be = |1| for the area (1/2 b*h) = 1.5
the y axis crossing occurs when x = 0
-1 = 5 (x-3)(x+k) sub in x = 0
-1/5 = (-3)(k)
k = 1/15
when y = +1 1 = 5 (0-3((0+k )
1/5 = - 3k
k = - 1/15
Here is a desmos graph:
Note that anything raised to the '0' power = 1
5^0 = 1 123^0 = 1
so the exponent = 0
x^2 -5x + 2 = 0
Quadratic Formula shows x = 1/2 ( 5 +-sqrt(17) ) sum = 5
