Answer:
80 minutes
Step-by-step explanation:
Rate and Time are inverses of each other
First,
Elise Time = 12
and
Katherine Time = 2 * 12 = 24
Their rates would be (inverses):
Elise Rate = 1/12
Katherine Rate = 1/24
Together their rate is 1/12 + 1/24 = 3/24
Now, the inverse of this rate would be the time it takes to complete 1 bag together, that is:
(3/24) ^ -1 = 24/3 = 8 minutes
So, 10 bags would take them:
8 * 10 = 80 minutes
Answer:
$522.99
Step-by-step explanation:
Fv = total amount plus interest over the given period of time
P = Principal amount deposited i.e $500
r = interest given 1.5% i.e 0.015
n = period of time the principal remains deposited. In this case annually i.e 12 months
FV = $522.99
THe amplitude is half of the distance from the highest and lowest phase of the wave..
4-(-1)=5
0.5*5=2.5
amp=2.5 units
X²+15x+36<0
at first solve quadratic equation
D=b²-4ac= 225-4*1*36= 81
x=(-b+/-√D)/2a
x=(-15+/-√81)/2= (-15+/-9)/2
x1=(-15-9)/2=-12
x2=(-15+9)/2=-3
we can write x²+15x+36<0 as (x+12)(x+3)<0
(x+12)(x+3)<0 can be 2 cases, because for product to be negative one factor should be negative , and second factor should be positive
1 case) x+12<0, and x+3>0,
x<-12, and x>-3
(-∞, -12) and(-3,∞) gives empty set
or second case) x+12>0 and x+3<0
x>-12 and x<-3
(-12,∞) and (-∞,-3) they are crossing , so (-12, -3) is a solution of this inequality
Answer:
b. (-1, 5)
Step-by-step explanation:
Since the first equation is already solved for y, we can use substitution.
Substitute y in the second equation with 3x + 8.
5x + 2y = 5
5x + 2(3x + 8) = 5
5x + 6x + 16 = 5
11x = -11
x = -11/11
x = -1
Now substitute x in the first original equation by -1 and solve for y.
y = 3x + 8
y = 3(-1) + 8
y = -3 + 8
y = 5
Answer: (-1, 5)
