Answer:
125x - 33x⁴
Pull out like factors :
125x - 27x⁴ = -x • (27x3 - 125)
Factoring: 27x³- 125
Theory : A difference of two perfect cubes, a³ - b³ can be factored into
(a-b) • (a² +ab +b²)
(a-b)•(a²+ab+b²) =
a³+a²b+ab²-ba²-b²a-b³ =
a³+(a2b-ba²)+(ab²-b²a)-b³ =
a³+0+0+b³ =
a³+b³
Check : 27 is the cube of 3
Check : 125 is the cube of 5
Check : x³ is the cube of x¹
Factorization is :
(3x - 5) • (9x² + 15x + 25)
Answer: 11
Step-by-step explanation:
Exponential Functions:
y=ab^x
y=ab
x
a=\text{starting value = }550
a=starting value = 550
r=\text{rate = }18.8\% = 0.188
r=rate = 18.8%=0.188
\text{Exponential Decay:}
Exponential Decay:
b=1-r=1-0.188=0.812
b=1−r=1−0.188=0.812
\text{Write Exponential Function:}
Write Exponential Function:
y=550(0.812)^x
y=550(0.812)
x
Put it all together
\text{Plug in y-value:}
Plug in y-value:
60=550(0.812)^x
60=550(0.812)
x
\frac{60}{550}=\frac{550(0.812)^x}{550}
550
60
=
550
550(0.812)
x
Divide both sides by 550
0.109091=0.812^x
0.109091=0.812
x
\log 0.109091=\log 0.812^x
log0.109091=log0.812
x
Take the log of both sides
\log 0.109091=x\log 0.812
log0.109091=xlog0.812
use power rule to bring x to the front
\frac{\log 0.109091}{\log 0.812}=\frac{x\log 0.812}{\log 0.812}
log0.812
log0.109091
=
log0.812
xlog0.812
Divide both sides by log(0.812)
10.638757=x
10.638757=x
x\approx 11
x≈11
He saved $17.1
Yes yes yes yes yes
Answer:5
Step-by-step explanation:
This can be solved by fixing the position of shortest and tallest person in the first and second row respectively .
Rest we have four person remaining and we have to arrange 4 person in 4 positions therefore we can do it in
ways out of which we have to exclude the case when both the tall persons is in the first row and short person in second rows
Therefore a total of 6-1 ways is possible
Answer:
1:3
Step-by-step explanation:
7x3=21
or every striped tie there are 3 solid ties
