What is the factored form of the polynomial 27x2y-43xy2

lbvjy [14]

If $S$ denotes the sum of the first $n$ terms of a geometric series with first term $a$ and common ratio $r$ , then

$S=a+ar+ar^2+\cdots+ar^{n-3}+ar^{n-2}+ar^{n-1}$
$rS=ar+ar^2+ar^3+\cdots+ar^{n-2}+ar^{n-1}+ar^n$
$\implies S-rS=a+(ar-ar)+(ar^2-ar^2)+\cdots+(ar^{n-1}-ar^{n-1})-ar^n$
$\implies (1-r)S=a(1-r^n)$
$\implies S=a=\dfrac{1-r^n}{1-r}$

Using summation notation, you have

$S=\displaystyle\sum_{x=1}^nar^{x-1}=\sum_{x=0}^{n-1}ar^x=a\dfrac{1-r^n}{1-r}$

In this case, you have $a=2$ , $r=\dfrac12$ , and $n=16$ . So the value of the sum is

$\displaystyle\sum_{x=0}^{15}2\left(\frac14\right)^x=2\dfrac{1-\left(\frac14\right)^{16}}{1-\frac14}\approx2.67$

Rounded to the nearest whole number, the answer would be 3.

4 0

4 years ago

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I'm trying to find out the number of how much it cost to wrap each present, day one 41 small gifts were wrapped and 45 large wer

Licemer1 [7]

Answer:

Small gift: $2

Large gift: $7

Step-by-step explanation:

Let x represent cost of wrapping each small gift and y represent cost of wrapping each large gift.

We have been given that day one 41 small gifts were wrapped and 45 large were wrapped equaling $397.

We can represent this information in an equation as:

$41x+45y=397...(1)$

We are also told that day two 30 small gifts were wrapped and 47 large were wrapped equaling $389. We can represent this information in an equation as:

$30x+47y=389...(2)$

From equation (1), we will get:

$x=\frac{397-45y}{41}$

Upon substituting this value in equation (2), we will get:

$30(\frac{397-45y}{41})+47y=389$

$\frac{11910-1350y}{41}+\frac{47*41y}{41}=389$

$\frac{11910-1350y+1927y}{41}=389$

$\frac{11910+577y}{41}=389$

$\frac{11910+577y}{41}\cdot 41=389\cdot 41$

$11910+577y=15949$

$11910-11910+577y=15949-11910$

$577y=4039$

$\frac{577y}{577}=\frac{4039}{577}$

$y=7$

Therefore, cost to wrap a large gift is $7.

Upon substituting $y=7$ in equation $x=\frac{397-45y}{41}$ , we will get:

$x=\frac{397-45(7)}{41}$

$x=\frac{397-315}{41}$

$x=\frac{82}{41}$

$x=2$

Therefore, cost to wrap a small gift is $2.

8 0

3 years ago

Evaluate the Expression B^2-4 ac given by that a = -2 ,, b= -2 and c =2

Lapatulllka [165]

F* you B*!!!!!! Your so S*! That's the easiest thing in the world!!

4 0

4 years ago

HELPPPPPP ASAP What is the length of the third side of the window frame below? (5 points) (Figure is not drawn to scale.) 58a 1)

ollegr [7]

Answer:

The answer is 3) 40.

Step-by-step explanation:

since you're working with the Pythagorean theorem, you should know that a^2+b^2=c^2, therefore, we know that we only have two sides. we have a and c. we know that a = 42 and c = 58, giving us the equation of 42^2+b^2=58^2,

we want to find b!

so we would simply subtract the two.

58^2 - 42^2 = b

b = 1600

now we want to square root,

b = sqrt1600

which in the end, gives us the answer of 40.

4 0

3 years ago

GCF of the numbers 15 and 27

balandron [24]

Three would be your answer :)

6 0

4 years ago

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