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3 years ago

The sum of the measures of the interior angles of a convex polygon is 1080° Classify the polygon by the number of sides

Mathematics

2 answers:

lozanna [386]3 years ago

6 0

Answer:

(n-2)×180=1080

180n -360=1080

180n = 1080+360

180n =1440

dividing by 180

n=8

hence it is a regular polygon with 8 sides .I.e it is an octagon

Step-by-step explanation:

we are given the total interior angles in the polygon and we know that the formula to find the total interior angles of a polygon is (n-2) ×180

where n is the number of sides

Firlakuza [10]3 years ago

6 0

Answer:

the answer is A

Step-by-step explanation:

just trust me.

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Eight less than the quotient of x and 3

yKpoI14uk [10]

Quotient is basically the answer you get when you divide two numbers.
For example, the quotient of 6 and 3 is 2 because when I divide 6 by 3, I get 2.

Quotient of x and 3 = $\frac{x}{3}$

Eight less than quotient of x and 3 is $\frac{x}{3} - 8$ .

Hence, the answer is C.

6 0

2 years ago

The total amount of spending per year, in billions, on pets in a certain country x years after 2000 is given by the following

Kamila [148]

Answer:

40.4502 billion dollars

51.3432 billion dollars

Step-by-step explanation:

Given :

Total amount spent in billions in pets x years after year, 2000 ;

P(x)=2.1786x + 25.2

Amount spent in 2007 ;

x = 2007 - 2000 = 7 years

Put x = 7 in the equation :

P(7)=2.1786(7) + 25.2 = 40.4502

Amount spent in 2012 :

x = 2012 - 2000 = 12 years

Put x = 12 in the equation :

P(12) = 2.1786(12) + 25.2 = 51.3432

The amount spent in billik dollars on pets in :

2007 = $404502 billion

2012 = $51.3432 billion

8 0

2 years ago

Binomial Expansion/Pascal's triangle. Please help with all of number 5.

Mandarinka [93]

$\begin{matrix}1\\1&1\\1&2&1\\1&3&3&1\\1&4&6&4&1\end{bmatrix}$

The rows add up to $1,2,4,8,16$ , respectively. (Notice they're all powers of 2)

The sum of the numbers in row $n$ is $2^{n-1}$ .

The last problem can be solved with the binomial theorem, but I'll assume you don't take that for granted. You can prove this claim by induction. When $n=1$ ,

$(1+x)^1=1+x=\dbinom10+\dbinom11x$

so the base case holds. Assume the claim holds for $n=k$ , so that

$(1+x)^k=\dbinom k0+\dbinom k1x+\cdots+\dbinom k{k-1}x^{k-1}+\dbinom kkx^k$

Use this to show that it holds for $n=k+1$ .

$(1+x)^{k+1}=(1+x)(1+x)^k$
$(1+x)^{k+1}=(1+x)\left(\dbinom k0+\dbinom k1x+\cdots+\dbinom k{k-1}x^{k-1}+\dbinom kkx^k\right)$
$(1+x)^{k+1}=1+\left(\dbinom k0+\dbinom k1\right)x+\left(\dbinom k1+\dbinom k2\right)x^2+\cdots+\left(\dbinom k{k-2}+\dbinom k{k-1}\right)x^{k-1}+\left(\dbinom k{k-1}+\dbinom kk\right)x^k+x^{k+1}$

Notice that

$\dbinom k\ell+\dbinom k{\ell+1}=\dfrac{k!}{\ell!(k-\ell)!}+\dfrac{k!}{(\ell+1)!(k-\ell-1)!}$
$\dbinom k\ell+\dbinom k{\ell+1}=\dfrac{k!(\ell+1)}{(\ell+1)!(k-\ell)!}+\dfrac{k!(k-\ell)}{(\ell+1)!(k-\ell)!}$
$\dbinom k\ell+\dbinom k{\ell+1}=\dfrac{k!(\ell+1)+k!(k-\ell)}{(\ell+1)!(k-\ell)!}$
$\dbinom k\ell+\dbinom k{\ell+1}=\dfrac{k!(k+1)}{(\ell+1)!(k-\ell)!}$
$\dbinom k\ell+\dbinom k{\ell+1}=\dfrac{(k+1)!}{(\ell+1)!((k+1)-(\ell+1))!}$
$\dbinom k\ell+\dbinom k{\ell+1}=\dbinom{k+1}{\ell+1}$

So you can write the expansion for $n=k+1$ as

$(1+x)^{k+1}=1+\dbinom{k+1}1x+\dbinom{k+1}2x^2+\cdots+\dbinom{k+1}{k-1}x^{k-1}+\dbinom{k+1}kx^k+x^{k+1}$

and since $\dbinom{k+1}0=\dbinom{k+1}{k+1}=1$ , you have

$(1+x)^{k+1}=\dbinom{k+1}0+\dbinom{k+1}1x+\cdots+\dbinom{k+1}kx^k+\dbinom{k+1}{k+1}x^{k+1}$

and so the claim holds for $n=k+1$ , thus proving the claim overall that

$(1+x)^n=\dbinom n0+\dbinom n1x+\cdots+\dbinom n{n-1}x^{n-1}+\dbinom nnx^n$

Setting $x=1$ gives

$(1+1)^n=\dbinom n0+\dbinom n1+\cdots+\dbinom n{n-1}+\dbinom nn=2^n$

which agrees with the result obtained for part (c).

4 0

2 years ago

Which property is used in the first step to solve this equation?

Nat2105 [25]

Answer:

distributive property

4 0

2 years ago

Read 2 more answers

If 3x + c = 4, then x equals <br>A: 4-c <br>B: 4 -c/3 <br>C: c-4/3 <br>D: c-4

Colt1911 [192]

Answer:

4-c/3 is ans

Step-by-step explanation:

3x+c=4

3x=4-c

x=4-c/3

4 0

2 years ago

The sum of the measures of the interior angles of a convex polygon is 1080° Classify the polygon by the number of sides​

The sum of the measures of the interior angles of a convex polygon is 1080° Classify the polygon by the number of sides