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MA_775_DIABLO [31]
2 years ago
10

Classify each angle of the degrees

Mathematics
1 answer:
zhuklara [117]2 years ago
6 0

Answer:

acute

right angle or obtuse

obtuse

Step-by-step explanation:

those are the answers

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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
3 years ago
Jean has $280 in her savings account. Starting next week, she will deposit $30 in her account every week.
Sophie [7]
It’s not proportional
8 0
2 years ago
How can you best describe a stop sign using polygons? the sign has sides, so it is . it appears to be because the sides and angl
USPshnik [31]

A polygon is a two-dimensional closed object. The polygon that best describes a stop sign is a regular octagon.

<h3>What is a polygon?</h3>

A polygon is a two-dimensional closed object with n number of straight sides that is flat or planar and the value of n is always greater than 2 (n>2).

<h3>What is an octagon?</h3>

An octagon is a polygon that has 8 number of sides.

As we know that a stop sign has 8 sides, therefore, the polygon that is in the shape of the stop sign is an octagon.

An octagon has 8 sides, and as it is mentioned in the problem that sides and angles appear to be congruent, therefore, the polygon must be a regular polygon.

Hence, the polygon that best describes a stop sign is a regular octagon.

Learn more about Polygon:

brainly.com/question/17756657

3 0
1 year ago
Read 2 more answers
Henrietta bought 5 cupcakes and 2 brownies for $16.25. She went back to the bakery the next day and bought 7 cupcakes and 6 brow
serious [3.7K]

Answer:

cost of one cupcake = $2.75

cost of one brownie = $1.25

Step-by-step explanation:

Let c = number of cupcakes

Let b = number of brownies

Equation 1:  5c + 2b = 16.25

Equation 2:  7c + 6b = 26.75

Multiply equation 1 by 3:

⇒ 15c + 6b = 48.75

Now subtract equation 2 from this equation to eliminate 6b:

⇒ 8c = 22

Divide both sides by 8:

⇒ c = 2.75

Substitute c = 2.75 into one of the original equations and solve for b:

⇒ 5(2.75) + 2b = 16.25

⇒ 13.75 + 2b = 16.25

⇒ 2b = 2.5

⇒ b = 1.25

Therefore, cost of one cupcake = $2.75 and cost of one brownie = $1.25

6 0
2 years ago
In ASTU, S = 3.8 inches, t = 9.8 inches and u=9.6 inches. Find the measure of ZU to
Dahasolnce [82]

Answer: 75.8

Step-by-step explanation:

6 0
3 years ago
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