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3 years ago

What is the next number in the sequence 28, 26, 24, 22,

Mathematics

2 answers:

yaroslaw [1]3 years ago

8 0

Answer:

Step-by-step explanation:

subtract by 2

jajakkalalallalalslsl [ignore this]

zhannawk [14.2K]3 years ago

7 0

Answer:

Step-by-step explanation:

it counting by 2s but backwards

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Find the value of x. If necessary, write your answer in simplest radical form.<br> 12<br> 9

Kobotan [32]

Answer:

3√7

Step-by-step explanation:

9²+B²=12²

simplify

81+B²=144

minus the 81

B²= 63

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2 years ago

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guapka [62]

Answer:

Step-by-step explanation:

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3 years ago

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soldier1979 [14.2K]

Answer:

Parent Function: y = x^2

Vertex: (1,3)

Axis of Symmetry: x = 1

Y-Intercept(s): (0,1)

X-Intercept(s): (1−√62,0),(1+√62,0)

Step-by-step explanation:

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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

A snail sets out on a 3 3/5 -mile journey, traveling at a speed of 2/65 miles per hour. a. How many hours will the journey take?

fiasKO [112]

Answer:a)117 hours b)4.875days.

Step-by-step explanation:

Using the formula

Speed =Distance / Time

Given Distance = 3 3/5 -mile

and Speed=2/65 miles per hour.

Time =Distance / Speed

Time = (3 3/5)/(2/65)

Time =18/5÷2/65

Time =18/5 x 65/2 =117 hours

Now 24 hours =1 day

therefore 117hours =(117hours x 1 day )/ 24 =4.875days.

3 0

3 years ago