which statement correctly compares the shapes?

Answer:

Hope the picture will help you!!

I bet the sum you're referring to is supposed to be

[tex]\displaystyle \sum_{r=0}^{20} r^2 \times {}^{20}C_r[/tex]

or equivalently,

[tex]\displaystyle \sum_{r=0}^{20} r^2 \binom{20}r[/tex]

where [tex]\binom nk = \frac{n!}{k!(n-k)!}[/tex] is the binomial coefficient.

Recall the binomial series,

[tex](1+x)^\alpha = \displaystyle \sum_{r=0}^\infty \binom\alpha r x^r[/tex]

which is valid for |x| < 1. (Note that if r > α, the binomial coefficient is defined to be zero, so there really are only α many terms when α is a whole number.)

Differentiating both sides with respect to x gives

[tex]\alpha (1+x)^{\alpha-1} = \displaystyle \sum_{r=0}^\infty r \binom\alpha r x^{r-1}[/tex]

Multiply both sides by some arbitrary x in |x| < 1 :

[tex]\alpha x (1+x)^{\alpha-1} = \displaystyle \sum_{r=0}^\infty r \binom\alpha r x^r[/tex]

Repeat:

[tex]\alpha (1+x)^{\alpha-1} + \alpha(\alpha-1) x(1+x)^{\alpha-2} = \displaystyle \sum_{r=0}^\infty r^2 \binom\alpha r x^{r-1}[/tex]

[tex]\alpha x (1+x)^{\alpha-1} + \alpha(\alpha-1) x^2 (1+x)^{\alpha-2} = \displaystyle \sum_{r=0}^\infty r^2 \binom\alpha r x^r[/tex]

Let α = 20, and let x approach 1 from below. The right side converges to the sum we want, while the left side converges to

[tex]20 \times 2^{19} + 20\times19\times 2^{18} = (20 + 10\times19)\times2^{19} = \boxed{210\times2^{19}}[/tex]

Answer:

8/3

Step-by-step explanation:

Answer:

Step-by-step explanation:

General form of the linear differential equation can be written as:

[tex]\frac{dy}{dx}+P(x)y=Q(x)[/tex]

For this case, we can rewrite the equation as:

[tex]\frac{dy}{dx}+\frac{1}{2x}y=\frac{\sqrt{x}}{x}[/tex]

Here [tex]P(x) =\frac{1}{2x}; Q(x)=\frac{\sqrt{x}}{x}[/tex]

To find the solution (y(x)), we can use the integration factor method:

[tex]Fy(x)=\int Q(x)Fdx+C \rightarrow F=e^{\int P(x)dx[/tex]

Then [tex]F=e^{\int \frac{1}{2x}dx}=e^{\frac{1}{2}\ln|x|\right}=\sqrt{|x|}[/tex]

So, we can find:

[tex]y\sqrt{|x|}=\int \frac{\sqrt{x}\sqrt{|x|}}{x}dx+C[/tex]

Suppose that [tex]x\in \double R[/tex], then [tex]\sqrt{|x|}=\sqrt{x}[/tex] , and we find:

[tex]y\sqrt{x}=x+C \rightarrow y(x)=\sqrt{x}+\frac{C\sqrt{x}}{x}[/tex]

To check our solution is right or not, put your y(x) back to the ODE:

[tex]y' = \frac{1}{2\sqrt{x}}-\frac{C}{2\sqrt{x^{3}}}[/tex]

[tex]2xy'=\frac{x-C}{\sqrt{x}}[/tex]

[tex]2xy'+y=\frac{x-C}{\sqrt{x}}+\sqrt{x}+\frac{C\sqrt{x}}{x}=2\sqrt{x}[/tex]

(it means your solution is right)

Answer:

-331/140

Step-by-step explanation:

Answer:

B. Pentagon

Step-by-step explanation:

A Pentagon is a polygon with 5 sides like this one.

Hope that helps!

Answer:

15/2 min/m

Step-by-step explanation:

Minuters per meter = min/m

4.5 min/(3/5) m

4.5 x 5/3 = 7.5

7.5 = 15/2

Hope this helps!

Answer:

The answer is D

Step-by-step explanation:

(7/x² × x²)+(1/3×x²)+(x+2/x × x²)

(7 + x/3 + x²+2x) times 3 to eliminate the 3 under x/3

so u will get 21+x+3x²+6x

Final answer = 3x²+7x+21

Answer:

B 1/5

Step-by-step explanation:

there is 20 combinations

4 of the twenty are ribs or chicken with a red sauce

4/20 = 1/5

Answer:

above 84°/. of the vehicles have a gas mileage greater then 24 mpg

Answer:

Step-by-step explanation:

Hello:

an equation   for the line is : y =mx +b    (m: is a slope )

given : m = -1

the equation is : y = -x+b

through the point (-2,-3) :-3 =-(-2)+b....... b=-5

the equation is : y = -x-5

Answer:

7, -9

Reasoning:

When x is 7 or -9, the denominator equates to zero, making the expression undefined because nothing can be divided by zero.

un punto en un gráfico de líneas es un valor específico que normalmente es un valor de entrada y salida (x)

Answer:

e) 36x² - 32y³ = (4)(9x² - 8y³)

f) 45a⁴ - 54a³ = (9a³)(5a - 6)

Step-by-step explanation:

e) 36x² - 32y³ = (4)(9x² - 8y³) becuase 4*9 = 36 and 4*8 = 32

f) 45a⁴ - 54a³ = (9a³)(5a - 6) becuase 9*5 = 45 and 9*6 = 54 and when a is multiplied by a³ you get a⁴

(the exponent are added)

PLEASE RATE!! I hope this helps!!
If you have any questions comment below

Answer: B and C

Step-by-step explanation:

404 + 50 + 50 = 504

you are buying  144 magazines total

504/144 = cost of one magazine

cost of one = 3.50

you are paying $60 a year for 12 years

60 x 12 = 720

720/144 = 5

5 - 3.50 = 1.50

2.

120x + 180x = 1080

300x = 1080

x = 1080/300

x = 3.6

3.6 x 60 = 216

Answer:

the answer is

[tex] \frac{12 {c}^{8} }{ {d}^{2} } [/tex]

Step-by-step explanation:

[tex] \frac{12}{ {c}^{ - 8} {d}^{2} } [/tex]

Answer:

A.  Complementary and Adjacent

B.  ∠KLM = 22°  and  ∠MLN = 68°

Step-by-step explanation:

Question A

As ∠KLN is a right angle, ∠KLN = 90°

⇒ ∠KLM + ∠MLN = 90°

When the sum of two angles is 90°, they are called complementary angles.

∠KLM and ∠MLN have a common side of ML and a common vertex (corner point) L.

When two angles have a common side and a common vertex but do not overlap in any way, the are called adjacent angles.

Question B

First find n:

∠KLM + ∠MLN = ∠KLN

⇒ 2n + (6n + 2) = 90

⇒ 2n + 6n + 2 = 90

Combine like terms:

⇒ 8n + 2 = 90

Subtract 2 from both sides:

⇒ 8n = 88

Divide both sides by 8:

⇒ n = 11

Now substitute the found value of n into the expressions for the two angles:

⇒ ∠KLM = 2(11) = 22°

⇒ ∠MLN = 6(11) + 2 = 68°

Answer:

The opposite sides in a rectangle are equal.

Step-by-step explanation:

If all sides were equal, you would have a square.

If the opposite sides were not parallel, you would not have 4 sides that meet at 90 degrees.

All angles in a rectangle are 90 degrees.

Answer:

The opposite sides in a rectangle are equal.

Step-by-step explanation:

hope this helps  hope you get it correct

Answer: 907.46

Step-by-step explanation:

Answer:

Step-by-step explanation:

vector e is (-1,5),f is (3,-4),g is (2,1)

2i+j=x(-i+5j)+y(3i-4j)

2=-x+3y (multiply by 5)

10=-5x+15y

1=5x-4y

add

11=11y

y=1

2=-x+3(1)

x=3-2=1

2i+j=1(-i+5j)+1(3i-4j)

Answer:

39

Step-by-step explanation:

all angles of a triangle equal to 180, so you just have to subtract those two known angles from 180, and you will get the answer.

Find the value of angle x .

The concept of this question belongs to angles of triangle . We know that the sum of all the three angles of triangle is 180°.

As we know that all the angles of triangle is equal to 180° . So :

Therefore , angle x is of 39° .

Answer:

$37.5+$3r

Step-by-step explanation:

We can assume that the number of rides is r. Since each ride is $3.00, all rides are $3r ($3xr).

We also know that there are FIVE people going to the fair, with Tory being one and each of her friends. Since the entrance fee is 7.50, we can do 7.50x5 which is $37.5.

Then, you can add it which is $37.5+$3r

Answer:

TRUE

Step-by-step explanation:

Do the pencil test . It doesnt have repeating X's.

Answer:

It is actually True so when you do it press true

Answer:

c. 3/5

Step-by-step explanation:

Answer:

[tex]\bf C)\: -\cfrac{1}{32}[/tex]

Step-by-step explanation:

[tex]\tt \cfrac{1}{2^{-2}x^{-3}y^5}[/tex]

[tex]\tt x=2\\y=-4[/tex]

~

Substitute ''x'' with '2' & 'y' with "-4":-

[tex]\tt \cfrac{1}{2^{-2}\times \:2^{-3}\left(-4\right)^5}[/tex]

First let's solve [tex]\tt 2^{-2}\times \:\:2^{-3}\left(-4\right)^5[/tex]

[tex]\tt 2^{-2}\times \:2^{-3}=\boxed{\cfrac{1}{32} }[/tex]

[tex]\tt \cfrac{1}{32}\left(-4\right)^5[/tex]

Calculate exponents:- -4^5= -1024

[tex]\tt \cfrac{1}{32}\left(-1024\right)[/tex]

Remove parentheses, apply rule:- [tex]\tt a\left(-b\right)=-ab[/tex]

[tex]\tt-\frac{1}{32}\times \:1024[/tex]

[tex]\tt \cfrac{1}{32}\times \cfrac{1024}{1}[/tex]

Apply fraction rule:-

[tex]\tt -\cfrac{1\times \:1024}{32\times \:1}[/tex]

[tex]\tt \cfrac{1024}{32}[/tex]

Divide numbers:-

[tex]\tt -32[/tex]

Now that we're done factoring the denominator let's bring down the numerator which is ' 1 ':-

[tex]\tt -\cfrac{1}{32}\;\; \bf Answer[/tex]

☆-------☆-------☆-------☆

[tex]\dfrac 1{2^{-2}\cdot x^{-3}\cdot y^5}\\\\=\dfrac 1{2^{-2} \cdot2^{-3} \cdot (-4)^5}\\\\=-\dfrac 1{2^{-2} \cdot 2^{-3} \cdot (2^2)^5}\\\\=-\dfrac{1}{2^{-2} \cdot 2^{-3} \cdot 2^{10}}\\\\=-\dfrac{1}{2^{-2-3+10}}\\\\=-\dfrac 1{2^{5}}\\\\=-\dfrac 1{32}[/tex]

Answer:

Blank 1. is 2 feet

Blank 2. is 28 grams

Blank 3. is 8 mililiters

Step-by-step explanation:

Answer:

135 degrees

Step-by-step explanation:

The image shows how i had my answer please

Answer:

Step-by-step explanation: