Plz, Solveeeeeeeeeeeeeeeeeeee! I will give you all my points

Given:

First term of a geometric series = a

Common ratio of the geometric series = [tex]\sqrt{3}[/tex]

To prove:

[tex]S_{10}=121a(\sqrt{3}+1)[/tex]

Solution:

The sum of first n terms of geometric series is

[tex]S_n=\dfrac{a(r^n-1)}{r-1}[/tex]

Where, a is the first term and r is the common ratio.

Putting n=10 and [tex]r=\sqrt{3}[/tex] in the above formula, to get the sum of 10 terms.

[tex]S_{10}=\dfrac{a((\sqrt{3})^{10}-1)}{\sqrt{3}-1}[/tex]

[tex]S_{10}=\dfrac{a(243-1)}{\sqrt{3}-1}[/tex]

[tex]S_{10}=\dfrac{242a}{\sqrt{3}-1}[/tex]

Rationalizing the denominator, we get

[tex]S_{10}=\dfrac{242a}{\sqrt{3}-1}\times \dfrac{\sqrt{3}+1}{\sqrt{3}+1}[/tex]

[tex]S_{10}=\dfrac{242a(\sqrt{3}+1)}{(\sqrt{3})^2-1^2}[/tex]

[tex]S_{10}=\dfrac{242a(\sqrt{3}+1)}{3-1}[/tex]

[tex]S_{10}=\dfrac{242a(\sqrt{3}+1)}{2}[/tex]

[tex]S_{10}=121a(\sqrt{3}+1)[/tex]

Hence proved.

Answer:

okay bro, but I need some time

Answer:

72

Step-by-step explanation:

.75x96=72

Answer:

Step-by-step explanation:

Given the expression 3 * 2 2/3

This can also be expressed as;

3 * 2 2/3

= 3 * 8/3

= (24/3)

= 8

hence the product of both numbers is 8

The equivalent value of the fraction is A = 8

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the first fraction be represented as p

Let the second number be represented as q

Now , A = pq

when the value of p = 2 2/3

And , when the value of q = 3

On simplifying the equation , we get

A = ( 2 2/3 ) / ( 3 )

So , the left hand side of the equation is equated to the right hand side by the value of ( 2 2/3 ) / ( 3 )

A = ( 2 2/3 ) / ( 3 )

A = ( 8/3 ) / ( 3 )

On simplifying , we get

Multiply by 3 on the fraction , we get

A = ( 8 x 3 ) / 3

A = 8

Therefore , the value of A = 8

Hence , the fraction is A = 8

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Answer:

1

Step-by-step explanation:

I did it in the calculator

Answer:

-7/2

Step-by-step explanation:

After multiplication of pair of complex numbers, the results of product are respectively 45, 41, 73

The complex number is a combination of real number and imaginary number. The representation of complex number is like, a + bi.

where a is real part and b is imaginary part, the value of i is √-1.

i × i = -1

i⁴ = 1

Given that, pair of complex numbers

(6 +3i )×( 6 - 3i) =  6×6 -6×3i + 6×3i - (3i × -3i)

                         = 36 - 18i + 18i + (-3i × 3i)

                         =  36 + 9

                         =  45

(4-5i) × (4+5i)   =  4×4 + 4×5i - 4×5i - (5i × -5i)

                        = 16 - 20i + 20i + (-5i × 5i)

                        = 16+25

                        = 41

(-3+8i) × (-3-8i) = -3×-3 + (-3× -8i) - 3×8i + (8i × -8i)

                        = 9 +24i-24i +64

                        =  73

Hence, The result of products are 45, 41, 73

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Answer: (6 + 3i)(6 − 3i) = 45, (4 − 5i)(4 + 5i) = 41, (−3 + 8i)(−3 − 8i) = 73

Step-by-step explanation:

9514 1404 393

Answer:

  z + y = 52; z - y = 10; z = 31; y = 21; $9.85 total

Step-by-step explanation:

The variables are defined in the problem statement. The equations could be ...

  z + y = 52 . . . . . . total number of coins

  z - y = 10 . . . . . . . 10 more quarters than dimes

These equations can be solved by adding them together.

  (z +y) +(z -y) = (52) + (10)

  2z = 62 . . . . . . . simplify

  z = 31 . . . . . . . . . divide by 2

  31 -10 = y = 21 . . . . find the number of dimes

There are 31 quarters and 21 dimes.

The value of the coins is ...

  31($0.25) +21($0.10) = $7.75 +2.10 = $9.85

Answer:

Step-by-step explanation:

a₂₁ = -10 + 5(21) = 95

[tex]2x + 3y - x - (8 + 1)[/tex]

[tex]2 x - x + 3y -9[/tex]

[tex]x + 3y - 9[/tex]

Answer:

After calculating, your answer should be:

(0.80-0.5 m/s)/(4.0 s) = (0.075 m)/s^2

I hope this helps you! (This was for the 100 point brainly thing you said you wiuld give me 100 points?)

Answer:

4 pitches

Step-by-step explanation:

if a cylinder with height 9 inches and radius r is filled with water, it can fill a certain pitcher. how many of these pitchers can a cylinder with height 9 inches and radius 2r fill? explain how you know.

Solution:

The volume of a cylinder is given by:

V = πr²h;

where V is the volume, r is the radius of the cylinder and h is the height of the cylinder.

A cylinder with height 9 inches and radius r can fill a certain pitcher. Therefore the volume of the cylinder is:

V = πr²h = πr²(9) = 9πr²

V = volume of pitcher = volume of cylinder with radius r = 9πr²

For a cylinder with height 9 inches and radius 2r its volume is:

V2 = πr²h = π(2r)²(9) = 36πr²

Therefore, the number of pitchers a cylinder with height 9 inches and radius 2r can fill is:

number of pitches = 36πr² / 9πr² = 4

Therefore a cylinder with height 9 inches and radius 2r can fill 4 pitches.

Answer:

The equation for your graph is Y=2x+1

Answer:

Step-by-step explanation:

(10 - 4)/(4 -1)= 6/3= 2

y - 4 = 2(x - 1)

y - 4 = 2x - 2

y = 2x + 2

Answer:

a triangle, I'm guessing 20ft and 24 ft on the outsides,

would be:

Equation to get the area of a triangle: (A*B)/2

(20*24)/2=Area

20*24= 480

480/2= 240

area= 240

Answer: 240 ft²

Step-by-step explanation:

1. Multiply the base and the height.

2. Divide the product you get by 2.

=> 20 * 24 = 480

=> 480 / 2 = 240

Answer:

5.75 days

Step-by-step explanation:

Given data

let the number of days be x and the number and the number of miles be y

so that the cost of the rental will be

c= 38.38x+ 0.14y---------1

we are told that the amount at hand is $270

hence

270=38.38x+ 0.14*(350)

solve for x

270= 38.38x+49

270-49= 38.38x

221= 38.38x

divide both sides by 38.38

x= 221/38.38

x= 5.75 days

Hence the  number of days is 5.75 days

Answer:

Aqua para chica gamer? te sirve?

Since there is a negative on the y term, we need to get rid of that and thus flip the sign at the same time. Getting.

-43>8/3y

Now we just need to divide 8/3 on both sides dividing 8/3 on left can also be written as *3/8

-43*3/8>y

Now flip this entire equation

y<-43*3/8

y<-129/8

If your teacher want you to calculate just divide the fraction, but I recommend not to if your teacher don't ask for it and just leave it this way.

Hope it helps! :D

Answer:

C. 2.7 repeating

Step-by-step explanation:

25/9 = 2.777777777777777

eㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

watch wonder egg priority & sk8 Infinity

on 4anime dot to

Answer:

Meat

Step-by-step explanation:

The only thing he can practically think about is Meat, Pirate King, and his pirate crew.

9514 1404 393

Answer:

  ML = 7.5

Step-by-step explanation:

The parallel lines divide the transversals proportionally.

  ML/LK = JH/HG

  ML/10 = 6/8

  ML = 10(6/8) = 7.5

The length of ML is 7.5.

__

We don't need to solve for x. If ML = x-2, then x=9.5.

the value of the 5 in 590 is hundred

Answer:

thousands I think you can still double check if you want

Answer:

isn't it 36cm^2

Step-by-step explanation:

sqaure is even so i think you do 6×6

Answer:

36cm

Step-by-step explanation:

Area of a square= Side^2

= 6^2

= 36

Answer:

I plot the points to a graph but I don't have access to a 14 I only have a 10 grid graph but I was able to plot the other points this is wht I got

Step-by-step explanation:

let me know if u can't see it..... I would say it's nonlinear

Answer:

use a calculator

Step-by-step explanation:

Answer:

2520

Step-by-step explanation: Calculator

Answer:

42.54 inches

Step-by-step explanation:

Answer:

30

Step-by-step explanation:

This is a 30 60 90 triangle. Since it tells us it a right triangle (which means it has a 90 degree angle). Also it tells us that there is a 30 degree. Using the triangle interior theorem, the third angle is a 60 degree

angle

The longest side or hypotenuse is twice the length of the shortest side. So the hypotunes is 30.

Answer:

B. -1/3

Step-by-step explanation:

replace x with 34 and solve it.

Answer:

2 sides are 38cm long

The third is 46cm long

Step-by-step explanation:

We can use the following equation to solve

[tex]122 =x + x + (x + 8)[/tex]

Reduce

[tex]122 = 3x + 8[/tex]

114÷3 = x

x = 38

We then add 38 and 8 because the 3rd side is 8cm longer