Find the equation of the line shown

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:

3 11/25 pints of white paint

Step-by-step explanation:

8 6/10 is the same as 43/5

if 3/5 of the total pints are blue then 2/5 are white

so multiply 43/5 x 2/5 to get 86/25 which equals 3 11/25

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:

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

Answer:

1. 40

2. 124

3. 160

Step-by-step explanation:

1. 12x - 20 = 60 - 20 = 40

2. 12x - 20 = 144 - 20 = 124

3. 12x - 20 = 180 - 20 = 160

Answer:

C. 2.7 repeating

Step-by-step explanation:

25/9 = 2.777777777777777

Answer:

3/4

Step-by-step explanation:

To find 24/32 in its simplest form, you need to find the biggest common factor.

24: 1, 2, 3, 4, 6, 8, 12, 24

32: 1, 2, 4, 8, 16, 32

For these two numbers, it's 8. Divided 24 and 32 by 8.

3/4

Answer:

1 1/23

Step-by-step explanation:

Answer:

I believe the answer is $455

Answer:

the answer from IXL is $455

Step-by-step explanation:

Answer:

okay bro, but I need some time

Answer:

72

Step-by-step explanation:

.75x96=72

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

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

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

Answer:

Step-by-step explanation:

a₂₁ = -10 + 5(21) = 95

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:

that is very cool

Step-by-step explanation:

v

e

r

y

c

o

o

l

Answer:

you'll need 20 cups of cranberry

Answer:

-3a + 14c

Step-by-step explanation:

4a+7(2c-a)

4a + 14c - 7a

-3a + 14c

Answer:

-3a + 14c

Step-by-step explanation:

4a + 7(2c - a)

4a + 14c - 7a            <- Distribute

-3a + 14c                  <- Add like terms

Answer:

28 is the number of parents.

Step-by-step explanation:

84/3

Step-by-step explanation:

all audiences 84 people

parents = 1/3 of all 84 people

parents = 1/3 × 84 = 28 people

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.

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

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.

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:

4x

3x

Step-by-step explanation:

1.)

we see that when x=0 y=0 which means that our equation

y=mx+b

b=0

(this is shown if we plug in 0 for x)

0= 0x+b

0=b

Next, we notice that each time it's increasing by four which means our slope is just 4

the answer is 4x

The y intercept (or b) is the same deal as question one

we can also see that when x=1 y=3 which means that

3=x+0

3=x

our slope is 3

Answer:

The value of 8 in the number 33.086 would be the hundredth

Step-by-step explanation:

30 would be the ten

3 would be the one

.0 would be tenth

.8 is the hundredth

.6 is the thousandth

Answer:

hundredths

Step-by-step explanation:

0 is tenths

8 is hundredths

6 is thousandths

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:

2.5198421 is yhe answer of 3^√16

Answer:

42.54 inches

Step-by-step explanation:

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:

9 blueberry muffins

Step-by-step explanation:

24*3/8 = 9