he sum of the first two terms of a G.P is 27 whereas the sum of the second and third term is 54. Find the first term and the common ratio.​

Answers

Answer 1

Answer:

[tex]{ \tt{sum = \frac{a(r {}^{n - 1} )}{n - 1} }} \\ 27 = \frac{a(r {}^{2 - 1} )}{2 - 1} \\ { \bf{27 = ar - - - (i)}} \\ \\ 54 = \frac{a( {r}^{3 - 1} )}{3 - 1} \\ { \bf{108 = a {r}^{2} - - - (ii) }} \\ { \tt{(ii) \div (i) : }} \\ r = \frac{108}{27} \\ { \bf{common \: ratio = 4}} \\ { \bf{first \: term = \frac{27}{4} }}[/tex]


Related Questions

In this 3x3 square, you can use only numbers from 1-9, to make all the rows and columns equal to 15. Good luck to the person solving this and just know that I and lots more people thank you for solving this!

Answers

Answer:

Hello,

Step-by-step explanation:

The well-known magic square. (first apparition in China).

Here it the methode du Marquis de Liouville: (odd square:3,5,7,9,11,13,...)

We are going to put successively the number from 1 to n² (here n=3)

We imagine that the square is put on a sphere;

We begin in the middle of the last line where we put 1

ICI:

We move in direction SE of one case and put le next number

until we reach of multiple of n

After have reached a multiple of n, we move verticaly of one case

and we go to ICI until we reach n²

On a piece of paper graph
f(x) = {-1 if -1 <= x < 0}
{ -2 if 0 <= x < 0}
{ -3 if 1 <= x < 2

Answers

In this question, a piece-wise function is asked to be graphed.

Piece-wise function:

A piece-wise function is a function that has different definitions, depending on the input.

In this question, the function has three different definitions:

For x between -1(inclusive) and 0, y takes a constant value of -1.

For x between 0(inclusive) and 1, y takes a constant value of -2.

For x between 1(inclusive) and 2, y takes a constant value of -3.

Additionally:

At the inclusive points, the interval is circled, and thus, the graphic is given at the end of this answer.

For another example of the graphic of a piece-wise function, you can check https://brainly.com/question/16855064

Answer:

Step-by-step explanation:

1. (1, 3); (2, 3)

2. (0, 0) (1, 0)

3. (-1, 1) (0,0)

A circle is represented by the equation below:

(x − 9)2 + (y + 8)2 = 16

Which statement is true?

a) The circle is centered at (−9, 8) and has a radius of 8.
b) The circle is centered at (9, −8) and has a diameter of 8.
c) The circle is centered at (9, −8) and has a radius of 8.
d) The circle is centered at (−9, 8) and has a diameter of 8.

Answers

Answer:

The center is (9,-8) and the diameter is 8

Step-by-step explanation:

(x − 9)^2 + (y + 8)^2 = 16

A circle is in the form

(x − h)^2 + (y -k)^2 = r^2  where (h,k) is the center and r is the radius

(x − 9)^2 + (y -  -8)^2 = 4^2  

The center is (9,-8) and the radius is 4

The diameter is 2 times the radius so the diameter is 8

The center is (9,-8) and the diameter is 8


The circumference of a circle is 14 meters. Which of the following represents the area of the circle

Answers

Answer:

A = 49/pi

Step-by-step explanation:

C = 2 * pi *r

14 = 2 * pi *r

Divide each side by 2 pi

14/2pi = r

7/pi = r

The area is given by

A = pi r^2

A = pi ( 7/ pi)^2

A  = pi * 49 / pi^2

A = 49/pi

Answer:

[tex]area = {15.61m}^{2} [/tex]

explanation is attached to the picture

Hope this helps you

What is the percent change from 75 to 14?

Answers

Answer:

the change is -81.33% (the 3 is repeating)

Is the quotient of a rational number and
an irrational number always irrational?
Explain.

HELP ASAP

Answers

Is the quotient of a rational number and an irrational number always irrational?

Answer = No,It can be either rational or irrational.

________________________________

Prroof —

4 ÷ √8 = √2 { Which is an irrational number }

________________________________

Now, Here comes a twist,

We know that — 0 is a rational number.

And, 0 ÷ √56666 = 0 ________________________________

Note—

But, √56666 ÷ 0 = Error ( Lol )

________________________________

help find the height

Answers

Answer:

A

Step-by-step explanation:

Heron's formula finds the area of any triangle.

Area = sqrt(s*(s - a)*(s-b)*(s-c) )

s = (a + b + c)/2

a = 8

b = 16

c = 12

s = 36/2 = 18

s-a = 18 - 8 = 10

s-b = 18 - 16 = 2

s-c = 18 - 12 = 6

Area = sqrt(18*10*2*6) = sqrt(2160)

Area = 12*sqrt(15)

Area = 46.4758

Now x is easily found. It is the altitude to 16

Area = 1/2 16 * h

46.4758 * 2 / 16 = h

h = 3*sqrt(15)/2

h= 5.81

What is the range of the function?

Answers

Answer:

all real numbers greater than or equal to 11

please HELP ME!!! (16 POINTS) due today :)))

Answers

Answer:

Step-by-step explanation:

I'm not sure what the question is asking, but if you mean the angles in the blue lines

First one, we know that the full length is 90, and it has gacen us 80, so the angle would be 10

Second one, we see that the angle is still 90, and since the given degree is 30, the unkown angle would be 60

Third one, the given angle is 75 so 90-75=15.

The answers would be 10, 60, and 15.

Answer:

4. 170*

5. 330*

6. 285*

Step-by-step explanation:

4. Explanation: 90* is added by the other angle in the right + 80* for the same angle

90* + 80* = 170*
————————————————————

5. Explanation: we are trying to find out the total among every angle measure except for 30.

Total angle measure = 360*

360 - 30 = 330*
—————————————————————

6. Explanation: 360 - 75 = 285*


Factor completely 3x - 15.
O 3(x - 5)
O 3(x + 5)
O 3x(-15)
O Prime

Answers

Answer: First Choice. 3 ( x - 5 )

Step-by-step explanation:

Concept:

When we are doing factoring, we should try to find any Greatest Common Factor (GCF) of all constants in the given expression.

The Greatest Common factor is the largest value of the values you have, that multiplied by the whole number is able to "step onto both".

Solve:

Factors of 3: 1, 3

Factors of 15: 1, 3, 5, 15

As we can see from the list above, 3 appears in both lists of factors and is the greatest for 3. Therefore, [3] is the GCF of 3 and 15

Divide 3 for both numbers to find the remaining.

3x / 3 - 15 / 3x - 5

Check whether or not the remaining can be divisible

Ans: NO

Put the factored out 3 and remaining together

3 ( x - 5)

Hope this helps!! :)

Please let me know if you have any questions

find the area of triangle
i. b=6cm ,h=4cm
ii. b=5cm ,h=7cm
iii. b=8.4 cm ,h=5cm
answer
[tex]i.12cm {}^{2} [/tex]

[tex]ii.17.5cm {}^{2} [/tex]
[tex]iii.21cm {}^{2} [/tex]




Answers

Answer:

Step-by-step explanation:

What are we supposed to do? You already have the answers and they’re all correct if that’s what you wanted to know

Sweatshirts at the school store cost $30. They currently sell about 4 shirts per month. They have decided to decrease the price of the shirts. They found the for each each $1.50 decrease, they will sell 2 more shirts per month. How many decreases in prices will give the max value?

A. 30

B. 9

C. 363

D. 16.50

Answers

a club usually sells 1200 shirts a year at $20 each. A survey indicates that
for every $2 increase in price, there will be a drop of 60 sales a year.
What price they should charge for each shirt to maximize the revenue?
:
Let x = no. of $2 increases
also
Let x = no. 60 shirt sales reductions
:
Price = (20 + 2x)
No. of shirts = (1200 - 60x)
:
Revenue = price * no. of shirts sold, therefore:
R = (20 + 2x)*(1200 - 60x)
FOIL
R = 24000 - 1200x + 2400x - 120x^2
Arranges as a quadratic equation
R = -120x^2 + 1200x + 24000
Find the axis of symmetry to find the price for max revenue: x = -b/(2a)
In this equation; a=-120; b=1200
x = %28-1200%29%2F%282%2A-120%29
x = %28-1200%29%2F%28-240%29
x = +5 ea $2 increases
and
5*60 = 300 reduction in shirt sales:
:
Price for max sales; 20 +2(5) = $30, will sell 1200 - 300 = 900 shirts
:
Max revenue: 30 * 900 = $27,000

8. The value of [3 - 4 * (3 - 4) ^ 4] ^ 3 is
a) 1
b) -1
c)0
d) 7
help me please ​

Answers

Answer:

-1

Step-by-step explanation:

[3-4(-1)^4]^3

=>(3-4)^3

=>(-1)^3

=>-1

Answer From Gauth Math

Answer:

-1

Step-by-step explanation:

[tex][3-4*(3-4)^4]^3[/tex]        

[tex](3-4)^4= 1\\Therefore, [3-4*1]^3= -1^3\\So, -1^3= -1\\\\[/tex]

Cube of any negative integer will be negative, or, a negative integer raised to any odd number will be negative. Likewise, a negative integer raised to an even number will be positive.

Maya just bought a refrigerator for $642. She paid $160.40 in a down payment and will pay the rest in 4 equal installments. How much does she need to pay for each installment?

Answers

Answer:

120.40 per payment

Step-by-step explanation:

Subtract the down payment

642 - 160.40

481.60

Divide this by 4

481.60 / 4

120.40

2.1: Solve the one step equation

9. 70 = -5x
10. x4 = 36
11. 7x = -54

Answers

Answer:

-14, 9 and - 54/7

Step-by-step explanation:

70=-5x, x=-144x=36, x=97x=-54, x=-54/7

rationalize the denominator of 7+3√2​

Answers

Answer:

31

Step-by-step explanation:

To rationalise 7 + 3[tex]\sqrt{2}[/tex] , multiply by its conjugate

The conjugate of 7 + 3[tex]\sqrt{2}[/tex] is 7 - 3[tex]\sqrt{2}[/tex] , then

(7 + 3[tex]\sqrt{2}[/tex])(7 - 3[tex]\sqrt{2}[/tex]) ← expand using FOIL

= 49 - 21[tex]\sqrt{2}[/tex] - 21[tex]\sqrt{2}[/tex] - (3[tex]\sqrt{2}[/tex])²

= 49 - 18

= 31

A grocer purchased 200 eggs at rs.9each. 20 of them were broken and he/she sold the rest at rs.9.50 each.Find his /her profit or loss percent.​

Answers

Answer:

5.55%

Step-by-step explanation:

Hope this helped you

If this helped you, plz mark me as brainiliest

Sorry for bad handwriting.

Thank you

Please help me ill give brainliest!!​

Answers

Answer:

3744.64

Step-by-step explanation:

To know the answer to this question you need to know the formulas to find the volume of the cylinder and the rectangular prism. The volume of a cylinder is pi*r^2*h while the volume of the rectangular prism is l*w*h. The cylinder is 1808.64 cubic in while the rectangular prism is 1936 cubic. Together, they are 3744.64 cubic in.

Answer:

cylinder= A=πr²h

=3.14×4²×9

=452.16

rectangle=A=l×w×h

=19×11×11

=2299

total area=452.16+2299

=2751.16

Step-by-step explanation:

Question 1 (1 point)
The perimeter of an iPad Air is 820 mm. Its length is 100 mm less than twice the
width.
If x = the length of the iPad Air and y = the width of the iPad Air, the linear system of
equations that could be used to model this situations is,
2x + 2y = a
bx = cy-d
The value of a is:

Answers

Answer:

a is the perimeter which is given as 820 mm.

Step-by-step explanation:

Perimeter, P = 820 mm

Length is 100 m less than twice of width

let the length is x and the width is y.

So,

x = 2 y - 100

P = 2 (x + y)

820 = 2 (2y - 100 + y)

410 = 3 y - 100

3 y = 510

y = 170 mm

x = 2 x 170 - 100 = 240 mm

The equation is

2 x = 2 y = a

where, a is the perimeter which is given as 820 mm.

Which of the following graphs best represents the solution to the pair of equations below?

y = −x + 6

y = 2x − 3

Answers

May you post the graph please or else I cannot answer your question for you

Rút gọn bthuc
7x(4y-x) + 4y(y-7x) - (4y^2 -7x)

Answers

¢✓¢==¢=

Step-by-step explanation:

==`==¢=¢✓%✓™€✓✓€=€✓€✓

dbshhshs

shhsshsh

g(x) = x3 + 2x2 - x - 2 to answer all the questions in Part II. 1. Use synthetic division to show that x = -2 is a zero of the polynomial.

Answers

Answer:[tex]x^{2} -1[/tex]

Step-by-step explanation:

Given :[tex]g(x)=x^{3} +2x^{2} -x-2[/tex]

Factor x+2,x=-2

Using synthesis division:

-2 )  1 2   -1  -2

        -2    0   2

      1  0   -1   0

[tex]x^{2} +0x-1[/tex]

Yes,  x = -2 is a zero of the polynomial.

Given that,

The function g(x) = x³ + 2x² - x - 2 is divided by (x + 2)

Now apply the synthetic division to show that x = -2 is a zero of the polynomial.

When we divide by using synthetic division as shown in the attached image.

Remainder = 0

Hence, this shows that x = -2 is a zero of the polynomial.

Therefore, x = -2 is a zero of the polynomial.

To learn more about the divide visit:

https://brainly.com/question/28119824

#SPJ4

what is the scale factor from figure A to figure B

Answers

Answer:

scale facor is 1/3

Step-by-step explanation:

Can someone help me I don't understand

Answers

Answer:

79.605

Step-by-step explanation:

sin 31° = 41/x

x = 41/sin 31°

x = 79.605

I think the answer is 79.605

how many line of symmetry is this figure​

Answers

Answer:

There are sixteen lines.

help me with this math question pls!! Find the value of x

Answers

Answer:

x = 3

Step-by-step explanation:

using the mid segment formula since quadrilateral WZYP is similar to that of MZYT, this is expressed as;

29 = 1/2(23 +11x+2)

Cross multiply

2(29) =  23+11x+2

58 = 25 + 11x

11x = 58 - 25

11x = 33

Divide both sides by 11

11x/11 = 33/11

x = 3

Hence the value of x is 3

In right triangle ABC, if AC = 5/13 and AB = 1, what is the length of BC?

Answers

Answer:

BC = [tex]\frac{12}{13}[/tex]

Step-by-step explanation:

Using Pythagoras' identity in the right triangle

BC² + AC² = AB²

BC² + ([tex]\frac{5}{13}[/tex] )² = 1²

BC² + [tex]\frac{25}{169}[/tex] = 1 ( subtract [tex]\frac{25}{169}[/tex] from both sides )

BC² = [tex]\frac{169}{169}[/tex] - [tex]\frac{25}{169}[/tex] = [tex]\frac{144}{169}[/tex] ( take square root of both sides )

BC = [tex]\sqrt{\frac{144}{169} }[/tex] = [tex]\frac{12}{13}[/tex]

( x-3 ).( 2x-3 ) = 0

Answers

Answer:

Step-by-step explanation:

Assuming you want to find x, we can set two equations:

x-3=0

2x-3=0

This is so that we can individually find x within the two paranthesis and not have to do more work. It helps for standardized tests.

solve for x on both sides, and you get 3 and 1.5

Answer:

[tex]x=3, x=\frac{3}{2}[/tex]

Step-by-step explanation:

[tex]\left(x-3\right)\left(2x-3\right)=0[/tex]

The zero product theorem will be used here to solve this non-linear problem.

means that in the original equation, each variable component must be set to zero.

[tex]\begin{cases} x-3=0\\2x -3=0\end{cases}[/tex]

To solve this linear equation, we need to group all of the variable terms on one side of the equation and all of the constant terms on the other.

so,  -3  will be moved to the right side

Notice that when a term moves from one side of the equation to the other, it changes sign.

[tex]\begin{cases} (x-3)+3=3\\(2x-3)+3=3 \end{cases}[/tex]

[tex]x\left \{ 3,\frac{3}{2} \}[/tex]

OAmalOHopeO

for a mathematical statement to be an equation, the quantities on each side of an equal sign must be?

Answers

Answer:

equal or balanced

Step-by-step explanation

the = demonstrates the amounts need to be the same

Answer: Balanced.

Step-by-step explanation:

For an equation each side shall be equal (balanced) or else it's NOT an equation.

What is the value of 2.3 + 8 – 1/2?

a ) 10.8
b) 10.03
c) 9.8
d) 9.5

Answers

Answer:

9.8

Step-by-step explanation:

2.3 + 8 – 1/2

Rewriting the fraction as a decimal

2.3 + 8 – .5

9.8

the answer is C. 9.8
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