the 3 term of a G.P is 360and the 6 term is 1215. find the common ratio and the sum of the first term​ pls I need d answer quickly its urgent

Answers

Answer 1

Answer:

First term = 160

Common ratio = 3/2

Step-by-step explanation:

The 3rd term and the 6th term of a G.P are 360 and 1215

The terms are 3 terms apart so find the cube root of the ratio between the 6th and the 3rd term as;

[tex]\frac{1215}{360} =\frac{27}{8} \\\\\sqrt[3]{\frac{27}{8} } =\frac{3}{2} \\\\\\=\frac{3}{2}[/tex]

The common ratio is : 3/2

To find the first term, divide the third term by the common ratio to get the second term then do that to the second term to get the first term

360 / 3/2

360 *2/3 = 240  -----2nd term

240/ 3/2

240 * 2/3 = 160 ------1st term


Related Questions

Joseph recently noticed that this time next year he will be twice as old as Jasmine. I couldn't help noticing that when I am 66 at this time of the year the combined future ages of Joseph and Jasmine will also be 66. Also, 6 years from now my future age will be a multiple of the sum of Joseph and Jasmine's future ages. Of course, all ages are non-negative integers. How old. are Joseph Jasmine, and I now?

Answers

Joseph and Jasmine are both 33

Someone help me with this please!!​

Answers

Answer:

1

Step-by-step explanation:

x - 5 (x-1) = x - (2x - 3)

Answers

Answer:

x=2/3

Step-by-step explanation:

hope this helps :)

The solution to the equation is x = 2/3.

We have,

To solve the equation x - 5(x - 1) = x - (2x - 3), follow these steps:

- Distribute the -5 to the terms inside the parentheses:

x - 5x + 5 = x - 2x + 3

- Simplify the terms on both sides of the equation:

-4x + 5 = -x + 3

- Add -x from both sides of the equation:

-4x + x + 5 = -x + 3 + x

-3x + 5 = 3

-3x = 3 - 5

-3x = -2

x = 2/3

Therefore,

The solution to the equation is x = 2/3.

Learn more about equations here:

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x² + 4x + 3 = 0

Can someone please help me solve this quadratic equation

Answers

Answer:

Step-by-step explanation:

x= -1 and -3

What when multiplied is +3 but when added is 4? 3 and 1. You then get (x+3)(x+1) is the first part of the answer. If you want to find x, set x+3 to 0. x+3=0. Then subtract 3 from both sides to get x by itself. x= -3. Do the same with the x+1.

a) The y-intercept of the line with the largest slope
is _____
b) For the two lines with a negative slope, the difference
in the value of their x-intercepts is _____
c) For the line with the y-intercept -3, its equation in
slope-intercept form is ____
d) For the line with a slope of 2, the input of _____
gives an output of 17

Answers

Answer:

a) the largest y-intercept is 1

b) 13.5

c) y=x-3

d) 8

Step-by-step explanation:

the question was worded very strangely and I will answer the way I precieved it.

for question d, I simply considered the question to be asking what is X when y is 17 and since the equation of that line is 2x-1

When you can.. please answer these! THANK YOU SO MUCH WAHHH

Match the corresponding rational expressions with the letter of the correct answer.

Answers

Answer:

1-C

2-F

3-A

4-D

5-B

6-E

Step-by-step explanation:

Here's a screenshot of my problem does someone mind helping me

Answers

Answer:

B. Find the ratio of minutes to miles, 4:1. Multiply 7.5 by 4.

Step-by-step explanation:

Look for a pattern within the table.

10 : 2.5

16 : 4

? : 7.5

48 : 12

10/2.5 = 4

16/4 = 4

14/12 = 4

this means that if we multiply 7.5 by 4 we will be able to find the missing number!

Therefore, the answer is B.

Hope this helps! :)

Last night, the temperature fell from 0°F to -13 1/5 in 4 2/5 hours. What was the average temperature change per hour? Solve the division problem.
-13 1/5 ÷ 4 2/5

Answers

Answer:

-16

Step-by-step explanation:

Answer:d

Step-by-step explanation:

The length of a rectangle is 3cm longer than its width.
If the perimeter of the rectangle is 70cm, find its length and width.

Answers

Answer:

width=8cm

lenth=11

Step-by-step explanation:

The x-intercept shows that you can buy short-sleeve shirts and long-sleeve shirts. The y-intercept shows that you can buy long-sleeve shirts and short-sleeve shirts.

Answers

Question:

You are ordering short-sleeve shirts (x) for $10 and long-sleeve shirts (y) for $15. Your budget is $300. Write the equation and find the intercepts.

Interpret their meaning.

Answer:

The x-intercept shows that you can buy 30 short-sleeve shirts and 0 long-sleeve shirts.

The y-intercept shows that you can buy 20 long-sleeve shirts and 0 short-sleeve shirts.

Step-by-step explanation:

Given

$10 per short sleeve

$15 per long sleeve

Budget = $300

The above can be represented as:

Total Cost of Short Sleeve + Total Cost of Long Sleeve = Budget

i.e.

[tex]10 * x + 15 * y =300[/tex]

[tex]10x + 15y =300[/tex]

To solve for the y intercept, we set x to 0

[tex]10 * 0 + 15y =300[/tex]

[tex]15y =300[/tex]

Divide through by 15

[tex]y = 20[/tex]

This implies that, you can buy 0 short sleeves and 20 long sleeves

To solve for the x intercept, we set y to 0

[tex]10x + 15 * 0 = 300[/tex]

[tex]10x = 300[/tex]

Divide through by 10

[tex]x = 30[/tex]

This implies that, you can buy 0 long sleeves and 30 short sleeves

What is 3.258 x 105 written in standard form?

Answers

3.258 x 105=342.09

Brainliest plz!

If a check is written for 2023 does the cheque have to wrong date or just post dated.

Answers

Answer:

it is post-dated

Step-by-step explanation:

What are the differences between a recursive
and explicit rule?

Answers

Answer:

the recursive formula gives the value of a certain term based on the previous term but the explicit formula gives the value of a specific term based on the position.

Step-by-step explanation:

John and gary are playing a game. john spins a spinner numbered with integers from 1 to 20. gary then writes a list of all of the positive factors of the number spun except for the number itself. gary then creates a new spinner with all of the numbers on his list. john then spins this spinner, and the process continues. the game is over when the spinner has no numbers on it. if john spins a 20 on his first spin, what is the maximum number of total spins (including the one he already made) that john can make before the game is over?

Answers

Answer:

4

Step-by-step explanation:

So let's say he gets a result of 20 from the first spin. This means that the factors of 20 would be:

1, 2, 4, 5 and 10. Since 20 is not taken into account when building the next spinner.

now, the possibilities for each of the given factors are:

1:  1

2: 1, 2

4: 1, 2, 4

5: 1, 5

10: 1, 2, 5, 10

So let's take the one with the biggest amount of possible factors, in this case it would be the 10. So let's say that on the second spin, he gets a 10.

So our possible factors for 10 would be:

1, 2, 5  since we don't take 10 itself into account.

So let's see the possible factors for 1, 2 and 5

1: 1

2: 1, 2

5: 1, 5

For the third spin, you could either get a 2 or a 5, it doesn't matter which result you get since for theh last spinner, it would only have a result of 1.

so for the fourth spin, you would get a 1 as an answer and the game ends there with a total of four spins.

Answer:

4

Step-by-step explanation:

If John spins a 20, then Gary's list contains the numbers 1, 2, 4, 5, 10. Thus, these are the numbers on the second spinner.

If John spins a 1, then Gary's list will be empty because there are no positive factors of 1 besides itself. Thus, the game will be over. This yields a maximum of 1 additional spin.

If John spins a 2, then Gary's list will only contain the number 1. Then on John's next spin, we will have the same scenario as above. This yields a maximum of 2 additional spins.

If John spins a 4, then Gary's list will contain the numbers 1 and 2. As we have already found above, spinning a 2 yields more additional spins than a 1, so the maximum additional spins in this case is 3 spins.

If John spins a 5, then Gary's list will only contain the number 1. As above, this will yield a maximum of 2 additional spins.

Finally, if John spins a 10, then Gary's list will contain the numbers 1, 2, and 5. Of these numbers, 2 and 5 have the highest maximum number of additional spins, so this case has a maximum of 3 additional spins.

Thus, of all of the possibilities, spinning a 4 or 10 next could result in 3 additional spins, so the maximum total number of spins is [tex]$\boxed{4}$[/tex]. These would be achieved by spinning 20, 10, 2, 1 or 20, 10, 5, 1 or 20, 4, 2, 1.

Carmen drew this figure to represent the dividend of a division expression.

A number line going from negative 4 to positive 12. An arrow goes from 0 to 9.

What number is represented by the arrow?
–9
0
1
9

Answers

Answer

D:9

Step-by-step explanation:

i took the test and got it right

Answer:

D- 9

Step-by-step explanation:

good luck :)

Each piece of paper is 910 inch long. Each ballot needs to be 310 inch long. How many ballots can be cut from one piece of paper?

Answers

Answer:

about 3 pages can be cut.

Step-by-step explanation:

910/310=2.9

Answer:

3

Step-by-step explanation:

Use this if your teacher asks you how.

By dividing 910/310 you get 2.9. notice that on the calculator it shows 2.9 then infinity but dont mind that. as said to get 3 you round 2.9 to the nearest whole number. which is 3 :)

Pls Help!!! Worth 99 Pts!!
Explain how to sketch a graph of the function f(x) = x3 + 2x2 – 8x. Be sure to include end-behavior, zeroes, and intervals where the function is positive and negative.​

Answers

Answer:

First, for end behavior, the highest power of x is x^3 and it is positive. So towards infinity, the graph will be positive, and towards negative infinity the graph will be negative (because this is a cubic graph)

To find the zeros, you set the equation equal to 0 and solve for x

x^3+2x^2-8x=0

x(x^2+2x-8)=0

x(x+4)(x-2)=0

x=0   x=-4   x=2

So the zeros are at 0, -4, and 2. Therefore, you can plot the points (0,0), (-4,0) and (2,0)

And we can plug values into the original that are between each of the zeros to see which intervals are positive or negative.

Plugging in a -5 gets us -35

-1 gets us 9

1 gets us -5

3 gets us 21

So now you know end behavior, zeroes, and signs of intervals

Hope this helps

Answer:

The degree of the function is odd and the leading coefficient is positive – so the function goes to negative infinity as x goes to negative infinity and to positive infinity as x goes to positive infinity. The zeroes are –4, 0, and 2, all with multiplicity 1. The function is negative from negative infinity to –4 and from 0 to 2. The function is positive from –4 to 0 and from 2 to infinity.

Step-by-step explanation:

sample response on edge 2022

PLEASE HELP
ONLY ANSWER IF YOU KNOW
I WILL REPORT IF IT HAS NOTHING TO DO WITH THE TOPIC ​

Answers

Answer:

One would be -3 and the other would be 0.

Step-by-step explanation:

first would be 0 because it's already an answer

second, we take -3 from the left side and subtract it from 0 from the other side which is -3

Answer:

x=3

Step-by-step explanation:

x−3=0

2) Add 3 to both sides.

x=3

please someone answer no trolls please this is very serious will give brainliest

Answers

Answer:

Required equation of line in point-slope form is:

[tex]y-5 = -\frac{3}{5}(x+5)[/tex]

Step-by-step explanation:

Given equation of line is:

[tex]y = \frac{5}{3}x+2[/tex]

The slope-intercept form of line is:

[tex]y = mx+b[/tex]

Comparing both we get

m = 5/3

We have to find the equation of a line that is perpendicular to given line and passes though (-5,5)

The product of slopes of two perpendicular lines is -1

Let m1 be the slope of line perpendicular to given line then

[tex]m.m_1 = -1\\\frac{5}{3} . m_1 = -1\\m_1 =-\frac{3}{5}[/tex]

Point-slope form is given by:

[tex]y-y_1 =m_1(x-x_1)\\[/tex]

Putting m = -3/5 and (x1,y1) = (-5,5)

[tex]y-5 =-\frac{3}{5}(x-(-5))\\y-5 = -\frac{3}{5}(x+5)[/tex]

Hence,

Required equation of line in point-slope form is:

[tex]y-5 = -\frac{3}{5}(x+5)[/tex]

Which equation represents the perpendicular
bisector of AB whose endpoints are A(8,2) and
B(0,6)?

Answers

Answer:

y = ½x + 2

Step-by-step explanation:

We are given the coordinates of the endpoint as;A(8,2) and

B(0,6)

The midpoint coordinates will be;

((8 + 0)/2, (2 + 6)/2) = (4, 4)

The slope of the midpoint using gradient formula will be;

m = (6 - 2)/(0 - 8)

m = 4/-8

m = -2

Thus, slope of a line perpendicular to the midpoint is;

m_p = -1/m

m_p = -1/-2

m_p = 1/2

Thus, using slope intercept concept, the equation to represent the perpendicular bisector is;

y - 4 = ½(x - 4)

Multiply both sides by 2 to get;

2y - 8 = x - 4

Add 8 to both sides to get;

2y - 8 + 8 = x - 4 + 8

2y = x + 4

Divide through by 2 to get;

y = ½(x + 4)

y = ½x + 2

19-5/2x = 34 Solve for X

Answers

Answer: -6

Step-by-step explanation:

The solution is: solve of the equation 19-5/2x = 34 is: x = -6.

Here, we have,

given that,

the equation is: 19-5/2x = 34

now, we have to solve this.

so, we have,

19-5/2x = 34

isolating the like terms, we get,

5/2 x = 19- 34

or,  5/2 x = - 15

dividing both side by 5 we get,,

x/2 = -3

cross-multiplying, we get,

x = -6

Hence, The solution is: solve of the equation 19-5/2x = 34 is: x = -6.

To learn more on equation click:

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NEED ASAP . Plz help

Answers

It’s 4 and what they said

A new car is purchased for 24600 dollars. The value of the car depreciates at 5.5% per year. To the nearest year, how long will it be until the value of the car is 11300 dollars?

Answers

Answer:

The number of years until the value of the car is 11300 dollars is 9 years.

Step-by-step explanation:

This can be calculated using the following formula:

Value of the Car = Purchase cost - (Annual depreciation expenses * N) ........ (1)

Where;

N = Number of years until the value of the car is 11300 dollars

Purchase cost = $24,600

Annual depreciation rate = 5.5%

Annual depreciation expenses = $24,600 * 5.5% = $1,353

Value of the car = $11,300

Substituting the value into equation (1) and solve for N, we have:

$11,300 = $24,000 - ($1,353 * N)

$1,353 * N = $24,000 - $11,300

$1,353 * N = $12,700

N = $12,700 / $1,353

N = 9.38654841093865

Rounding to the nearest year as required by the question, we have:

N = 9

Therefore, the number of years until the value of the car is 11300 dollars is 9 years.

Answer:

14

Step-by-step explanation:

What is the value of y? Enter your answer in the box​

Answers

Y=20 because angles b and c are both 25, so that equals 50. 180-50=130. Then you just make 3y+70 = 130 and solve for y.

parts of complex numbers

z = 4- 2i

Answers

Step-by-step explanation:

This is the trigonometric form of a complex number where

|

z

|

is the modulus and

θ

is the angle created on the complex plane.

z

=

a

+

b

i

=

|

z

|

(

cos

(

θ

)

+

i

sin

(

θ

)

)

The modulus of a complex number is the distance from the origin on the complex plane.

|

z

|

=

a

2

+

b

2

where

z

=

a

+

b

i

Substitute the actual values of

a

=

4

and

b

=

2

.

|

z

|

=

(

2

)

2

+

4

2

Find

|

z

|

.

|

z

|

=

2

5

The angle of the point on the complex plane is the inverse tangent of the complex portion over the real portion.

θ

=

arctan

(

2

4

)

Since inverse tangent of

2

4

produces an angle in the fourth quadrant, the value of the angle is

0.4636476

.

θ

=

0.4636476

Substitute the values of

θ

=

0.4636476

and

|

z

|

=

2

5

.

2

5

(

cos

(

0.4636476

)

+

i

sin

(

0.4636476

)

)

Replace the right side of the equation with the trigonometric form.

z

=

2

5

(

cos

(

0.4636476

)

+

i

sin

(

0.4636476

)

)

A kangaroo can jump at a speed of 40 miles per hour. Which representation shows the distance a kangaroo can jump at this rate?

Answers

Answer:

y=40x

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Parker owns a food truck that sells tacos and burritos. He sells each taco for $3.25 and each burrito for $7. Yesterday Parker made a total of $552 in revenue from all burrito and taco sales and there were twice as many burritos sold as there were tacos sold. Write a system of equations that could be used to determine the number of tacos sold and the number of burritos sold. Define the variables that you use to write the system.

Answers

Answer:

let t= the number of tacos sold

let b= the number of burritos sold

3.25t+7b=552

b=2t

Step-by-step explanation:

Since there were twice as many burrito sold as tacos sold, there were more burritos sold, so if we multiply by 2 the number of tacos sold, we will get the number of burritos sold, meaning b=2t.

The system of equation should be considered as the  3.25t+7b=552 and the value of b should be equivalent to 2t.

Calculation of the equation:

here we assume that

t= the number of tacos sold

And, b= the number of burritos sold

As per the situation, the equation be like

3.25t+7b=552

b=2t

So,

put b value in the first equation

3.25t + 14t = 552

t = 3.01

And, b = 1.51

Learn more about an equation here: https://brainly.com/question/24603753

Which triangles must be congruent?

Answers

Answer:

It stands for "side-side-side". If two triangle both have all of their sides equal (that is, if one triangle has side lengths a, b, c, then so does the other triangle), then they must be congruent.

Three years ago , Ahmed was one third of his sister's age. In a years time ,Ahmed's age doubled will match his sisters age. How old is Ahmed now.


Help the due is tomorrow

Answers

let the age of ahmed three years ago be x years old. since 3 years ago ahmed as one third of his sister's age, his sister would be 3x years old 3 years ago.

in a year's time, ahmed would be x+4 years old and his sister would be 3x+4. we also know that in a year's time ahmed's age doubled will match his sister's age. hence 2(x+4)=3x+4
2x+8=3x+4
4=x
x is the age of ahmed three years ago. hence, now ahmed is 7 years old.

PLEASE HELP MEE!!! Which ordered pair is a solution to the linear system? –4x – 5y = 12 and 6x + 5y = 2



A)


(7,7)


B)


(7,–8)


C)


(–8,–6)


D)


(–8,–7)

Answers

Answer:

The answer is negative 8 and negative 7

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