The sum of the first six terms of an A.P is 72 and second term is seven times the fifth term. find the first term and common difference.​

Answers

Answer 1

Hello,

if A.P means arithmetic progression then

let's say a the first term and r the common difference.

[tex]\left\{\begin{array}{ccc}(a)+(a+r)+(a+2r)+...+(a+5r)&=&72\\a+r&=&7*(a+4r)\end{array}\right.\\\\\\\left\{\begin{array}{ccc}6a+15r&=&72\\6a+27r&=&0\end{array}\right.\\\\\\\left\{\begin{array}{ccc}a&=&\dfrac{-9}{2}*r\\-9r+5r&=&24\end{array}\right.\\\\\\\left\{\begin{array}{ccc}r&=&-6\\a&=&27\end{array}\right.\\\\[/tex]


Related Questions

A baby can crawl ¾ foot in ¼ minute. How far does the baby get per minute?

Answers

Answer:

3 feet per minute

Step-by-step explanation:

Find how far the baby gets per minute by multiplying 3/4 by 4:

3/4(4)

= 3

So, the baby crawls 3 feet per minute

The expression 2r^2+18x +40 has a greatest common factor of 2.
Once the GCF is factored out, what are the two binomial factors
left that complete the equation.
what are the 2 missing binomial factors?

Answers

2(x^2+9x+20)

2(x^2+5x+4x+20)

2{x(x+5)+4(x+5)}

2(x+5)(x+4)

What would be the 1st step in solving this problem:
(4-2+6) +9x7

Answers

Answer:

doing whatever is in the brackets or paranthesis

My brain has stopped working, can you answer this?

Answers

Answer:

$40.00, $30.00, B

Step-by-step explanation:

We can first write an expression for the cost of each plan.

Given x amount of texts and y amount of minutes, plan A costs 15 cents per text sent (so given x amount of texts, plan A costs 15 * x for texts) and 10 cents per minute (so given y amount of minutes, plan A costs 10 * y for minutes). Adding these up, plan A costs 15 * x + 10 * y. Plugging Jaden's 200 texts in for x and 100 minutes in for y, we have

15 * x + 10 * y = 15 * 200 + 10 * 100 = 4000 cents. 100 cents = 1 dollar, and the conversion rate for cents to dollars is divide by 100, so we divide 4000 cents by 100 to get $40.00 as the cost for plan A

For plan B, the flat rate is 15 dollars. To convert from dollars to cents, we multiply by 100, so 15 * 100 = 1500 cents for the flat fee.

Texts cost 5 cents per text, so 5 * x is the cost for texts in cents for plan B. Similarly, 5 * y is the cost for minutes in cents for plan B. Adding these up, we get

1500 + 5 * x + 5 * y

combine like terms

1500 + 5 * (x+y)

plug 200 in for x and 100 in for y

1500 + 5 * (200+100)

1500 + 5 * (300)

1500 + 1500

3000

divide by 100 to convert to dollars

$30.00 is the cost for plan B

$30 < $40, so plan B will be cheaper for Jaden

Given that v=√u*u- 2qs. Make q the subject of the equation. Find the value of q in the equation if v=8, u=12, and s=40​

Answers

Answer:

Step-by-step explanation:

v=√u*u- 2qs

[tex]\sqrt{20}[/tex] x 20 - 2q40 = 8[tex]2\sqrt{5}[/tex] x 20 - 2q40 = 840[tex]\sqrt{5}[/tex] - 2q40 = 8- 2q40 = 8 - 40[tex]\sqrt{5}[/tex]-80q = 8 - 40[tex]\sqrt{5}[/tex] q = (8-40[tex]\sqrt{5}[/tex] ) / -80 = [tex]\frac{-1 + 5\sqrt{5} }{10}[/tex] = 1.018

Above given answer is correct.

I don't need a language ABC​

Answers

Answer:

yes

Step-by-step explanation:

Answer:

?

Step-by-step explanation:

Find the volume of the prism. 3m 5m 36m

Answers

Answer:

540m^3

Step-by-step explanation:

There are many kinds of prisms, if you were asking for a rectangular prism, then we do 3 * 5 * 36 = 540m^3.

Answer:

the answer is 540

Step-by-step explanation:

because 3x5x36=540

Plz tell me how to do question 18

Answers

Answer:

750kmph

Step-by-step explanation:

Average is sum of all parts divided by the number of parts.

Let Stot be average speed for total trip (800kmph).

Let S1 be speed for first quarter of trip (950kmph).

Let S2, S3, and S4 be the speeds of each of the remaining quarters respectively.

Let Sans be the average speed for the remaining three quarters of the trip (a.k.a. The Answer!).

Stot = (S1 + S2 + S3 + S4) / 4

800kmph = (950kmph + S2 + S3 + S4) / 4

3200kmph = 950kmph + S2 + S3 + S4

3200kmph - 950kmph = 2250kmph = S2 + S3 + S4

Divide both sides by 3.

2250kmph / 3 = (S2 + S3 + S4) / 3 = Sans

Sans = 750kmph

1. Mrs. Jones picks 3 flowers a day starting on Monday. How many does she have by Sunday?
2. 603 cats have 4 kittens each. How many kittens are there in total?

Answers

Answer:

1. 18

2. 2412

Step-by-step explanation:

1. Monday 3

Tuesday 6

Wensday 9

Thursday 12

Friday 15

Sunday 18

_____________________________________________________

2.

603*4=2412

What are the solutions to this quadratic equation? -2x2+x+4=0

Answers

Answer:

=1±33√4

Step-by-step explanation:

Answer:

[tex]x =\frac{1+/-\sqrt{33} }{4}[/tex]

Step-by-step explanation:

It wouldn't let me put the symbol in the equation but +/- is just the same thing as ±

This answer is correct on edmentum/plato

State if the triangles are similar. If so, how do you know they are similar and complete the similarity statement.

ΔSTU ~ ____

Answers

Answer:

D. similar; AA similarity; ∆CSD

HELP ASAP! correct answer gets brainly and 50 points!!!

Solve the equation for π.
A=12πr2

Answers

Answer:

π is equal to 3.14

A=πr^2 is the equation to get the area of a circle where r is the radius.

Answer:

π=A/12r2

Step-by-step explanation:

A=12πr2

divide both sides by 12r2

A/12r2=12r2/12r2

π=A/12r2

PLS HELP! Given the angles in the diagram below, what is m<2

Answers

Your question answer is d 98 is right.

I need help asap!!
Solve for d and show your work:
16d- (4 -5d) =-67

Answers

Step-by-step explanation:

16d-4+5d= -67

21d-4= -67

21d= -67+4

d= -63/21

d = -3

hope it helps

Answer: d = -3

Step-by-step explanation:

⇒16d -(4-5d) = -67

⇒16d -4 +5d = -67

⇒21d = -67+4

⇒21d = -63

⇒d = -63/21

⇒d = -3

Therefore d = -3

please click thanks and mark brainliest if you like :)

pi = c/d solve for d?

Answers

Answer:

[tex]d=\displaystyle\frac{C}{\pi}[/tex]

Step-by-step explanation:

Hi there!

[tex]\pi =\displaystyle\frac{C}{d}[/tex]

Multiply each side by d:

[tex]d\pi =\displaystyle\frac{C}{d}*d\\\\d\pi=C[/tex]

Divide both sides by π:

[tex]d=\displaystyle\frac{C}{\pi}[/tex]

I hope this helps!

jack wants to run at least 275 miles before the baseball season begins. he has already run 25 miles. he plans to run 2.5 miles each day. at this rate what is the fewest number of days he will need to reach his goal

Answers

Hey there! I'm happy to help!

We see that Jack has already run 25 miles.

25

He also wants to run 2.5 miles every day. This means we will multiply 2.5 miles by the number of days he runs. We will call the number of days x.

25+2.5x

And he needs this to equal 275.

25+2.5=275

We subtract 25 from both sides.

2.5x=250

We divide both sides by 2.5

x=100

So, Jack will need to run 100 days to meet his goal.

Have a wonderful day and keep on learning! :D

A new scooter is valued at $15 000.
At the end of each year its value is reduced
by 15% of its value at the start of the year.
What will it be worth after 3 years?

Answers

here

p= 15000

r=15%

t= 3 yrs

now

depreciation = p(1-r/100)^t

= 15000(1-15/100)^3

=9211.875

=9212 or 9211.88

i really need your help

Answers

I would help you but I don’t know this stuff

Need help ASAP please

Answers

Answer:

10  

Step-by-step explanation:

1. AB

2 BC

3. CD

4. DE  

5. AC  

6. B D

7.CE

8.AD

9.BE

10. A E

if f(x)= 3x + 10x and g(x)=5x - 3 find (f+g)(x)

Answers

Answer:

18x-3

Step-by-step explanation:

f(x)= 3x + 10x

g(x)=5x - 3

f(x)+g(x) = 3x + 10x + 5x - 3

Combine like terms

             = 18x -3

Answer:

3^x+15x-3

Step-by-step explanation:

this is the right answer i just did it

\

Which of the following is an integer?
95.2
73
54
41
-26

Answers

Answer:

95.2 is not an integer

and other are integers

pls help asap !!!!!!!

Answers

Answer:

I think that the answer is 1 to1

LOL….HEY

(Btw I’m not new to brainly, but I just forgot my old password) *sigh* ughh I start school August second and it’s gonna be my first year in high-school ….I- first of all summer break was wayyyyyyyyy too short basically 2 months and a half while the rest of the year I have to bust my behind preparing for test that don’t have anything to do with MY future plans….eeeee every time I think about it my anxiety levels raise higher and higher …..if any upper class men have some advice plz tell me…cuz I am legit terrified ngl (I checked out some freshmen tips on yxutube but that didn’t really help that much) *and btw this is kind of academically related so need to report me*

Answers

Answer:not a man but I think you should just relax and be yourself, high school isn’t scary at all. When you go in for orientation walk around the school and find your classes so you have a good map of where you need to go in your head already! Best of luck

Step-by-step explanation:

3 angles
triangle
in
ratio 1:3:3
3:.
Find the angles

Answers

Answer:

1st angle = 30

2nd angle = 60

3rd angle = 90

Step-by-step explanation:

let ,1st angle be x , 2nd angle be 2x and 3rd angle be 3xx+2x +3x =1806X =180x =180/6x =30

Please help!!!!!!
Find the radical equivalent 8-2/3 and compute It.

Answers

Answer:

2.71

Step-by-step explanation:

Given 8 - 2/3 = 8(3/3) - 2/3 = 24/3 - 2/3 = 22/3 = 7.333 then the radical is

7.333**(1/2) = 2.71


someone help please

Answers

Answer:

x=4

Step-by-step explanation:

3/4x +4 = 7

3/4x +4-4 = 7-4

3/4x = 3

Multiply each side by 4/3

4/3 * 3/4x = 3 *4/3

x = 4

Answer:

x = 4

Step-by-step explanation:

3/4x + 4 = 7

3/4x = 3

To remove the denominator, we multiply by 4 on both sides

3x = 12

x = 4

Given the function h(x) = x^2 + 10x + 32, determine the average rate of change
of the function over the interval 3 < x < 11.

Answers

Answer:  24

================================================

Explanation:

Plug in x = 3 to get

h(x) = x^2 + 10x + 32

h(3) = 3^2 + 10*3 + 32

h(3) = 71

Repeat for x = 11

h(x) = x^2 + 10x + 32

h(11) = 11^2 + 10*11 + 32

h(11) = 263

Now use the average rate of change formula

m = average rate of change

m = ( h(b) - h(a) )/(b - a)

m = ( h(11) - h(3) )/(11 - 3)

m = (263 - 71)/(11 - 3)

m = 192/8

m = 24

Consider the first month's sales data for the Midwest region.
Select the correct answer from each drop-down menu.

1. 85
2. 15
3. 37
4. 18

1. Significantly different from
2. Relatively close to

1. inconsistent
2. consistent

Answers

Answer:

The correct options are:

1. Significantly different from

1. Inconsistent

Explanation:

Sales Data for Midwest:

Midwest region total stores Sales equal to 63.1%. The percentage for current store is less than total stores therefore data in the given table is not consistent. The data given is relatively for the first month sales and is significantly different from the other stores.

Answer:

In the picture

Step-by-step explanation:

From Plato / Edm

what is x 4 +7x 2 +10

Answers

Answer:

[tex]\quad \left(x^2+2\right)\left(x^2+5\right)[/tex]

Step-by-step explanation:

[tex]x^4+7x^2+10:\quad \left(x^2+2\right)\left(x^2+5\right)[/tex]

The last four years of stock returns are as follows: Year 1 is -4% Year 2 is +28% Year 3 is +12% Year 4 is + 4% (a). What is the average annual return?

Answers

Answer:

The Average annual return is:

= 10%.

Step-by-step explanation:

a) Data and Calculations:

Year        Stock Returns

Year 1                 -4%

Year 2             +28%

Year 3              +12%

Year 4              + 4%

Total returns = 40%

Average annual returns = 10% (40%/4)

b) The average annual return is computed as the total returns for the four years divided by 4.  It shows that on the average, the return earned per year from the stock investment is 10%, during the four-year period.  It is the mean of the total returns.

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