(b) The sum of the first 13 terms of an arithmetic progression is 312 and the sum of the next 13 terms is 819. Find the first term and common difference of this arithmetic progression. Hence, find the S40​

Answers

Answer 1

Answer:

Step-by-step explanation:

[tex]\displaystyle u_1+u_2+u_3+...+u_{13}=\sum_{i=1}^{13}u_i=\dfrac{(u_1+u_{13})*13}{2} \\=\dfrac{(u_1+u_1+12*d)*13}{2} \\=(u_1+6d)*13=312\\\\u_1+6d=24\ (1) \\\\----------------------------\\\displaystyle u_{14}+u_{15}+u_{16}+...+u_{26}=\sum_{i=14}^{26}u_i=\dfrac{(u_{14}+u_{26})*13}{2} \\=\dfrac{(u_1+13*d+u_1+25*d)*13}{2} \\=(u_1+19d)*13=819\\\\u_1+19d=63\ (2)\\\\(2)-(1) ==> 13d=39 ==> d=3\\\\u_1=24-6*3=6\\\\S_{40}=2580[/tex]


Related Questions


The temperature is dropping 3 degrees every 4 hours.
It started at 62 degrees. What will the temperature be
in 16 hours? Please and Thank you !!

Answers

Answer: It will be 50º :)

Step-by-step explanation: 4 hours * 4 = 16, 3*4 = 12, 62- 12 = 50

Answer:

50 degrees

Step-by-step explanation:

16/4 = 4

4 * - 3 = - 12

62 - 12 = 50 degrees

-3n-4n-17=25
i'm stuck

Answers

[tex] \large \mathfrak{Solution : }[/tex]

let's solve for n :

-3n - 4n - 16 = 25

-7n = 25 + 16

n = = 42 ÷ -7

n = - 6

Pleas help me and show me the answer
thx;)

Answers

Answer:

Hello, I am not sure if this is correct or not but I gave it a try.

So,

-125+-86+54+-35 = -192

-192 ÷ 4 = (-48)

4 because there are 4 weeks.

Find the Least Common Multiple (LCM) of 50 and 90​

Answers

Answer:

450

(I can't post the answer if it's less than 20 letters so just ignore this I'm trying to fill up)

What is the LCM of
12 and 40

Answers

Answer:

120

Step-by-step explanation:

12 and 40

Multiples of 12 = 12,24,36,48,60,72784,96,108,120..

Multiples of 40 = 40,80,120..

Common in both = 120

Answer:

120

Explanation:

The least common multiple (LCM) of two or more whole numbers is the smallest whole number that is divisible by each of those numbers. Basically, the LCM is the smallest number that all the numbers divide into evenly. So for 12 and 40, we get 120 since 120 ÷ 12 = 10, 120 ÷ 40 = 30

Hero and his coworkers had lunch at a restaurant near their work and 18% tip on the bill was $10.08 how much was the bill not including the tip!

Answers

Answer:

$8.27

Hope this is right <3

Find A in degrees C= 120° b= 5 c= 11

Answers

Answer:

36.8

Step-by-step explanation:

I think A=36.8

Hope it will help you (:

inductive reason what is next number in sequence 400, 200, 300, 150, 250​

Answers

Answer:

125

Step-by-step explanation:

400÷2 = 200

300÷2 = 150

so,

250÷2 = 125

Answer the question please

Answers

Answer:Perimeter: 99.4 feetArea: 609.4 feet^2Step-by-step explanation:Perimeter:

To find the perimeter of a rectangle, you add up 2 times the length and 2 times the width. Here's the expression: [tex]2l+2w[/tex]. In this case l=22 or l=27.7 and w=27.7 or w=22. In the end, you get: [tex]2l+2w=99.4[/tex]. [tex]22*2=44. \\27.7*2=55.4[/tex].

Area:

To find the area of a rectangle, you multiply the length by the width. Here's the expression: [tex]lw[/tex].  In this case l=22 or l=27.7 and w=27.7 or w=22. In the end, you get: [tex]22*27.7=609.4[/tex].

Side note:

It doesn't matter what l or w equal because There's a property in addition that says it doesn't matter which order the values go in. There's also a property in multiplication that it doesn't matter which order the values go in (same as addition).

Write an equation in slope-intercept form for the line with slope 15 and y-intercept −3. Then graph the line.

Answers

Answer:

Step-by-step explanation:

y  = mx + b

y = 15x + (-3)

y = 15x - 3

18931 divided by 83 =

Answers

228.0843373493976
This is the answer
The answer: 18931/83=228.084337

Hello can you help me with this question please no scam :/
h(x)=2x−4 and g(x) = x3−3 Find (h+g)(4).

Answers

[tex]\large \mathfrak{Solution : }[/tex]

h(x) = 2x - 4

g(x) = x³ - 3

(h+g)(x) = 2x - 4 + x³ - 3 = x³ + 2x - 7

(h+g)(4) :

(4)³ + (2 × 4) - 7

64 + 8 - 7

65

Kerry owes her dad $25 and she owes her mom $4. How much does she owe them all together? Write the equation and the answer.


PLEASE HELP

Answers

29 thats how much she owes them all together so yeah I hope it helped

69. Evaluate ( a + 1) 2 - 5 when a = -3

Answers

Answer:

- 9

Step-by-step explanation:

( a + 1) 2 - 5

(Putting value of a = -3)

=> (-3 + 1) 2 - 5

=> -2 × 2 - 5

=> -4 - 5

=> - 9 (Ans)

A softball team has a budget of $200 for visors they athletic Director pays $90 for 12 visors is there any money in the budget to purchase 15 more sunvisors

Answers

Answer:

No. There is not enough money in the budget to buy 15 more sunvisors. The softball team's budget is short by $2.50.

Step-by-step explanation:

If the director pays $90 for 12 visors, then we need to calculate the price of each visor to find out if the director can buy 15 more.

[tex]90/12= 7.50[/tex]

90 divided by 12 = $7.50 per sunvisor.

The budget is $200, so now we need to multiply 15 by 7.50.

[tex]15*7.50=112.50[/tex]

Then you add the product of that to the $90 spent previously.

[tex]90+112.50=202.50[/tex]

And the answer is No. There is not enough money in the budget to buy 15 more sunvisors. The softball team's budget is short by $2.50.

Find the degree measure of each angle.

Answers

Step-by-step explanation:

The angle between EF = 90 - 39 = 51°

Th angle between ED = 90 - 73 = 17°

[297÷3 + { 4 × 3 ( 20 – 36 ÷ 5 – 2)}]​

Answers

Here is the answer to your problem:

https://brainly.in/question/10886862

how to calculate area of coloured part

plsss help

Answers

Answer:

Step-by-step explanation:

The need is to find the area of the elongated plus sign inside the rectangle. The area of the rectangle itself is not needed. That elongated plus sign is where we will run into trouble. The center of that plus sign is included in both the vertical strip and the horizontal strip. So when we go to find the area of the plus sign, we include the center in one or the other, NOT BOTH. I included the area in the vertical strip so I eliminated it in the horizontal strip, creating 2 shorter strips on either side of the center.

The area for the vertical strip, including the center:

A = 3 * 26 (3 is the width and 26 is the length)

A = 78 square meters

Now for the horizontal strip...

The horizontal strip minus the center is

14 - 3 = 11; divide that 11 in half and we get the length of each short horizontal strip on either side of the center to be 5.5 meters long. Therefore, each short strip measures 5.5 (we have 2 of them).

A = 3(5.5) + 3(5.5) and

A = 16.5 + 16.5

A = 33

The sum of the long vertical and the 2 shorter horizontal areas is

78 + 33 = 111

Therefore, the total area of the colored portion is 111 square meters.

0.3546875 Rounded to the nearest tenth

Answers

Answer:

0.4

Step-by-step explanation:

0.35 is hundredth, and since you always round 5 up, it makes 0.4

Answer:

0.4

Step-by-step explanation:

To figure out the answer, first we need to know how to round. Find the tenths place. That's the first 3 you come upon. Look at the number beside it. It is a five which means you would round up (this is because of the 5 or more raise the floor, four or less let it rest rule) The 3 would then turn into a 4.

Peter Piper bought 5 pickled pepper plants. Each plant cost $110. He also needed a
planter in which to plant his pickled pepper plants. The cost of the planter was $3.25.
Fortunately, there was no sales tax on his purchase since he worked for a non-profit
organization. If he gave the cashier $10, how much change did he receive?

Answers

Answer:

6.75

Step-by-step explanation:

10.00-3.25= 5.75

the first pieces of information are irrelevant

Without using a calculator, determine where the following numbers go on the number line.
Be sure to label your number line.
V5,
ထlယ
1.3, 4%, i, 1.70, V8, 1.07, 32, -38, T
0


Please answer the bottom question also

Answers

Answer:

Without using a calculator, determine where the following numbers go on the number line.

Be sure to label your number line.

V5,

ထlယ

1.3, 4%, i, 1.70, V8, 1.07, 32, -38, T

0

Please answer the bottom question also

Find the distance between the pair of points A(7,8) B(-8,4)

Answers

Answer:

Formula:

[tex]length = \sqrt{ {(x _{1} -x_{2} )}^{2} + {(y_{1} -y_{2}) }^{2} } [/tex]

substitute:

[tex]l = \sqrt{ { \{7 - ( - 8) \}}^{2} + {(8 - 4)}^{2} } \\ \\ l = \sqrt{225 + 16} \\ l = \sqrt{241} \\ { \boxed{ \boxed{length = 15.5 \: units}}}[/tex]

99 students are in a class, 46 play hockey and 42 play football, 17 play both football and hockey. Find the number of students who do not play neither of the two games

Answers

Step-by-step explanation:

let H and F be the sets of students who like hockey and football respectively.

here,

total number of students n(U)=99n(H)=46n(F)=42n(H n F)=17

then,

n(H U F)=n(H) + n(F) - n(H n F)

=46+42-17

=88-17

=71

now,

n(H U F)' = n(U) - n(H U F)

=99-71

=28..

Therefore, the number of students who don't play both games are 28.

I hope this will be helpful for you....

1. What is equivalent to the value of the complex number:
i² + 2

Answers

i^2 = -1
i^2 + 2 = -1 + 2 = 1

931278 rounded to the nearest hundredth thousands

Answers

Answer:

900000

Step-by-step explanation:

the closest hundred thousands are 900000, or 1000000.

officially 900000 is closer.

8736 divided by 32 with work showed

Answers

Answer:

273

Step-by-step explanation:

8736/32 math problems division = 273. Therefore 273 to 2 decimal places= 273

8736/32 divided by 2 » (8736/32) ÷ 2 » 273 ÷ 2 = 136.5

Determine which of the given points are on the graph of the equation.
Equation: x² + y2 = 2
Points: (1, -1), (-1,0), (1,1)
Which of these points are on the graph of the equation? Select all that apply.
A. (1, -1)
B. (1,1)
C. (-1,0)
D. None of the points are on the graph.

Answers

Answer:

D. none

Step-by-step explanation:

to figure out if the point is on the graph, take the x value and plug it in to the x coordinate, do the same for y. if the values truly add up to 2, then it is on the graph. Since none of the values add up to 2, they are not on the graph.

A footbal team won.8 games and lost 2 and tie 1 what percent of games they won

Answers

first i would add 8+2+1= 11 so 11 games total. then i think you would divide 8 by 11 which would be 0.7272. you would round up to 73% and i think that would be the percent of games won.

what should be added to 1 to get 3

Answers

Answer:

2 should be added to 1 to get 3.

Step-by-step explanation:

Answer:

1+2=3

Step-by-step explanation:

use a calculator or just search it up

14 divided by 3.92!!!!

Answers

the answer is 3.571428571428571