1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
My name is Ann [436]
3 years ago
13

The third term of an arithmetic sequence is-8, and the sum of the first 10 terms of the sequence is -230. Find:

Mathematics
1 answer:
mixas84 [53]3 years ago
4 0

Answer:

The first term of the sequence is a = 4

The sum of the first 13 terms is -480

Step-by-step explanation:

Given that:

The third term is: a + 2d = - 8 --- (1)

The \  sum  \ of  \ the \  first \ 10  \ terms  \ is:

-230 = \dfrac{10}{2}[2a+ (10-1)d]

-230 =5[2a+ (9)d]

-230 = 10a + 45d

10a + 45d = -230     ----(2)

From (1) and (2)

a + 2d = - 8

10a + 45d = -230

From (1), let a = -8 - 2d

Replace, the value of a in (1) to equation (2)

10(-8 -2d) + 45d = -230

-80 -20d +45d =-230

25d = -230 + 80

25d = -150

d = -150/25

d = -6

From equation (1);

a + 2(-6) = -8

a -12 = -8

a = -8 + 12

a = 4

Thus,the first term of the sequence a = 4

The \  sum  \ of  \ the \  first \ 13  \ terms  \ is:

S_n = \dfrac{n}{2}[2a+(n-1)d]

S_n = \dfrac{13}{2}[2(4)+(13-1)*-6]

S_n =7.5 [8+(12)\times -6]

S_n =7.5 [8-72]

= -480

You might be interested in
I have 6 apples in a bag. what is the probability i will draw a worm out of the bag. 
Anit [1.1K]
Your going to have to elaborate on this question
7 0
3 years ago
Help pls
ki77a [65]

Answer:

Distance between the school and the theater = 2\sqrt{13} units

Step-by-step explanation:

Use distance formula to calculate the distance from the school (8, 7) and the theater (2, 3):

d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

Let,

school (8, 7) = (x_1, y_1)

theater (2, 3) = (x_2, y_2)

Plug in the values into the distance formula

d = \sqrt{(2 - 8)^2 + (3 - 7)^2}

d = \sqrt{(-6)^2 + (-4)^2}

d = \sqrt{36 + 16} = \sqrt{52}

Simplify

d = \sqrt{4 \times 13}

d = 2\sqrt{13}

3 0
3 years ago
If the wwight of a package is multiplied by 7/10 the result is 65.8 find the weight of the package
ANTONII [103]

Answer:

The answer is 94

Step-by-step explanation:

divide 7/10 because thats the fraction = 0.7

divide 65.8 by 0.7

to get 94

to check

multiply 94 by 0.7


8 0
3 years ago
A full grain silo
Kazeer [188]

Answer:

m is the slope.

b is the y-intercept.

the slope is the same as he constant rate.

let y = the number of feet of grain left in the silo.

let x = the number of seconds.

you get y = -3.5 * x + b.

when x = s seconds, the equation becomes y = -3.5 * s + b.

b is the y-intercept which is the value of y when x = 0.

when x = 0, no seconds have elapsed and the silo is therefore at whatever height it was before you started to empty it.

that would be the value of b.

if we assume that the height of the grain in the silo was 150 feet, then the formula would become

Step-by-step explanation:

y = -3.5 * x + 150

after s seconds, the formula would become y = -3.5 * s + 150.

if s was equal to 20, then the formula would become y = -3.5 * 20 + 150 which would then become y = -70 + 150 which would then become y = 80.

after 20 seconds, there would be 80 feet of grain left in the silo.

the graph of the equation would look like this.

from the graph, you can see that the height of the grain in the silo is 150 feet when you start and gets down to 80 feet after 20 seconds and that the silo will be empty somewhere between 42 and 43 seconds.

7 0
3 years ago
I need help ASAP!!Please make sure u sure the answer is correct.
Alina [70]

Answer:

(x-8)^2+(y-16)^2 = 4

Step-by-step explanation:

The equation of a circle is given by

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

(x-8)^2+(y-16)^2 = 2^2

(x-8)^2+(y-16)^2 = 4

6 0
3 years ago
Other questions:
  • If f(x) = -2x^2 + 3 then f(-5) = ??
    15·1 answer
  • Write a 3 dighit 5,9,and 2 then write your number using
    15·1 answer
  • Which expression can be used to find 80% of 120?
    14·1 answer
  • How many different 4-digit numbers can be formed using the digits 2, 4, 5, 6, and 7 such that no digits repeat and the number is
    15·1 answer
  • A tree stands 22 feet tall and is 382 feet from a building. The tree casts a shadow that is 40 feet long. How tall is the buildi
    8·1 answer
  • 25 Points!!!!
    14·1 answer
  • If 2x+3+7x=-24, what is the value of x?
    10·2 answers
  • BRAINLIEST, THANK AND 5 STARS FOR RIGHT ANSWER!!!!
    12·1 answer
  • In one day, 72 people take group tennis lessons at Cherry Hills Country Club. The club provides 9 lessons each day. If an averag
    5·1 answer
  • Bill $42 , tax 9% , tip 18%
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!