the sum of the first ten terms of a linear sequence is -60 and the sum of the first fifteen terms is -165. Find the 18th term of the sequence​

Answers

Answer 1

Answer:

         a₁₈ = - 31

Step-by-step explanation:

[tex]S_{10}=\dfrac{2a_1+d(10-1)}{2}\cdot 10\\\\\dfrac{2a_1+9d}{2}\cdot 10=-60\\\\\dfrac{2a_1+9d}{2}=-6\\\\2a_1+9d=-12\\\\2a_1=-12-9d\\\\\\S_{15}=\dfrac{2a_1+d(15-1)}{2}\cdot 15\\\\\dfrac{2a_1+14d}{2}\cdot 15=-165\\\\\dfrac{2a_1+14d}{2}=-11\\\\2a_1+14d=-22\\\\-12-9d+14d=-22\\\\ 5d=-10 \\\\ d=-2\\\\\\2a_1=-12-9(-2)=-12+18=6\\\\a_1=3\\\\\\ a_{18}=a_1+17d=3+17(-2)=3-34=-31[/tex]


Related Questions

An airplane is 16,000 feet above the ground. It begins to descend at a rate of 140 feet per minute. Write an equation you could use to solve for x, the number of minutes it will take until the plane is 12,600 feet above the ground.​

Answers

Answer:

16000=140x

It will take 90 minutes to hit 12,600 ft above ground.

Step-by-step explanation:

Just swap out 16000 for 12600. Then solve from there.

Hope it helped!

Your goal is to fill a right circular cylinder shaped bucket with water. The bucket has a radius of 6 inches and a height of 12 inches. If you use a right circular cone with a 3 inch radius and a 4 inch height, how many scoops of water will it take to fill the bucket ?

Answers

Answer:

36

Step-by-step explanation:

to answer this question :

determine the volume of the cylinder and the cone. Divide the volume of the cylinder by the volume of the cone

Volume of a cylinder = nr^2h

n = 22/7

r = radius = 6

h = height = 12

(22/7) x (6^2) x (12)  = 1357.71 in^3

Volume of a cone 1/3(nr^2h)

n = 22/7

r = radius = 3

h = height =

4

(1/3) x (22/7) x (3^2) x (4) = 37.71

1357.71 / 37.71 = 36 times

Whats the common ratio of the geometric sequence 6, 36, 216,

Answers

Answer:

Common ratio is 6.

Step-by-step explanation:

The geometric sequence is being multiplied by 6 each time because 6x6=36, and 36x6=216.

Answer: Find the common ratio of the geometric sequence 6, 36, 216,...6,36,216,...

a_1=6                                       a_2=36                               a_3=216

a

1

=6a

2

=36a

3

=216

\text{Common Ratio:}

Common Ratio:

r=\frac{a_2}{a_1}

r=

a

1

a

2

r=\frac{36}{6}

r=

6

36

r=6

r=6

Use the drawing given. (Please answer first blank and let me know it the second blank is correct.)

Answers

Answer:

EF = 12

arc AG = 62°

Step-by-step explanation:

since ED = 13, EC = 13, so DF = 10/2 = 5

EF² + 13² - 5² = 169 - 25 = 144

EF = √144 = 12

∠AEG = 90° - 28° = 62°

arc AG = 62°

A dartboard has a diameter of 30 inches. What are its radius and circumference?

Answers

Answer:

radius = 15 in.

circumference = 94.2 in.

Step-by-step explanation:

radius = diameter/2 = 30 in./2 = 15 in.

circumference = (pi)d = 3.14 * 30 in. = 94.2 in.

1. You roll a number cube numbered from 1 to 6.
P( a number divisible by 3).

Answers

1/2

Step-by-step explanation:

there are two numbers 3 and 6 so 2/6 is 1/3

The ratio of boys to girls at school today 4:7. If there are 350
boys at school today, how many girls are there? Round
down.

Answers

Answer:

There should be about 612 girls

Step-by-step explanation:

350 divided by 4 = 87.5

87.5 x 7 = 612.5

round 612.5 down, which gets 612

The largest tree in the United States is growing in Sequoia National Park in California. The tree is a giant sequoia whose trunk is roughly circular and has a circumference of 998 inches. Find the diameter of the tree. Use 3.14 for pi and round your answer to the nearest tenths place.

Answers

Answer:

318 (rounded)

Step-by-step explanation:

d = diameter

c = circumference

d = c/3.14

hope this helps you

circumference formula - diameter x pi
diameter = 998/3.14
diamter = 318 inches

How do you get 4y-4x=16 into slope intercept form simplifying all fractions?

Answers

To begin, you can divide the equation by 4 to get y-x = 4. Next, the slope-intercept form of any equation is y=Mx+b, so your answer will be y=x+4

The perimeter of a rectangle is represented by the expression 6x + 4. If the width of the rectangle is represented by the expression x – 1, which expression represents the length? 4x + 6 4x – 6 2x + 3 2x + 6

Answers

Answer:

2x + 3

Step-by-step explanation:

two sides measure (x-1) which gives 2(x-1) or 2x - 2

subtract 2x - 2 from 6x + 4 to get 4x + 6

4x + 6 represents twice the length so divide it in half to get:

2x + 3

Answer:

The perimeter of a rectangle is represented by the expression 6x + 4. If the width of the rectangle is represented by the expression x – 1, which expression represents the length?

4x + 6 4x – 6 2x + 3 <<<CORRECT 2x + 6

Step-by-step explanation:

EDGE 2021

how many ways can 5 friends sit together at the movies in 5 seats?

Answers

Answer:

120

Step-by-step explanation:

The number of friends is 5 and there are 5 seats only. So , we can find it out with the help of permutations ,

[tex]\implies ^n P_r = \dfrac{n! }{(n-r)!} [/tex]

⇒ 5! / (5-5)!

⇒ 5! / 1!

⇒ 5!

⇒ 5 × 4 × 3 × 2 × 1

120

Hence there are 120 ways by which 5 friends sit together at the movies in 5 seats.

I NEED HELP QUICKLY

No Links or Files you will be reported

Based on the graph, what is the solution set to the equation −30+9x=−0.5x|x−1|−2?
The solution set to the equation is {____}.

Answers

Answer:

{ 3 }

Step-by-step explanation:

-30+9x=-0.5 |x-1| -2

from the graph, we can see that both curves intersect at (3,-3)⇒x=3

put x=3 in LHS&RHS

⇒LHS=-30+9(3)=-3

RHS=-0.5 |3-1|-2=

-1/2×2-2=-1-2=-3

so the answer will be 3..

hope it helps..

have a great day!!

Daniel had $30 to spend at the fair if she admission to the fair is $7 and the rides cost 1.50 each what is the greatest number of rides Daniel can go on write an inequality that represents Daniels situation. How many rides can Daniel go on?

Answers

Answer:

Daniel can go on 22 rides.

Step-by-step explanation:

Use the information to answer the following question.

The quadratic function f is represented by the equation f(x) = x2 - 2x + 2.



The table gives some of the values of the exponential function g.



x

-1

0

1

2

3

g(x)

-0.5

0

1

3

7



Which of the following statements is FALSE?

A.
f(3) > g(3)

B.
Both functions have a domain of all real numbers.

C.
The y-intercept of f(x) is greater than the y-intercept of g(x).

D.
The functions f(x) and g(x) have the same value at x = 1.

Answers

Answer:

Step-by-step explanation:

A 20-ounce soft drink costs $1.80. A 12-ounce soft drink costs $1.32.

Answers

Answer:

rfgvsdgsgvbd fs e gbaebg g

Step-by-step explanation:

the 20oz soft drink is cheaper because you pay 9 cents per ounce and you pay 11 cents per ounce for the 12 oz can
you can find this by diving 1.80/20 and 1.32/12

please answer this for me

Answers

Answer:

70

Step-by-step explanation:

you add 95 and 15 and get 110 then you do 180-110 getting 70

In which step did Montiah make an error?
3(x+8)2 + 8 = 83
3(x+8)2 = 75
Step 1
(x + 8)2 = 225
Step 2
X + 8 = +15
Step 3
X = 7 or x = -23 Step 4

Answers

Answer:

Step-by-step explanation:

I think you mean 3(x+8)², not 3(x+8)2. If you cannot type ², use ^ to mark the exponent: 3(x+8)^2.

3(x+8)² + 8 = 83

3(x+8)² = 75

(x+8)² = 25

x+8 = ±√25

x+8 = ±5

x = -8 ± 5 = -3, -13

Answer:

Step 2

Step-by-step explanation:

5x^2 + 19x + 12=0
how do i figure this out

Answers

Answer:

x=−4/5 or x=−3

Step-by-step explanation:

Step 1: Factor left side of equation.

(5x+4)(x+3)=0

Step 2: Set factors equal to 0.

5x+4=0 or x+3=0

x=−4/5 or x=−3

There are 1,024 players in a tennis tournament. In each round, half of the players are eliminated. Which function can be used to find the number of players remaining in the tournament at the end of x rounds?

A: f(x)=1,024(1.50)x
B: f(x)=1,024(0.50)x
C: f(x)=1,024(1.05)x
D: f(x)=1,024(0.05)x

Answers

Answer:

f(x) = 1,024(0.50)x

Step-by-step explanation:

i just took the test :)

Sydney bought 3 cookies for 1.80 at this price how much would a dozen cookies cost

Answers

Answer:

$7.20

Step-by-step explanation:

A dozen = 12, Sydney bought 3 cookies for $1.80, 12 divided by 3 = 4, so 4 times $1.80 = $7.20

hope this helps :D

Answer:

7.20

Step-by-step explanation:

Posted Mar 22
Lana bought a sports car for $75,700. If the value of her car decreases 4.3% annually.
When using the exponential DECAY formula, what would be the value of r?

Answers

Answer:

The value of r will be 0.043

Step-by-step explanation:

Firstly, we need to write the exponential decay formula

the general form of the formula is;

A = P(1-r)^t

where A is the price after a certain year t

P is the initial value

r is the decay rate

t is the time

From the question, we have that;

r = 4.3%

4.3% in decimal will be 4.3/100 = 0.043

In the terminal side of an angle in standard position lies on -4y=3x and x>0, find the exact values of the trigonometric functions of 0

Answers

Answer:

sec ∅  =  5/4

cosec ∅  = -5/3

cot ∅  = -4/3

Tan ∅ = - 3/4

sin ∅   = -3/5

cos ∅   =4/5

Step-by-step explanation:

Given : -4y = 3x  , x > 0

i.e. 3x + 4y = 0 ,  x >0

4y = -3x  ∴ y = - 3/4 x

The values of trigonometric functions of  ∅  are

Tan ∅  = opposite / adjacent

           = - 3/4   ( given that y = slope which is = Tan  ∅ )

now we will find the hypothenuse ( c )

c^2 = a^2 + b^2 = 9 + 16 = 25

therefore ; c = √25 = 5

hence the trig functions are :

sin ∅   = -3/5

cos ∅   =4/5

sec = 5/4

cosec = -5/3

cot = -4/3

HELPPPPPPPPPPPPP MEEEEEEEEEEEEEEEEEEE

Answers

Answer:

angle KJG = angle FGJ (by alternateinteriorangle)

can someone help me with this please

Answers

Answer:

Alternate Interior angles

Alternate Interior angles are angles that are within two parallel lines.

So for the above question, our pairs of Alternate Interior angles are:

= Angle 4 and Angle 6

Angle 3 and Angle 5

Alternate exterior angles

Alternate exterior angles are angles that are found outside the two parallel lines

For our above question, our pairs of Alternate exterior angles are:

= Angle 1 and 7

Angle 2 and Angle 8

Corresponding angles

= Angle 1 and Angle 5

Angle 2 and Angle 6

Angle 4 and Angle 8

Angle 3 and Angle 7

Step-by-step explanation:

Alternate Interior angles

= Angle 4 and Angle 6

Angle 3 and Angle 5

Alternate exterior angles

= Angle 1 and 7

Angle 2 and Angle 8

Corresponding angles

= Angle 1 and Angle 5

Angle 2 and Angle 6

Angle 4 and Angle 8

Angle 3 and Angle 7

What’s the answer to this?

Answers

Answer:

45  degrees

Step-by-step explanation:

Have a grate Day :)

Unit 7: Polygons & Quadrilaterals
Nomework 4: Rhombi and Squares

Answers

Answer:

Hey mate, here is your answer. Hope it helps you.

Step-by-step explanation:

6x-21 —->

x=21+6

=27

Answer:

x=11°

Step-by-step explanation:

PSRQ is square ⇒ ∠PQR=90°⇒ ∠PQS=45° ⇒ 6x-21=45 ⇒6x=66 ⇒x=11°

Find the value of x. ​

Answers

Answer:

this question doesnt make a lot of sence but i think its 90

Step-by-step explanation:

45+45 = 90

since ats a triangle 180-90 = 90

also the right angle with the red aquare is 90 degrese so i its 90

Answer:

Its a vertical angel, x + 45 =90.

Step-by-step explanation:

29*9
It's too short. Write at least 20 characters to get a great answer.

Answers

Answer:

261

Step-by-step explanation:

The length of a tropical garden at a conservatory is 5 feet more than its width. A
walkway 2 feet wide surrounds the outside of the garden. If the total area of the
walkway and garden is 126 square feet, find the dimensions of the garden,

Answers

Don’t open that file it take your info

CAN SOMEONE HELP ME, ILL GIVE BRAINIES AND PLEASE NO LINKS












A business owner receives a $5,000 loan with 13%
interest,charged at
the end of each year.
Write an expression to represent the amount owed, in dollars, after the
given number of years of making no payments.

1. after 1 year

2. after 2 years

3. after tyears

Answers

Answer:

Step-by-step explanation:

Given;

Loan = $5,000

Interest rate = 13% charged at the end of each year

Question 1. Expression to represent the amount owed, in dollars, after;

a. After 1 year.

Owed amount = Loan + accrued interest= $5000 + ( 13% * $5000 * 1 year )

= 5650

b. After 2 years.

Owed amount = Loan + accrued interest

= $5000 + ( 13% * $5000 * 2 years )

= $6300

c. After t years

Owed amount = Loan + accrued interest= $5000 + ( 13% * $5000 * t years )= $5000 + $650t

Question 2. Explain how to convince someone that your expression for t years is correct.

Amount owned= borrowed amount + accrued interest

Accrued interest = Interest rate per year * Loan amount * time in years ( for simple interest case )

Loan amount = $5000

Time = t years

Interest rate = 13% per year

Accrued interest = 13% * $5000 *t years= $650t

Amount owned will therefore be; = Loan amount + Accrued interest

= $5000 + $650t

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