Sequence of 2,-6,-14,-22 determine the n term

Answers

Answer 1

Answer:

[tex]a_{n}[/tex] = - 8n + 10

Step-by-step explanation:

the sequence has a common difference between consecutive terms , that is

- 6 - 2 = - 14 - (- 6) = - 22 - (- 14) = - 8

this indicates the sequence is arithmetic with nth term

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = 2 and d = - 8 , then

[tex]a_{n}[/tex] = 2 - 8(n - 1) = 2 - 8n + 8 = - 8n + 10


Related Questions

I need some help with this question.

Answers

Answer:

#1 d #2 c

Step-by-step explanation:

to get these answers I just did the math on all of them

Use mathematical induction to prove that, for n ≥ 1, n³ – n is divisible by 3.

Answers

Answer:

Step-by-step explanation:

The local animal shelter had 12 dogs at the beginning of the month. Since then, the number of dogs at the shelter has decreased by 75%. How many dogs are at the animal shelter today?

Answers

Answer:

3

Step-by-step explanation:

75% is equal to 3/4

The easiest way to do this is to divide 12 by 4.

12/4 = 3

Now multiply this by three to get 3/4 of 12.

3 x 3 = 9

9 dogs left the shelter.

12 - 9 = 3

There are three dogs left.

The points 1 , B and ( are (9 , 8) , ( 12, 4) and (4, - 2) respectively
(a) Find
(1)
the gradient of the line through d and B
(¡i)
the equation of the line through C which is parallel to AB
(b) Calculate the length of the line segment
(i)
[21
(11)
BC
[21
(c) Show that AB is perpendicular to BC 121
(d) Calculate the area of triangle ABC
[1)

Answers

Answer:

a.i.

[tex]mab = \frac{ya - yb}{ xa - xb} = \frac{8 - 4}{9 - 12} = \frac{4}{ -3} [/tex]

a.ii.

[tex]mc = mab = \frac{4}{ - 3} \\ (y - y1) = m(x - x1) \\ y - ( - 2) = \frac{4}{ - 3}(x - 4) \\ y + 2 = \frac{4}{ - 3}x + \frac{16}{3} \\ y = \frac{4}{ - 3} x + \frac{16}{ 3} - 2 \\ y = \frac{4}{ - 3}x + \frac{10}{3} [/tex]

HELP PLEASE!!!! What is the product? Assume x> 0. ( square root of 3x + square root of 5) ( square root of 15x + 2 square root of 30)

Answers

Answer:

3x√5 + 5√3x + 6√10x + 10√6 (Option 2)

Step-by-step explanation:

Applying the distributive property :

⇒ (√(3x) + √5)(√(15x) + 2√30)

⇒ √(3x)√(15x) + √5√(15x) + √(3x)(2√30) + √5(2√30)

⇒ √45x² + √75x + 2√90x + 2√150

3x√5 + 5√3x + 6√10x + 10√6

Let's see

(√3x+√5)(√15x+2√30)√3x(√15x+2√30)+√5(√15x+2√30)√45x^2+2√90x+√75x+2√150√9×5x²+2√(9×10)x+√25×3x+2√1503x√5+6√10x+5√3x+10√6

Option B

What is the surface area of the cylinder with height 4 km and radius 5 km? Round
your answer to the nearest thousandth.

Answers

[tex]\textit{surface area of a cylinder}\\\\ SA=2\pi r(h+r)~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ h=4\\ r=5 \end{cases}\implies \begin{array}{llll} SA=2\pi (5)(4+5)\implies SA=10\pi (9) \\\\\\ SA=90\pi \implies SA\approx 282.743~km^2 \end{array}[/tex]

Type in your answer:
X = ?
Angle KPN =?
Angle NPO =?

Answers

KPN is 62

NPO is 28

Answer:

x=31

KPN =62

NPO=28

Step-by-step explanation:

KPO = 90(right angle) =2x + (x-3)

3X=90+3

X= 31

NPO = 31-3

NPO=28

KPN = 2*31

KPN =62

Calculus, factor the given polynomial completely.

Answers

(X-8)(x-9)

-8x-9=72
-8+-9=-17

I need to solve for X

Answers

Check the picture below.

Match the numbers with the correct label.

Answers

Answer:

a = 1/7b = 0.2c = 3/9

Step-by-step explanation:

Converting all fractions to decimal (for easier comparison) :

0.21/7 = 0.143/9 = 0.33

Hence,

First point (a) = 1/7Second point (b) = 0.2Third point (c) = 3/9

In which of the following do you expect the correlation coefficient to be negative?

This is my last question I need please help

Answers

Answer:

The graph I expect to have a negative correlation is the third graph.

Step-by-step explanation:

Positive correlation is when the the x-values increase with a corresponding increase in y-values.

Negative correlation is when the x-values increases with a corresponding decrease in y-values.

No correlation is when only x or y variable changes.

From the graphs given the only one that has a negative correlation is the third graph.

They had taken 8 galons of water along the bus. If there were 62 sixth graders and 2 teachers how many cups did each person get

Answers

Answer:

2

Step-by-step explanation:

8gallons=16 cup

8x16=128

62+2=64

128÷2=64

Each person got 2 cups of water.

The first time the United States enacted a temporary income tax was ?

Answers

On August 5, 1861, President Lincoln imposes the first federal income tax by signing the Revenue Act. Strapped for cash with which to pursue the Civil War, Lincoln and Congress agreed to impose a 3 percent tax on annual incomes over $800.

A rideshare service charges a flat fee of $6.00, plus $1.50 for every mile driven. Let t represent the total cost of the ride, and m represent the number of miles driven. Determine the dependent and independent variables, write an equation to represent this relationship, and then complete the table to show the total cost for riding 3 to 10 miles.

Answers

Answer:

The independent variable is m, while the dependent variable is t.

Step-by-step explanation:

What is the independent variable?

An independent variable is a variable that does not rely on another variable to change its outcome. In this case, the variable 'm' does not rely on the ride's total cost.

What is the dependent variable?

The dependent variable is a variable that depends on another variable to give its amount. In this case, 't' is the dependent variable, because it depends on how many miles were driven, in order to provide the correct answer.

Write an equation representing this relationship:

t = $6 + ($1.50 x m)

Complete the table to show the total cost for riding 3 to 10 miles:

3 miles: t = $6 + ($1.50 x m) or $10.50 = $6 + ($1.50 x 3)

4 miles: t = $6 + ($1.50 x m) or $12 = $6 + ($1.50 x 4)

5 miles: t = $6 + ($1.50 x m) or $13.50 = $6 + ($1.50 x 5)

6 miles: t = $6 + ($1.50 x m) or $15 = $6 + ($1.50 x 6)

7 miles: t = $6 + ($1.50 x m) or $16.50 = $6 + ($1.50 x 7)

8 miles: t = $6 + ($1.50 x m) or $18 = $6 + ($1.50 x 8)

9 miles: t = $6 + ($1.50 x m) or $19.50 = $6 + ($1.50 x 9)

10 miles: t = $6 + ($1.50 x m) or $21 = $6 + ($1.50 x 10)

Shawna says her mug holds 100 milliliters.
Shelly says that the mug holds 1 liter.
Is Shelly correct?

Answers

Answer:

In 1 liter there are 1000 milliliters so because 100 ≠ 1000 the answer is no

Amortization for 2021, $3.Record on adjusting entry

Answers

The adjusting entry for the Software of Northland Physical Therapy is as follows:

Adjusting Journal Entry:

December 31, 2018:

Debit Amortization Expense $3

Credit Accumulated Amortization $3

To record the amortization expense for the year.

What is an Adjusting Entry:

An adjusting entry for Amortization records the amortization expense for the period, which is debited.  It also credits the Accumulated Amortization, increasing the amount of the amortization expense.

For instance, the Amortization Expense for Northland Physical Therapy's Software is recorded as above.

Learn more about adjusting entries at https://brainly.com/question/13035559

#SPJ1

The radius of a circle is 1 meter. What is the circle's area?
r=1 m
Use 3.14 for л.
square meters

Answers

Answer:

A= 3.14

Step-by-step explanation:

The formula for finding the area of a circle is A=  π r²

A= 3.14*1²

The angle of depression of the top and the foot of a flagpole as seen from the top of a building 145 metres away are 26° and 34° respectively. Find the heights of the pole and the building.

Answers

The height of the pole and the building are 27.1 meters and 97.8 meters respectively.

How to find the height of the pole and the building?

The situation forms a right angle triangle. The height of the building can be found using trigonometric ratios,

Therefore,

tan 34 = opposite / adjacent

tan 34 = h / 145

h = 145 tan 34

h = 145 × 0.67450851684

h = 97.8037349422

Therefore,

height of the building = 97.8 meters

tan 26 = x / 145

x = 145 tan 26

x = 70.721225342 meters

Therefore,

height of the flagpole = 97.8 - 70.7 = 27.1 meters

learn more on right triangle here: https://brainly.com/question/15322533

#SPJ1

anyone? giving brainliest to correct answer

Answers

Answer:

im not really sure what that means im so sorry

Step-by-step explanation:

A collectors item is purchased for $150 and it’s value increases by 3% each year. Which graph can be used to determine approximately how many years it will take for the value to double

Answers

Answer:

we are given A collector’s item is purchased for $150so, its value increases by 3% each yearso, t is time in yearsLet's assume cost of item after t years is C(t)so, we can use formula now, we can plug values so, equation is After doubling C(t)=2*150=300so, we can set C(t)=300and then we can solve for twe get so, doubling time is 23.44977 years

Answer:

B works ; it starts at 150, is positive, and slowly reaches 300

Step-by-step explanation:

Edge

Matthew had to make a bridge for his math class. It had to be at least 1 1/2 feet long. Harold made a bridge that was 2 1/3 times as long as Matthew’s. What equation would you use to find out how long Harold’s bridge is?

Answers

The equation used for finding the length of Harold's bridge will be 3H-7M=0 Length will be H = 1/√2

What is an equation?

The equation in mathematics is the relationship between the variables and the number and establishes the relationship between the two or more variables.

Here we have the following data:-

Matthew's bridge length is

 1(1/2)=3/2

Now we have that Harold made a bridge that was 2 1/3 times as long as Matthew’s. From this data the equation will be:-

[tex]H=2\dfrac{1}{3}M\\\\\\H-\dfrac{7}{3}M=0\\\\\\3H-\dfrac{7\times 3}{2}=0\\\\\\H=\dfrac{1}{\sqrt{2}}[/tex]

The equation used for finding the length of Harold's bridge will be 3G-7M=0 Length will be H = 1/√2

To know more about equations follow

https://brainly.com/question/2972832

#SPJ1

Please help me do this question mathematics expert

Answers

Answer:

[tex]\textsf{i)} \quad \text{T} &=2 \pi r^2 + \dfrac{26}{r}[/tex]

ii)  radius = 1.27 cm (3 sf)

   height = 2.55 cm (3 sf)

Step-by-step explanation:

[tex]\text{Volume of a cylinder}=\pi r^2 h \quad \text{(where r is radius and h is height)}[/tex]

Given volume = 13 cm³, rewrite the equation making h the subject:

[tex]\implies 13=\pi r^2 h[/tex]

[tex]\implies h=\dfrac{13}{\pi r^2}[/tex]

Substitute found expression for h into the Surface Area equation to find the expression for the total surface area, T:

[tex]\begin{aligned}\text{Surface Area of a cylinder} & =2 \pi r^2 + 2 \pi r h\\\implies \text{Surface Area} & =2 \pi r^2 + 2 \pi r \left(\dfrac{13}{\pi r^2}\right)\\& =2 \pi r^2 + \dfrac{26 \pi r}{\pi r^2}\\ \implies \text{T} &=2 \pi r^2 + \dfrac{26}{r}\end{aligned}[/tex]

To find the radius of the minimum surface area, differentiate T with respect to r:

[tex]\begin{aligned}\text{T}& =2 \pi r^2 +26r^{-1}\\\implies \dfrac{dT}{dr} & =(2)2 \pi r^{(2-1)}+(-1)26r^{(-1-1)}\\ & =4 \pi r-26r^{-2}\\ & =4 \pi r-\dfrac{26}{r^2}\\ & = \dfrac{4 \pi r^3-26}{r^2} \end{aligned}[/tex]

Set it to zero, and solve for r:

[tex]\begin{aligned}\dfrac{dT}{dr} & = 0 \\\implies \dfrac{4 \pi r^3-26}{r^2} & = 0 \\\impliles 4 \pi r^3-26 & = 0 \\4 \pi r^3 & = 26 \\r^3 & = \dfrac{13}{2 \pi} \\r & = \sqrt[3]{\dfrac{13}{2 \pi}} \end{aligned}[/tex]

To find the height, substitute the found value of r into the equation for height (found previously):

[tex]\begin{aligned}h & =\dfrac{13}{\pi r^2} \\\implies h & =\dfrac{13}{\pi \left(\sqrt[3]{\dfrac{13}{2 \pi}}\right)^2} \\& =2.548499134\end{aligned}[/tex]

Therefore,

radius = 1.274249567... = 1.27 cm (3 sf)height = 2.548499134... = 2.55 cm (3 sf)

Shade the mode model. Then write the decimal.​

Answers

Answer:

no picture

Step-by-step explanation:

just search it up

WILL MARK BRAINLIEST

Answers

Answer:

The sum of the given sequence is 180

Step-by-step explanation:

Find each term

t₁ = 2*1 + 7 = 9t₂ = 2*2 + 7 = 11t₃ = 2*3 + 7 = 13...t₉ = 2*9 + 7 = 25t₁₀ = 2*10 + 7 = 27

The series is

9, 11, 13, ..., 25, 27

The sum of series can be shown as

9 + 11 + 13 + ... + 25 + 27

Find the sum

S₁₀ = 10/2*(9 + 27) = 5*36 = 180

Answer:

180

Step-by-step explanation:

The given series means to sum the first 10 terms of the sequence [tex]a_t=2t+7[/tex]

[tex]\begin{aligned}\displaystyle \sum^{10}_{t=1}2t+7 & = (2 \cdot 1+7)+(2 \cdot 2+7)+...+(2 \cdot 9+7)+(2 \cdot 10+7)\\ & =2(1+2+...+9+10)+10(7)\\\\& = 2(1+2+...+9+10)+70\\\\ & = 2(55)+70\\\\& = 110+70\\\\ & = 180 \end{aligned}[/tex]

H The price of a 2 pack Mini Brands is no more than $15. Write an inequality to represent this scenario.i​

Answers

H is less than or equal to 15


PLEASE HELP?! IM SO SORRY I AM NOT GOOD AT MATH

Answers

Answer:

C.

Step-by-step explanation:

-3 7/8 rounds down to -4

4.63 rounds up to 5

-4 x 6 + 5

-24 + 5

-19

her answer (-19.14) also rounds to -19

So yes, it is reasonable and the correct response is C.

Identify the pattern of the following sentences
1. I've already told the detective what I know about it.
2. They were very excited.
3. The police have identified the robbers.
4. I was eating a sandwich for lunch.
5. My cousin painted quite badly.
6. They are going to eat-out.
7. She never gives up.
8. I bought a drink for her.
9. The company has offered me a good job.
He usually spends all his money.

Answers

The pattern of the sentences are:

1. Subject + verb + object

2. Subject + verb.

3. Subject + verb + object

4. Subject + verb + adjectives.

What is Sentence pattern?

Sentence patterns is known to be a sentence that is said to be made of up of phrases and also clauses.

Therefore, The pattern of the sentences are:

1. Subject + verb + object

2. Subject + verb.

3. Subject + verb + object

4. Subject + verb + adjectives. is correct.

Learn more about Sentence pattern from

https://brainly.com/question/24320025

#SPJ1

3.
Given: AC = 4x-29
A 19 B 2x-18
X=
AC =
BC=
C

Answers

Answer:

x = 15
AC = 31
BC = 12

Explanation:

To setup the equation it is:

2x + 1 = 4x - 29

Because AC is the whole thing.
Meaning AB + BC = AC.

1 = 2x - 29
30 = 2x
30/2 = 15

15 = x

4(15) - 29 = 31
31 = AC

2(15) - 18
12 = BC

need help I don’t know what to do please help !!

Answers

Answer:

Yes, because the monthly service fee is approximately the same each month.

Step-by-step explanation:

At one month, the service fee is around $50, then from month one to month two the service fee is around $50, and so on. Just focus on the line and the points it makes in respect to the month to cost ratio.

Write an equation in slope-intercept form of the line that passes through the point (-6,8) and has a slope of 1/2

Answers

Answer:

Step-by-step explanation:

Remark

You can get 1/2 the unknown just by looking at the givens. The slope is just given -- no need to modify it.

The y intercept is a little harder. You need the point for that.

Givens

Slope = 1/2

point = (-6,8)

Formula

y = mx + b

Solution

m = 1/2

y = 1/2x + b              To find b,

x = -6y = 8

8 = 1/2(-6) + b

8 = -3 + b                 Add 3 to both sides

8 + 3 = b

b = 11

Answer

y = 1/2x + 11

Answer:

y = 1/2x+11

Step-by-step explanation:

Slope intercept form is

y = mx+b  where m is the slope and b is the y intercept

y = 1/2x +b

We can use the point on the line to find b

8 = 1/2(-6) +b

8 = -3+b

Add 3 to each side

8+3 =-3+3 b

11 = b

y = 1/2x+11

Other Questions
Find x. A) 3 B) 3.75 C) 4.25 D) 5 Mallory ordered a pizza with a 17-inch diameter. ricky ordered a pizza with a 20-inch diameter. what is the approximate difference in the area of the two pizzas? How can you train yourself to never give up before you reach you number one goal.For example, I want to go to college and either study to be a Certified nursing assistant or Registered nurse and in 11th grade I want to try to do Licensed practical nurse which I probably have to start off as Practical nurse. (This is for eighth grade) Is AABCADEF? If so, identify the similarity postulate or theorem thatapplies.A. Similar - AAB. Similar - SSSC. Similar - SASD. Cannot be determined If a gas has a volume of 350 mL at 780 mm Hg, what pressure will be needed to cause its volumeto be 500 mL?Could you state the law used? Question 9 of 20What are two reasons national governments struggle in Afghanistan?A. People in Afghanistan resist having freedom.B. The country is used to having a king and queen.O c. The population is divided among four major ethnic groups.O D. Ethnic and tribal conflict has been central to Afghan history.SUBMIT A ring is reduced to 840. This is a saving of 40% of the original price. What was the original price What ratio is equivalent to the rate 40 miles / 1 hour A store sells cooking oil of two different brands in bottles of the same size. The table below and the equation each show the price (y), in dollars, of different number of bottles of oil (x):Brand ANumber of Bottles, x Price (dollars), y222333444555Brand By = 17xHow many dollars more is the price of 8 bottles of brand B oil than the price of 8 bottles of brand A oil? $5 $6 $28 $48 how to make a histogram Helloppp i need hwlp with this plllss Kelly sits on a rock in a field. Which of the following correctly name force pairs? Fragments of _________ released from Gram-negative bacteria into the bloodstream produce fever and shock. Lipopolysacharide N-acetylmuramic acid Phospholipid N-acetylglucosamine A lunar eclipse occurs when the Moon casts a shadow on the Earth. Compare and contrast sources and types of credit, including costs and benefits of installmentcredit, collateralized loans versus unsecured credit, credit cards, mortgages, auto loans, andstudent loans. FILL IN THE BLANKS WITH THE (CORRECT ER OR IR VERB ENDING) Carlos va al caf. En el cafe el v ( ANSWER HERE 1 ) una mesa llbre y v (ANSWER HERE 2) al mesero. l abr (ANSWER HERE 3) el men y le (ANSWER HERE 4). El tien (ANSWER HERE 5) hambre y y com (ANSWER HERE 6) una hamburguesa y papas fritas. In Freudian theory, which one of the following is an example of an Eros instinct, which includes survival, social cooperation, and reproduction? mZRRS10x - 898 12x + 4QT Which behavior is a nonverbal way of communicating in a healthy romantic relationship? using nicknameslaughingsharing secretsmaintaining eye contact The graphs below have the same shape. f(x) = x.What is the equation of the graph of g(x)?