write a rule for the nth term of the arithmetic sequence
-11, -4, 3, 10...

Answers

Answer 1

Answer: aₙ = -11 + 7(n - 1)

Step-by-step explanation: The equation of an arithmetic sequence is

aₙ = a₁ + d(n - 1).

a₁ is the first term.

d is the common difference.


Related Questions

What is the directrix of the parabola defined by `(1)/(4)(y + 3) = (x − 2)^2`?

Answers

The directrix of the parabola is [tex]y = \frac {-49}{16}[/tex]

How to determine the equation of the directrix?

The parabola equation is given as:

[tex]\frac 14(y + 3) = (x -2)^2[/tex]

A parabola is represented as:

[tex]4p(y - k) =(x -h)^2[/tex]

By comparing both equations, we have:

4p = 1/4 ==> p = 1/16

-k= 3 ==> k = -3

The directrix is represented as:

y = k - p

So, we have:

[tex]y = -3 - \frac 1{16}[/tex]

Take the LCM

[tex]y = \frac {-16 * 3- 1}{16}[/tex]

Evaluate

[tex]y = \frac {-49}{16}[/tex]

Hence, the directrix of the parabola is [tex]y = \frac {-49}{16}[/tex]

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The diagram shows a circle inside a square (16cm)
work out the area of the circle ​

Answers

The area of the circle inside the square shape is 200.96 cm²

How to determine the area of the circle?

The length of the square is given as:

L = 16 cm

This represents the diamater (d) of the circle.

The area of the circle is then calculated as:

Area = π(d/2)²

This gives

Area = 3.14 * (16/2)²

Evaluate

Area = 200.96

Hence, the area of the circle is 200.96 cm²

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Which equation can be used to solve for x in the following diagram.

Answers

Answer:

C. (3x+12) + x = 180

Step-by-step explanation:

the 2 angles create a straight line which is 180 degrees, so (3x+12) + x = 180

Now explore a few more-difficult problems.
Which of the following statements are true for all the
problems?
The first step is always to divide.
○ The last step is always to subtract.
The decimal always moves one place to the right.
The next to last step is always to multiply.

Answers

The statement that is true for all the problems is " The last step is always to subtract.". Option B.  This is further explained below.

What is Arithmetic?

Generally, Arithmetic is simply defined as the area of mathematics concerned with the study and manipulation of numbers and their properties.

In conclusion, "The final step is always to subtract." is the universally true solution to the difficulties.

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Answer: B & D

Step-by-step explanation: I did this assignment.

Esther gave the storekeeper a twenty dollar bill for a purchase of $14.51. How
much change should she have received?

Answers

Answer:

She would have received $5.49 change

Answer:

$5.49 ~$5.50

Explanation: $20 - $15.51 = $5.49 therefore you have to round off which would initially equal to $5.50

Please solve with explanation (high points)

Answers

Answer:

see the attachment photo!

translate the question into an equation. Do not solve. Let n be the unknown number. what is 1% of 77?​

Answers

Answer:

1% × 77 = n

I used multiplication since "of" counts as multiplication.

Twenty-five bakery customers were surveyed to determine if they like cake or pie. The results are shown in the Venn diagram.

Circle C and P overlap. Circle C contains 10, circle P contains 8, and the intersection contains 4. Number 3 is outside of the circles.

Given that a randomly chosen customer likes cake, what is the probability that the customer also likes pie?

Answers

The probability that a customer likes cake and pie is 0.16.

What is the probability?

Probability is used to determine the odd that a random event would happen. The odds that the event happens usually lie between 0 and 1.

The probability that a customer likes cake and pie = total number of customers who like cake and pie / total number of customers

4/25 = 0.16

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What is the volume of this rectangular
pyramid?
3 m
4 m
Submit
5 m
cubic meters

Answers

Given:l= 5 meterb= 4 meterh= 3 meterNote that:l= length b= breadth h= height To find:

The volume of the given rectangular pyramid.

Solution:

[tex]\large\boxed{Formula:V=\frac{1}{3}lbh}[/tex]

First, multiply the length (5), breadth (4) and height (3).

[tex]5×4×3[/tex]

[tex]= 60 \: cm [/tex]

Now, divide 60 by 3.

[tex]\frac{60}{3}[/tex]

[tex]\large\boxed{V= 20 \: {m}^{3}}[/tex]

Therefore, the volume of the given rectangular pyramid is 20 cubic meters.

The height in feet of 25 trees is shown below (lowest to highest). 25, 27, 33, 34, 34, 34, 35, 37, 37, 38, 39, 39, 39, 40, 41, 45, 46, 47, 49, 50, 50, 53, 53, 54, 54

outlier if any

Answers

There are no outliers in the dataset of the heights in feet of 25 trees

How to determine the presence of outliers?

The sorted dataset is given as:

25, 27, 33, 34, 34, 34, 35, 37, 37, 38, 39, 39, 39, 40, 41, 45, 46, 47, 49, 50, 50, 53, 53, 54, 54

Outliers are relatively far from other elements of the dataset.

The highest and the least elements are 54 and 25, respectively.

Other elements of the dataset are relatively close to these two elements

Hence, there are no outliers in the dataset of the heights in feet of 25 trees

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Find the distance between the points (5,0) and (-5,3)

Answers

Answer:

10.4

Step-by-step explanation:

√(5--5)²+(0-3)²

√100+9

√109=10.4

For the arithmetic sequence beginning with the terms (11, 17, 23, 29, 35), what is the sum of
the first 17 terms?

a.) 1116
b.) 1003
c.) 1235
d.) 896

Answers

Option B is the correct answer.

The sum of 17 terms of the given arithmetic sequence is 1003.

What is Arithmetic Sequence?

An arithmetic sequence is a sequence where each term increases by adding/subtracting some constant k.

Here, given sequence :

  11, 17, 23, 29, 35, ......

first term a = 11

common difference d = 17 - 11 = 6

n = 17

Sₙ = n/2 {2a + (n-1)d}

S₁₇ = 17/2 { 2 X 11 + (17-1)X6}

S₁₇ = 17/2 { 22 + 16 X 6}

S₁₇ = 17/2 X 118

S₁₇ = 17 X 59

S₁₇ = 1003

Thus, the sum of 17 terms of the given arithmetic sequence is 1003.

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In the number 9,206.457138, what is the value of 1?​

Answers

Answer:

0.0001 or 1/10000 or 1 ten thousandths

Step-by-step explanation:

The 1 is 4 places after the decimal point so has a value of :

0.0001 or 1/10000 or 1 ten thousandths

Hope this helped and have a good day

f(x)=x^5+(x+3)^2 which value completed the table

Answers

Answer:

three boys shared D 10,500.00 in the ratio 6:7:8.find the largest share.

Thandi has decided to make grocery combo’s for her shop. The wholesaler where she buys from, sells sugar in packets of 20 in a carton, flour in packets of 12 a carton, and there are 15 bags of rice in a carton. How many of each item should she buy so there are an equal number of packets of sugar, packets of flour and bags of rice in each combo?

Answers

Answer:

3 cartons of sugar 5 cartons of flour and 4 cartons of rice

Step-by-step explanation:

First find the least common factor being 60 then divide by the number of packets each carton comes with to find how many cartons you need of each

Write an equation for a line perpendicular to y = − 4 x + 5 and passing through the point (-12,-4)

Answers

Answer:

[tex]y=\frac{1}{4} x-1.[/tex]

Step-by-step explanation:

1) if the lines are perpendicular, then the second slop is 0.25;

2) the equation of the 2d line is y=0.25x+i, where i - unknown intercept;

3) it is possible to calculate the unknown intercept, if to substitute the given coordinates into the equation y=0.25x+i:

-4=-12*0.25+i; ⇔ i=-1.

4) finally, the required equation is:

[tex]y=\frac{1}{4} x-1.[/tex]

Which of the following rational functions is graphed below

Answers

Answer:

A.

Step-by-step explanation:

if x≠-4, then the correct answer is

[tex]A. \ F(x)=\frac{1}{x+4}.[/tex]

two dozen of pen cost rupee 60.find the cost of 25 such pens.​

Answers

Answer:

it costs rupee 3000 of 50 such pens

Explanation:

first, you have to multiply 50 x 60 which is 3000

second, two dozens of pens, right? so i add double 25 up which is 50 pens.

hope it helps and stay safe! (brainliest me pls)

The ratio of black bags to blue bags is 5to 3 if there are a total of 10 black bags ,then how many blue bags are there

Answers

Answer:

6

Step-by-step explanation:

We can think of the 10 black bags as 2 sets of 5-black bags (10 divided into groups of 5; 10 / 5 ; is 2 groups/sets). So, we would also have two sets of 3 (3 x 2 = 6), or 6 bags.

5 : 3 = 10 : 6

(multiply both numbers by 2)

Solve 10x + 16 2 6x + 20.
A. x29
B. x=9
c. x=1
D. x21


Answers

An equation is formed of two equal expressions. The value of x for which the equation has a solution is 1.

What is an equation?

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The solution for 10x+16=6x+20 is,

10x + 16 = 6x + 20

10x - 6x = 20 - 16

4x = 4

x = 1

Hence, the value of x for which the equation has a solution is 1.

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which graph represents the linear function y=-5x+2

Answers

The answer would be the second picture. Also, if you have any questions like these you can go on desmos and put in the equation to see the answer. Hope this helps!

Find the number of students that play

A basketball and football but not volleyball
B basketball only
C none
#15 play
basketball and volleybal

Answers

Answer:

#16 play basketball and football

I need help to find the coordinates

Answers

We can solve by using the substitution method
y=-5/3x+3
y=1/3x-3
They are equal to each other because they are both equal to y
-5/3x+3=1/3x-3
Subtract both sides by 1/3 and subtract 3 from both sides

-5/3x-1/3x=-3-3
-2x=-6

Divide both sides by -2
x=3

Plug in x into one of the equation to solve for y
y=1/3(3)-3
y=1-3
y=-2

(3,-2)

Silas is researching the cost of a specific souvenir he wants to buy on his international trip. Use the table to answer the question.​

Answers

Answer:

Egypt.

Step-by-step explanation:

We need to set up our conversion factors for each currency.

British Pounds and Egyptian Pounds:

0.83 £ (Europe) = 1 U.S. Dollar

18 E£ (Egypt) = 1 U.S. Dollar

Cost of a Souvenir in Europe:

The cost of souvenir in Europe is 13£. Using our conversion rate, we get

[tex]13\pounds \cdot \frac{\$1}{0.83 \pounds}=\$15.66[/tex]

Cost of a Souvenir in Egypt:

The cost of a souvenir in Egypt is 342 E£. So we have

[tex]342 \text{ E}\pounds\cdot \frac{\$1}{18 \text{ E}\pounds}=\$19[/tex]

Based on our calculations, it is cheaper to buy a souvenir in Europe than in Egypt.

Given a polynomial function f(x) = –x2 + 2x + 1 and an exponential function g(x) = 2x, what key features do f(x) and g(x) have in common?

A.)Both f(x) and g(x) decrease over the interval of [1 , ∞).
B.) Both f(x) and g(x) have the same range of (–∞, 2).
C.) Both f(x) and g(x) have the same x-intercept of (–1, 0).
D.)Both f(x) and g(x) have the same y-intercept of (0, 1).

Answers

The only key feature that these functions have in common is that they have the same y-intercept. So the correct option is D.

What do these functions have in common?

Here we have the functions:

[tex]f(x) = -x^2 + 2x + 1\\\\g(x) = 2^x[/tex]

f(x) is quadratic, and g(x) is exponential.

Notice that the exponential function has a positive base, so it is increasing. For the quadratic equation we can see a negative leading coefficient, so it opens downwards.  So first and second options are false.

Also, g(x) never intersects the x-axis, so third option is false.

Finally, the y-intercepts of the given functions are:

[tex]f(0) = -0^2 + 2*0 + 1 = 1\\\\g(0) = 2^0 = 1[/tex]

So the y-intercepts are equal, meaning that the correct option is D.

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Answer:

Both f(x) and g(x) have the same y-intercept of (0, 1).

Step-by-step explanation:

I got it right on the test.

Factor out the GCF from the given polynomial.
14x-2

Answers

The answer is 1 is it helpful?

Answer:

2(7x-1)

Step-by-step explanation:

14 & 2 gcf 2 factor and wal lah!

Give the standard form 80,000+200+2

Answers

Answer:

80,202 = 8.0202 × 10⁴

I need to find values of product and quotient functions

Answers

The answers are 8 and 2

What is a function?

A function is an equation that establishes a relationship between two or more variables.

Analysis:

r(x) x s(x) = 2[tex]\sqrt{x}[/tex] x [tex]\sqrt{x}[/tex] = 2x

r2(4) = 2 x 4 = 8

r(x)/s(x) = 2[tex]\sqrt{x}[/tex]/ [tex]\sqrt{x}[/tex] = 2

In conclusion, the values of the product and quotient of the functions are 8 and 2 respectively.

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three students measured the width of the whiteboard. Reggie got 2, Jackson got 72, and Pete got 6. The teacher said they were all correct. Draw lines to match each student with the unit he was using.​

Answers

Answer:

2 yards ; 6 feet ; 72 inches ;

Step-by-step explanation:

2:6:72

1:3:12

1:3 is the ratio of Yards -> Feet

3:12 is the ratio of Feet -> Inch.

6ft = Pete

2 yards = Reggie

72 inches = Jackson

-- Gage Millar, Algebra 1/2 Tutor (Pending Pre-Calc Tutor)

Is this sequence arithmetic? Why or why not?

11, 11, 11, 11, 11

Answers

no because it’s the same number over and over, if it were arithmetic the next number would be x added to 11 to get a2
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