Look at the sequence of numbers.
6 12 18 24

a Write down the next number in the sequence.
b Write down the term-to-term rule.
C Write down the position-to-term rule.

Answers

Answer 1

Answer:

Here we have the sequence:

6, 12, 18, 24

We can assume that this is an arithmetic sequence, this is, the difference between any two consecutive terms is always the same, D.

To check this, let's find the difference between the consecutive terms:

12 - 6 = 6

18 - 12 = 6

24 - 18 = 6

So we can conclude that this is an arithmetic sequence, and the difference between any two consecutive terms is always 6.

a) Then the next number in the sequence will be equal to the previous number plus 6, this is:

24 + 6 = 30

The next number in the sequence is 30

b) The term-to-term rule is the rule that defines the n-th term based on the previous terms.

Here we already know that each term in this sequence is the previous one plus six, so we can write this as:

Aₙ = Aₙ₋₁ + 6

c) The position-to-term rule is the general one.

Here we need to know that, the first term, A₁ = 6

Then, the n-th term will be A₁ plus (n - 1) times 6.

Then the rule is:

Aₙ = A₁ + (n - 1)*6

Replacing A₁ by its value, the rule becomes:

Aₙ = 6 + (n - 1)*6


Related Questions

Write an equation of the line that passes through (0,9) and is parallel to the line y = 8x+7.

Answers

Answer:

[tex]y=8x+9[/tex]

Step-by-step explanation:

Hi there!

What we need to know:

Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)Parallel lines always have the same slopes and different y-intercepts

1) Determine the slope

[tex]y = 8x+7[/tex]

From the given equation, we can identify 8 to be in the place of m, making 8 the slope. Because parallel lines always have the same slopes, the line we're currently solving for will also have a slope of 8. Plug this into [tex]y=mx+b[/tex]:

[tex]y=8x+b[/tex]

2) Determine the y-intercept

[tex]y=8x+b[/tex]

The y-intercept occurs when x=0. The given point is (0,9), telling us the the y-intercept is 9. Plug this into [tex]y=8x+b[/tex]:

[tex]y=8x+9[/tex]

I hope this helps!

A recipe requires only blueberries and strawberries. This list shows the amounts required for 1/4 of the whole recipe: 1/2 cup blueberries 2/5 cup strawberries In this table, select the number of cups of blueberries and the number of cups of strawberries required for the whole recipe.HELP ASAP​

Answers

The whole recipe requires 1/2 cup of blueberries and 2/5 cup of strawberries.

To find the amounts required for the whole recipe, we can multiply the amounts required for 1/4 of the recipe by 4:

For blueberries:

1/4 x 4 x 1/2 = 1/2 cups

So, the whole recipe requires 1/2 cup of blueberries.

For strawberries:

1/4 x 4 x 2/5 = 8/20 = 2/5 cups

So, the whole recipe requires 2/5 cups of strawberries.

Therefore, the whole recipe requires 1/2 cup of blueberries and 2/5 cups of strawberries.

To learn more about multiplication;

https://brainly.com/question/19634536

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A school uses the function p(t)=t2−20t+175 to model the profit (in dollars) expected in a weekend when the tickets are sold at a certain price, t, to the school musical go on sale a. Write an equation to find out the prices at which the school would earn $100 in profit from the school musical each weekend. b. Find out at what prices the tickets should be sold at to make a $100 profit each weekend. SHOW ALL WORK.

Answers

Answer:

[tex](a)\ t^2 - 20t + 75= 0[/tex]

[tex](b)[/tex] [tex]t = 5; t -=15[/tex]

Step-by-step explanation:

Given

[tex]p(t) = t^2 - 20t + 175[/tex]

Solving (a): Equation when profit = 100.

This implies that:

[tex]p(t) =100[/tex]

So, we have:

[tex]100 = t^2 - 20t + 175[/tex]

Rewrite as:

[tex]t^2 - 20t + 175 - 100 = 0[/tex]

[tex]t^2 - 20t + 75= 0[/tex]

Solving (b): Calculate t, in (a)

In a, we have:

[tex]t^2 - 20t + 75= 0[/tex]

Expand

[tex]t^2 - 15t -5t + 75= 0[/tex]

Factorize

[tex]t(t - 15) -5(t - 15)= 0[/tex]

Factor out t - 15

[tex](t - 5)(t - 15)= 0[/tex]

Split

[tex]t - 5 = 0; t - 15 =0[/tex]

Solve

[tex]t = 5; t -=15[/tex]

The prices are $5 and $15, respectively

log(2x+5)+10=13 SHOW WORK PLEASE

Answers

Answer:

x = 497.5

Step-by-step explanation:

that's the correct answer with solution

Dani tracked the number of fish she caught per fishing trip and recorded the data in a frequency table. Fish caught Frequency 0 2 1 0 2 3 3 5 5 2 7 1 Create a dot plot for the data. Hover over each number on the number line. Then click and drag up to create the dots.

Answers

Answer:

Step-by-step explanation:

The dot plot of the recorded data in the frequency table is given below.

What is a dot plot?

A speck plot, otherwise called a strip plot or dab diagram, is a straightforward type of information perception that comprises information focuses plotted as spots on a chart with an x-pivot and y-pivot.

Dani tracked the number of fish she caught per fishing trip and recorded the data in a frequency table.

Fish caught Frequency 0 2 1 0 2 3 3 5 5 2 7 1 Create a dot plot for the data.

Hover over each number on the number line.

Then click and drag up to create the dots.

The graph is shown below.

More about the dot plot link is given below.

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Which of the following is a rational number

Answers

a. sqrt 36

bc it becomes 6

answer:

a. √36

step-by-step explanation:

a rational number is a number that is expressed as the ratio of two integers, where the denominator should not be equal to zero, whereas an irrational number cannot be expressed in the form of fractions

√36 = rational — the answer to this is 6 and it is a whole number

-√12 = -3.46410161514... — it is repeating without an order so irrational

5/0 = irrational — the denominator cannot be a 0

π = irrational — pi is always irrational

A quantity of tea is sold at Rs 48 per kg at a profit of 20%. The total gain is RS90 .What is the quantity of tea sold?​

Answers

Answer:

1.875kg

Step-by-step explanation:

48 - 1000g

90 - x

48x = 90000

x = 90000/48

  = 1875g = 1.875kg

Feel free to mark as brainliest :D

agregenme o baneo la preguntta

Answers

Answer:

translate; Assault me or ban the question

Step-by-step explanation:


What attributes were used to organize the shapes in Circle A and Circle B?

I need a answer ASAP! And I really want it to be right!!

Have a great day!

Answers

Left one: shapes with right angles
Right one: shapes where opposite sides are parallel (or shapes where opposite sides are congruent

For circle A, attribute used is right angle.

For circle B, attribute used is parallel lines.

What is right triangle?

A right triangle consists of two legs and a hypotenuse. The two legs meet at a 90° angle and the hypotenuse is the longest side of the right triangle and is the side opposite the right angle.

What are Similarities of square, rectangle and parallelogram?

A square, rectangle and parallelogram are quadrilaterals. Opposite sides of square, rectangle and parallelogram are parallel to each other. Adjacent angles of square, rectangle and parallelogram are supplementary. Diagonals of square, rectangle and parallelogram bisect each other.

Circle A consists of triangles.

By observing clearly that in circle A there are two right angled triangles.

For circle A, attribute used is right angle.

Circle B consists of 1 square, 1 rectangle and 2 parallelogram.

We know that in a square, rectangle and parallelogram, there are two pair of parallel lines. Opposite sides of square, rectangle and parallelogram are parallel to each other.

For circle B, attribute used is parallel lines.

Find out more information about Similarities of square, rectangle and parallelogram and right triangle here

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find the volume of a cylinder with a radius of 12 cm and a height of 20 cm show work​

Answers

Step-by-step explanation:

the volume = 3.14×12²×20

= 9043.2 cm³

HELP ME PLZPLZPZLZLZLZ

Answers

Answer:

sin x° = Opposite / Hypotenuse

x = 3.38

Step-by-step explanation:

sin 70° = x / 3.6

sin 70° × 3.6 = x

x = 0.93969262079 × 3.6

x = 3.38289343483 ~ 3.38

PICTURE INCLUDED!
A circle has a center point (4,1 and a point on the circle edge of (9, 1)​

Answers

Answer:

3rd choice

Step-by-step explanation:

i found it from online

What is 3x + y = 11 ir slope-intercept form?

Answers

Answer:

y= –3x+11

Step-by-step explanation:

hope it helps...

F
110°
H
G
Find angle G

Answers

Answer:

Any picture ?

Step-by-step explanation:

what is a 10th term and the first 3 terms of :(


2
)

Answers

Step-by-step explanation:

your question is quite easy but the way you put it makes it complicated for me to understand. please can you rewrite it in a more easier way

Find the sum of the first 30 terms for the given arithmetic sequence.
8, 1, -6, -13,...
-3107
-2805
-1705
-2508

Answers

Answer:

Step-by-step explanation:

Find the last term of the sequence.

a1 = 8

d = -7

n = 30

a30 = 8 + (n - 1)*(-7)

a30 = 8 + (30 - 1)*-7

a30 = 8 + 29*-7

a30 = 8 - 203

a30 = -195

Sum = (a + L)*n/2

Sum = (8 + -195) * 30/2

Sum = - 187  * 15

Sum = - 2805

Can anyone help me with this please?

Answers

Answer:

The ones selected are correct

I need help please I don’t understand it :(

Answers

Answer:

[tex](8)[/tex] → [tex]x-(8+2)[/tex]

[tex](9)[/tex] → [tex]x+(8-2)[/tex]

[tex](6)[/tex] → [tex]5-n[/tex]

[tex](5)[/tex] → [tex]8-x[/tex]

[tex](2)[/tex] → [tex]5-n[/tex]  

[tex](7)[/tex] → [tex]x+(5+7)[/tex]

[tex](4)[/tex] → [tex]x-8[/tex]

[tex](10)[/tex] → [tex]x+x[/tex]

[tex](1)[/tex] → [tex]n+5[/tex]

[tex](3)[/tex] → [tex]x+8[/tex]

-------------------------

hope it helps...

have a great day!!

which is greater ? -9/13 and-7/12 or. -8/9 and -9/10​

Answers

Answer:

-8/9 and -9/10​ is greater

Step-by-step explanation:

Answer:

greatest is -8 / 9 and - 9 / 10

Step-by-step explanation:

-7/ 12 is greater than -9 / 13

-8 /9 and -9 / 10 are equal because

-8/9 = 0.888 if we round off it's 0.9

and - 9 / 10 is 0.9 so that's why they are equal to each other

Hope this answer helps you :)

Have a great day

Mark brainliest

the town halls of havertville and north town are shown on the map if the distance between grid lines represents 1 mile what is the distance between the two town halls? round your answer to the nearest tenth

Answers

Answer:

7.2 miles

Step-by-step explanation:

See comment for complete question.

Let:

[tex](x,y) \to Havertville[/tex]

Northtown will be represented as:

[tex](x+6,y+4)[/tex] --- i.e 6 units right and 4 units up

The distance both is calculated using:

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

This gives:

[tex]d = \sqrt{(x - (x + 6))^2 + (y -( y + 4))^2}[/tex]

Remove brackets

[tex]d = \sqrt{(x - x - 6)^2 + (y - y - 4)^2}[/tex]

Evaluate like terms

[tex]d = \sqrt{(-6)^2 + (-4)^2}[/tex]

[tex]d = \sqrt{36 + 16}[/tex]

[tex]d = \sqrt{52}[/tex]

[tex]d = 7.2\ units[/tex] -- approximated

From the question, we understand that:

[tex]1\ unit = \ mile[/tex]

So:

[tex]d = 7.2\ miles[/tex]

What is the area of the hexagon? 5 cm 8 cm 9.28 cm​

Answers

Answer:

57.12 cm²

Step-by-step explanation:

The given dimensions of the hexagon are;

The side length of the hexagon, s = 5 cm

The distance across flats = 8 cm

The distance across corners = 9.28 cm

The area of a regular hexagon, 'A', is given as follows;

[tex]A = \dfrac{3 \cdot \sqrt{3} }{2} \cdot s^2= \dfrac{1}{2} \cdot P \cdot a = 3\cdot s\cdot h[/tex]

Where;

a = The side length of the hexagon

P = The perimeter of the hexagon

h = The height of one of the triangles in the hexagon

However with the given dimensions, the area of the hexagon can be found by finding the sum of the areas of the triangles that make up the rectangle

A₁ = A₃ = A₄ = A₆ = (1/2) × 4.64 cm × 4 cm = 9.28 cm²

A₂ = A₅ = (1/2) × 5 cm × 4 cm = 10 cm₂

The area of the hexagon, A = A₁ + A₃+ A₄ + A₆ + A₂ + A₅ = 4 × A₁ + 2 × A₂

∴ A = 4 × 9.28 cm² + 2 × 10 cm² = 57.12 cm²

2 × (5×4/2 + 2×9.28/4×4) = 57.12 cm²

The area of the hexagon, A = 57.12 cm²

What is x times -3 ?

Answers

Answer:

-x3

Step-by-step explanation:

its simple x = 1

Answer:

-3x

Step-by-step explanation:

Find the arc length of XY. Round to the nearest hundredth.

Answers

Answer:

12.22

Step-by-step explanation:

Use arc length formula in degrees

(70/360) x 2 x pi x 10

A mug can hold 15.38 oz of coffee without overflowing. The radius of the mug is 4 cm. Given that 1 cm3 equals approximately 0.034 oz, what is the height of the mug to the nearest centimeter?
A. 13 cm
B. 9 cm
C. 11 cm
D. 7 cm

Answers

A . 13 cm is the correct answer

Can you please Solve for x?

Answers

tan( 31 ) = x / 39

0.600860619 = x / 39

x = 0.600860619 × 39

x = 23.433564141

______________________________

Round to the nearest tenth :

x = 23.4

Round to the nearest hundredth :

x = 23.43

the radius of a circle is 14.2 m. Find the circumference to the nearest tenth.​

Answers

Answer:

C=89.2

Step-by-step explanation:

The formula of the circumference of a circle is C=2piR (or C=piD). Now, when calculating, plug in the numbers, giving you C=2pi14.2. Multiply everything, you get a super long irrational number; just round. You will get 89.2.

The difference between two positive numbers is 5 and the square of their sum is 169. find the two numbers.

Answers

Regards, !!!
ArmyCee:)

Answer:

The two number are 9 and 13

Step-by-step explanation:

9-4=5

9+4=13 and 13*13is 169

Sue is two years older then Lily who is twice as old as Heather. if the total ages of all the girls is 27, how old is each girl?

Answers

Answer:

sue = 12

lily = 10

heather = 5

Step-by-step explanation:

'l' = lily's age

'h' = heather's age

sue = 'l + 2' but, since 'l' is 2h we can say sue's age is '2h+2'

l = 2h

2h+2 + 2h + h = 27

5h = 25

h = 5

l = 2(5) = 10

sue is 10+ 2, or 12

Y/3+y/4=5/6
Find the LCD that would eliminate the fractions

Answers

Answer:

the answer is in the picture

A rec Eric Tangler prism as shown to have of 4 cm x 2 cm x 3 cm area

Answers

4 = Length
2 = Width
3 = Height

4x2x3=24 cm square
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