A certain arithmetic sequence has this explicit formula for the nth term: an = 11 + (n – 1)(4) The same sequence has this recursive formula: an = an–1 + What number belongs in the blank space in the recursive formula?
a.15
b.11
c.3
d.4

Answers

Answer 1

Answer:

I would say D


Answer 2

Answer:

4

Step-by-step explanation:

A certain arithmetic sequence has this explicit formula for the nth term:

[tex]a_n = 11 + (n- 1)(4)[/tex]

Substitute n = 1

[tex]a_1 = 11 + (1- 1)(4)[/tex]

[tex]a_1 = 11 [/tex]

Substitute n =2

[tex]a_2 = 11 + (2- 1)(4)[/tex]

[tex]a_2 = 15[/tex]

[tex]d= a_2-a_1=15-11=4[/tex]

So,[tex]a_2=a_1+d=11+4=15[/tex] --1

Substitute n = 3

[tex]a_3 = 11 + (3- 1)(4)[/tex]

[tex]a_3 = 19[/tex]

[tex]a_3=a_2+d=15+4=19[/tex] ---2

So, with 1 and 2

Recursive formula : [tex]a_n=a_{n-1}+d[/tex]

Since d is 4

So, the number belongs in the blank space in the recursive formula is 4.


Related Questions

Please help asap 25 pts

Answers

The answer would be B because since -8 is negative, you would flip its sign


its d. i know this ive done it before


Please help me!!! will give you brainlest.

Answers

4. The translation is considered an isometry or rigid motion. The figure's size, shape, area, etc has not changed. The only thing that changed is its position.

5. The rule stated means you shift the point 3 units to the right and 4 units up.

6. The rule would be (x,y) ---> (x-1, y-3) so we effectively subtract 1 from the x coordinate; subtract 3 from the y coordinate

7. Add 2 to the x coordinate to get x+2 = 2+2 = 4. Subtract 1 from they coordinate and we have 5-1 = 4. The point ends up at (4,4). Check out the attached image below.

7. Lakeisha is designing a rectangular sunroom. She wants the room to be 14 feet wide and have a perimeter that is greater than 108 feet. Select all of the possible lengths of lakeisha’s sunroom. A. 14 feet b. 27 feet c. 40 feet d. 54 feet e. 60 feet

Answers

Answer is D and E

D : 14+14+54+54
=136 which is the perimeter is greater than 108

E: 14+14+60+60
=148 also is the greater perimeter than 108

We are required to find all the possible length of lakeisha’s sunroom

The possible length of the rectangle are length greater than 40 which are 54 feet and 60 feet

perimeter of a rectangle = 2(length + width)

perimeter > 108 feet

Width of the sunroom = 14 feet

The inequality:

2(x + 14) > 108

2x + 28 > 108

2x > 108 - 28

2x > 80

divide both sides by 2

x > 80 / 2

x > 40 feet

Therefore, the possible length of the rectangle are length greater than 40 which are 54 feet and 60 feet

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A rectangular field is 300 meters long and 250 meters wide. What is the area of the field in square kilometers

Answers

Final answer:

The area of the field is obtained by multiplying length by width resulting 75,000 square meters. Converting this to square kilometers by dividing by 1,000,000 gives the area in square kilometers as 0.075 km².

Explanation:

To calculate the area of the rectangular field, we multiply the length by the width. Given that the length is 300 meters and the width is 250 meters, the area in square meters would be 300 meters * 250 meters = 75,000 square meters.

Keep in mind that 1 square kilometer (km²) is equivalent to 1,000,000 square meters (m²). So, to convert the area from square meters to square kilometers, we divide the area in square meters by 1,000,000. Therefore, the area of the field in square kilometers is 75,000 m² / 1,000,000 = 0.075 km².

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Numerical expression for the difference between 72 and 16

Answers

Answer:

72-16

Step-by-step explanation:

Difference is represented by the subtraction of 2 numbers. If we want to represent the difference of 2 numbers, we need to subtract one number from the other number.

Simplify. (h + 12) + (p +24) a) hp + 288 b) hp + 36 c) 12h + 24p d) h + p + 36

Answers

(h+12) + (p+24)

h+p+12+24 = h+p+36

Answer:

12h + 24p

Step-by-step explanation:

Kai is making a chessboard using pieces of wood that measure 1 square inch.
when he finishes, the chessboard will have an area of 64 square inches.
how many pieces of wood should he put along each side?


a.
64 pieces of wood

b.
642 pieces of wood

c.
8 pieces of wood

d.
82 pieces of wood

Answers

Answer:

The correct option will be:   c.  8 pieces of wood.

Step-by-step explanation:

Suppose, the number of pieces of wood along each side of the chess board is  [tex]x[/tex]

The area of each piece of wood is given as 1 square inch. So, the length of each piece of wood will be: [tex]\sqrt{1}= 1[/tex] inch.

And the total length of  [tex]x[/tex]  number of pieces of wood will be:  [tex]1x[/tex] inches.

Given that, the area of the chess board is 64 square inches. So, the length of each side will be:  [tex]\sqrt{64}=8[/tex] inches.

Thus, the equation will be.........

[tex]1x=8\\ \\ x=\frac{8}{1}=8[/tex]

So, he should put 8 pieces of wood along each side.

Answer: it will be 8

Step-by-step explanation: because 8×8=64

A _______ should follow a dependent clause when the dependent clause comes first in a sentence.
1.  colon2. Comma
3. Period
4. Semicolon

Answers

I think it A hop this helps

it’s not A. colon it didn’t give me an answer

a cedar chest has a length that is 3 feet longer than its width and a height that is 1 foot longer than its width. The volume of the chest is 30 cubic feet. What is the width? 1 foot 2 feet 3 feet 6 feet

Answers

The answer is 2 feet.

Answer:

3

Step-by-step explanation:

What is the lateral area of the cylinder?
A. 515.01 ft.2
B. 615.85 ft.2
C. 622.04 ft.2
D. 625.25 ft.2

Answers

Lateral area = circumference of circular  end * length

=  pi * diameter * length

= 22 * pi * 9

= 198 pi

= 622.04 ft^2  answer   Its C

Bob earns $9 an hour babysitting. One night he earned $47.25 for babysitting. How many hours did he babysit that night?

Answers

47.25/9 = 5.25 hours or 5 1/4 hours

How many cubes are needed to build the base of this structure?

Answers

10 cubes for the base

Answer:

Option (D) 10 cubes

Step-by-step explanation:

The given structure is formed by assembling the cubes.

Number of cubes required for upper layer of the structure = 7 cubes

Now we have to find how many cubes will be required to form the lower layer of the structure.

From the structure ⇒

Cubes in lower layer = cubes in upper layer + 3 more cubes

                                  = 7 + 3 = 10 cubes

Therefore, 10 cubes will be required to form the base of the structure.

Option (D) 10 cubes is the answer.

What is half of 5 3/4?

Answers

2 7/8 is half of 5 3/4

Which graph represents the solution set of the system of inequalities?
{y≥1/3x−3
{y<−3x−3

Answers

The answer would be the choice at the bottom right corner!

I'm positive the answer is correct! :)

Find the width (w)of a rectangular room with a length (l) of 60 meters and an area (a) of 2,400 square meters

Answers

To find the area of a rectangular shape, we need to have the length and width of the shape.

Here the room is rectangular in shape.

The length of the room is 60 meters and lets say the width of the room is 'w' meters.

The area of room is given which is 2,400 square meters.

The area of rectangle is given by:

[tex]length \times width[/tex]

Now, plugging the values of the length and width, we get:

[tex]Area = 60 \times width[/tex]

[tex]2400= 60 \times width[/tex]

Solving for width, we get:

[tex]Width= \frac{2400}{60} =40[/tex] meters.

So, the width of the rectangular room is 40 meters.

Answer:The answer is

Step-by-step explanation: W= 40 I just did the quiz on I ready

On six books shelves there are 72 books per shelf.How many books are there altogether? If 1/3 of these are non-fiction how many fictional books are there?

Answers

Answer:Part 1:

Given:

Total shelves: 6

Books per shelve: 72

Total books = ?

Solution:

Total books: 6 * 72 = 432

                                                           Total books = 432

Part 2:

Given:

Fiction books = 1/3 of total books

Solution:

Nonfiction books = Total books - 1/3 of total books

                              =   432 - 1/3 * 432

                               = 432 - 166 = 266

                                           Non- fiction books = 266

Solve by factoring 2x squared -6 = x squared+48

Answers

x = ± 3√6

2x² - 6 = x² + 48 ( subtract x² from both sides )

x² - 6 = 48 ( add 6 to both sides )

x² = 54 ( take the square root of both sides )

x = ± √54 = ± 3√6


-(2)/(5)x-9<(9)/(10)


step by step please <3

Answers

[tex]-\dfrac{2}{5}x-9<\dfrac{9}{10}\qquad|\text{multiply both sides by 10}\\\\10\cdot\left(-\dfrac{2}{5}x\right)-10\cdot9<10\cdot\dfrac{9}{10}\\\\2(-2x)-90<9\qquad|\text{add 90 to both sides}\\\\-4x<99\qquad|\text{change the signs}\\\\4x>-99\qquad|\text{divide both sides by 4}\\\\x>-24.75[/tex]

2.8 x 100 miles high. What is the approximate area of wyoming?

Answers

Assuming a regularly shaped rectangle, the formula for the area is given as:


A = L * W


where L and W are the length and width respectively


A = 3.6 x 10^2 miles * 2.8 x 10^2 miles


A = 100,800 square miles


or


A = 10.08 x 10^2 miles 


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please help on this one ?

Answers

c. y= [25,100]
you need brackets because the points actually touch the number

y [25, 100] is the range of the population of Blue Whales off the coast of Antarctica from months 5 to 10.

Therefore, the correct answer is:

C. y [25, 100]

Here,

To find the range of the population of Blue Whales off the coast of Antarctica from months 5 to 10,

we need to determine the minimum and maximum values of the population during this period based on the graph.

From the graph, we can see that the population values are between approximately 25 and 100 (inclusive) during months 5 to 10.

The square brackets [ ] denote that the endpoints are included in the range.

so, we get,

y [25, 100] is the range of the population of Blue Whales off the coast of Antarctica from months 5 to 10.

Therefore, the correct answer is:

C. y [25, 100]

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If a insect is 0.095 long how long is it if looking through a microscope 100 times how long would the insect be

Answers

9.5.....................


For carolina birthday her mom took her and 4 friendse to a waterpark.Carolina mom paíd 40 for 5 students tickets.What was the price for one student ticket

Answers

40 dollars per 5 students=9 dollars per 1 student

divide both sides by 5.

Which statement represents the biconditional statement of the conditional statements?

If the measures of two angles have a sum of 90º, then the angles are complements.

If two angles are complements, then their measures have a sum of 90º.




The measures of two angles do not have a sum of 90º if and only if the angles are complements.

The measures of two angles have a sum of 90º if and only if the angles are complements.

The measures of two angles do not have a sum of 90º if and only if the angles are not complements.

The measures of two angles have a sum of 90º if and only if the angles are not complements.

Answers

The measures of two angles have a sum of 90º if and only if the angles are complements.

if the angles are complementary they have to equal 90 otherwise they are not complementary

The measures of two angles have a sum of 90º if and only if the angles are complements.

if the angles are complementary they have to equal 90 otherwise they are not complementary

In one study, it was found that the correlation coefficient between two variables is -0.93.

Which statement is true?

A. There is a weak positive association between the variables.

B. There is a weak negative association between the variables.

C. There is a strong positive association between the variables.

D. There is a strong negative association between the variables.

Answers

the answer is d (i think) because anything aboveboard .90, whether it is positive or negative

Answer: D. There is a strong negative association between the variables.

Step-by-step explanation:

We know that when the value of the correlation coefficient lies between -1 to -.05 , then we say there is strong negative correlation between the variables.

OR

When the value of the correlation coefficient lies between 0.5 to 1, then we say there is strong positive correlation between the variables.

Given : In one study, it was found that the correlation coefficient between two variables is -0.93.

∵ -1< -0.93 <-0.5

Then , it  indicates that there is a strong negative association between the variables.

What is a correct congruence statement for the triangles shown?



Enter your answer in the box.

​ △ ______≅△NKW ​

Answers

For this one, look at the symbols inside each angle.  In math, the rounded edges inside of angles mean they are congruent.  So find which ones have the same amount of rounded edges and that would be your answer.

NKW ≅ UZE

put the corresponding angles in the middle.  Since the object you were comparing to had the one line as the middle point, then that is your middle as well.

Hope this helps! Comment with any questions you may have.

Answer:

[tex]\Delta UZE\cong \Delta NKW[/tex]

Step-by-step explanation:

We have been given a graph of two triangles and we are asked to find the correct congruence statement for our given triangles.

We can see in triangle NKW and triangle UZE.

[tex]EZ\cong WK[/tex],

[tex]\angle ZEU\cong \angle KWN[/tex],

[tex]\angle UZE\cong \angle NKW[/tex].

Since two angles and included side of triangle NKW is congruent to two angles and their included side of triangle UZE, therefore, [tex]\Delta UZE\cong \Delta NKW[/tex] by Angle-Side-Angle congruence theorem.

A news report says that 28% of high school students pack their lunch. Your high school has 60 students. How many students in your high school would you expect to pack their lunch?

Answers


[tex] \frac{28}{100} \times 60 = 16.8[/tex]

Ben has 3 times as many guppies as goldfish.If he had a total of 20 fish,how many guppies does he have

Answers

Answer: 60 Guppies.


Step-by-step explanation: If Ben has 3 times as much guppies as goldfish then it is 3 x 20 which = 60.


-4 < -2(2 + 7x) + 6(x + 8)

Please help and show work!!

Answers

[tex]-4 < -2(2+7x)+6(x+8)\ \ \ \ |\text{use distributive property}\\\\-4 < (-2)(2)+(-2)(7x)+(6)(x)+(6)(8)\\\\-4 < -4-14x+6x+48\\\\-4 < (-14x+6x)+(-4+48)\\\\-4 < -8x+44\ \ \ \ |+4\\\\0 < -8x+48\ \ \ \ |+8x\\\\8x < 48\ \ \ \ |:8\\\\\boxed{x < 6}[/tex]

The blueprint for landscaping a yard has a scale of 1/2" to 1 foot. If the bloeprint is a rectangle 18inches by 22 inches, what are the dimensions of the yard

Answers

Answer:

36x44 feet are the dimensions of the yard.

Step-by-step explanation:

Given that the blueprint for landscaping a yard has a scale of 1/2" to 1 foot.

i.e. scaling factor is 1/2 for one foot.

If real dimension is 1 foot, it is shown as 1/2 inch in blue print.

Using this we can find the real dimensions if given blue print dimensions.

The blueprint is a rectangle 18inches by 22 inches,

Hence real length of rectangle = 18(2) feet = 36 feet

Width of rectangle = 22(2) = 44 feet

i.e. the yard has dimensions as 36x44 feet.

At a college, 7 out of every 10 students worked either a full-time or part-time job in addition to their studies. If 4,900 students were enrolled at the college, how many students did not have a full-time or part-time job?

Answers

Remark

If 7/10 do have full or part time jobs then 3/10 do not.

That comes from 1 which represents all the students subtract 7/10 to get 3/10

Solution

Those without jobs = 4900 * 3/10 = 4900 *0.3 =  1470 that do not have any kind of job.

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