Find the nth term -1 8 19 32 47

Answers

Answer 1

[tex]\bold{\text{Answer:}\quad \text{Recursive formula:}\ a_n=a_{-1}+2n+5}\\.\qquad \qquad \ \text{Explicit formula:}\ a_n=2n^2+3n-6[/tex]

Step-by-step explanation:

-1 → 8 = +9

8 → 19 = +11

19 → 32 = +13

32 → 47 = + 15

a₁ = -1

d = 2n + 5

Recursive formula is: the previous term plus the difference (d)

                               [tex]\large\boxed{a_n=a_{n-1}+2n+5}[/tex]

Explicit formula is the first term plus the product of d and n-1:

[tex]a_n=a_1+d(n-1)\\a_n=-1+(2n+5)(n-1)\\a_n=-1+2n^2-2n+5n-5\\\large\boxed{a_n=2n^2+3n-6}[/tex]


Related Questions

I'll always give away 5 stars, thanks and Brainliest to the answer that's correct!
Naruto has a baseball card that is worth $45. The value of the card is increasing at the rate of 1.5% per year. How much will the card be worth in 15 years?
A: $366.17
B: $56.26
C: $89.21
D: $263.97

Answers

Answer:

a I believe sorry if I'm wrong

Answer:

I think its B: $56.26

A machine can wrap 360 packages of muffins in 12 minutes. At this rate, how
many packages will be wrapped in 1 hour?*

Answers

Answer:

1800 (packages )muffins

Step-by-step explanation:

360  muffins         x muffins

--------                 =    --------

12 min                       60 min

Answer:

1800 maybe

Step-by-step explanation:

in 12 minutes can wrap 360

in 1 hr have 60 minutes

60/12=5

than 360*5 = 1800

I need help please help

Answers

Answer:

21u-16v+18w

Step-by-step explanation:

(7u-4v+4w) 14u-12v+14w

21u-16v+18w

Answer:

= 21u−16v+18w

Step-by-step explanation:

Let's simplify step-by-step.

7u−4v+4w−2(−7u+6v−7w)

Distribute:

=7u+−4v+4w+(−2)(−7u)+(−2)(6v)+(−2)(−7w)

=7u+−4v+4w+14u+−12v+14w

Combine Like Terms:

=7u+−4v+4w+14u+−12v+14w

=(7u+14u)+(−4v+−12v)+(4w+14w)

=21u+−16v+18w

Answer:

=21u−16v+18w

PLEASE HELP ASAP THANKSSSS

Answers

Answer:

The correct answer is C

Step-by-step explanation:

As you can see Town A is on top of Town B this means that Town B has symetric points to town A. This also shows how Town A is Positively skewed.

the price of a CD was decreased by 2% to £14. what was the price before the decrease?

Answers

Answer:

£14.29

Step-by-step explanation:

0.98x=14

x=14.29

Answer:

14.28

Step-by-step explanation:

In a group of 45 students, 5 study both Art and Biology. 8 study Biology but not Art. 9 study neither subject. Given that a randomly selected student studies Art, what is the probability the student studies Art and Biology?

Answers

Answer:

[tex]\frac{1}{9}[/tex]

Step-by-step explanation:

Data provided in the question

There is a total group of 45 students

Art + biology = 5

8 study biology but not Art

Neither subject studied = 9

Based on the above information, the probability of student that studies

art and biology is

Since there is a group of 45 students out of which 5 study both art and biology

So, the ratio is

4: 5

Now divide both sides by 5

So, now the ratio is

9:1

Therefore it means the probability is [tex]\frac{1}{9}[/tex]

The police department uses a formula to determine the speed at which a car was going when the driver applied the breaks, by measuring the distance of the skid marks.The equation d=0.03r^2+r models the distance, d, in feet, r miles per hour (r is the speed of the car) Factor the equation. d=?

Answers

Answer:

0.03 feet

Step-by-step explanation:

d = 0.03r² + r

When d = 0: 0.03r² + r = 0

r(0.03r + 1) = 0

∴ r = 0

When r = 0: d = 0.03 feet

what is the volume of the cylinder below?​

Answers

Answer:

A

Step-by-step explanation:

vol of a cylinder = pie* r^2×h

r= 5

h= 9

......vol= 9×5^2 pie= 225pie units ^3

A square has side length x and a circle has radius (x - 1). At what value of x will the two figures have the same area?

Answers

Answer:

x=(π+√π)/1-π

or x=(π-√π)/1-π

Step-by-step explanation:

since it is a square all sides are equal

Area of square=x*x=x^2

Area of a circle=πr^2

A=π(x-1)^2

two areas are equal

x^2=π(x^2-2x_1)

x^2=πx^2-2πx-π  

x^2-πx^2-2πx-π=0

x^2(1-π)-2πx-π=0  

using quadratic formula with a=1-π , b=-2π and c=-π

equation of the form ax^2+bx+c=0 by using the quadratic formula:

x=(−b±√b2−4ac)/2a

x=(π+√π)/1-π

or x=(π-√π)/1-π

HELP ASAP PLEASE What is the measure of yz (the minor arc) in the diagram below? A.168 B.42 C.192 D.84

Answers

Answer:

B

Step-by-step explanation:

The measure of the tangent- chord angle XYZ is half the measure of its intercepted arc, thus

arc YZ = 2 × 84° = 168° → B

In a local ice sculpture contest, one group sculpted a block into a rectangular-based pyramid. The dimensions
of the base were 3 m by 5 m, and the pyramid was 3.6 m high. Calculate the amount of ice needed for this
sculpture

Answers

Answer:

Step-by-step explanation:

To calculate the amount of ice needed for this sculpture, we would apply the formula for determining the volume of a rectangular base pyramid which is expressed as

Volume = 1/3 × base area × height

Since the base is rectangular, base area = length × width = 3 × 5 = 15 m

Given that height = 3.6m, therefore, the amount of ice needed for this sculpture is

1/3 × 15 × 3.6 = 18 m³

Answer: To calculate the amount of ice needed for this sculpture, we would apply the formula for determining the volume of a rectangular base pyramid which is expressed as Volume = 1/3 × base area × heightSince the base is rectangular, base area = length × width = 3 × 5 = 15 mGiven that height = 3.6m, therefore, the amount of ice needed for this sculpture is 1/3 × 15 × 3.6 = 18 m³

Step-by-step explanation:

A man has a 10m X 10m square garden. In the center is a 2m X 2m square patch which he cannot use. He divides his usable space into four congruent rectangular patches, each of which measures

Answers

Answer:

4m X 6m

Step-by-step explanation:

This is because if there is a 2m square in the middle, there is 8 m of usable space left along both sides of the garden.

Because the 2m square was in the middle, there is 8/2 = 4m along each width of the 4 small rectangles.

Becuase 4m is the width, there is 10 - 4 = 6m along each rectangle's length.

The 4m is the width, there is 10 - 4 = 6m along each rectangle's length. the area he will use is 4m x 6m.

What is reflexive property of congruence?

The reflexive property of congruence says that the considered geometric quantity, whether it be angle, line segment, or shape etc, is congruent to itself.

Given information; A man has a 10m X 10m square garden. In the center is a 2m X 2m square patch we need to find which he cannot use.

He divides his usable space into four congruent rectangular patches.

If there is a 2m square in the middle, there is 8 m of usable space left along both sides of the garden.

The 2m square was in the middle, there is 8/2 = 4m along each width of the 4 small rectangles.

The 4m is the width, there is 10 - 4 = 6m along each rectangle's length.

Learn more about congruent triangles here:

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Which of the following investments could be represented by the function A = 250(1 + 0.08/12)12 × 4?

Answers

hello,

the first term is 250 so this is the initial invested amount

[tex](1+\dfrac{0.08}{12})^{12}=(1+\dfrac{8\%}{12})^{12}[/tex]

is to compute 8% annual interest compounded monthly (there are 12 months in a year)

and then multiply by 4 means that it is computed for 4 years so

finally the answer is

$250 is invested at 8% annual interest compounded monthly for 4 years

hope this helps

Complete the equation of the line through (-8,8)(−8,8)left parenthesis, minus, 8, comma, 8, right parenthesis and (1,-10)(1,−10)left parenthesis, 1, comma, minus, 10, right parenthesis.

Answers

Answer:

[tex]y = -2x - 8\\OR\\2x+y+8=0[/tex]

Step-by-step explanation:

Given that there are 2 points

[tex]A(-8,8)[/tex] and

[tex]B(1,-10)[/tex]

So, the coordinates are:

[tex]x_2 = 1\\x_1 = -8\\y_2 = -10\\y_1 = 8[/tex]

Equation of a line is given as:

[tex]y =mx+c[/tex]

where 'm' is the slope of the line, formula for 'm' is given as:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex](x,y)[/tex] are the points that satisfy the equation of the line.

[tex]c[/tex] is the [tex]y -[/tex] intercept.

Calculating the value of m using the given coordinates:

[tex]m=\dfrac{-10-8}{1-(-8)}\\\Rightarrow m=\dfrac{-18}{9} = -2[/tex]

So, the equation of line becomes:

[tex]y =-2x+c[/tex]

Now, putting the coordinates of point [tex]A(-8,8)[/tex]

[tex]8 =-2\times (-8)+c\\\Rightarrow 8 = 16+c\\\Rightarrow c = -8[/tex]

Please refer to the graph of given equation of line.

The equation of line is:

[tex]y =-2x+-8\\OR\\2x+y+8=0[/tex]

Which of the following are solutions to the equation below?
Check all that apply.
x2 + 4x-9 = 5x + 3
A. -3
B. 5
| C. 2
D. -4
E. 4
F-7

Answers

Answer:

The answers are options A and E

x² + 4x-9 = 5x + 3

Group like terms

x² + 4x - 5x - 9 - 3 = 0

x² - x - 12 = 0

Using factorization method

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

x = - 3 x = 4

Hope this helps

Which statement is true about the equations –3x + 4y = 12 and 1/4x-1/3y=1

Answers

Answer: No solution

Step-by-step explanation:

This system of equation has no solution because...

-3x+4y=12

1/4x-1/3y=1

[tex]-3x+4y-4y=12-4y[/tex]

[tex]-3x=12-4y[/tex]

[tex]\frac{-3x}{-3}=\frac{12}{-3}-\frac{4y}{-3}[/tex]

[tex]\frac{12}{-3}-\frac{4y}{-3}[/tex]

[tex]x=-\frac{12-4y}{3}[/tex]

substitute

[tex]\frac{1}{4}\left(-\frac{12-4y}{3}\right)-\frac{1}{3}y=1[/tex]

[tex]-1=1[/tex]

-1=1 is false so therefore this system has no solution

Write 23 /2 as a mixed number. Give your answer in its simplest form.

Answers

Answer:

11 1/2

Step-by-step explanation:

Convert improper fraction to mixed number

23 over 2

= 11 and 1/2

23 ÷ 2 = 11 remainder 1

Answer:

11whole,1 and a half

Step-by-step explanation:

divide 23 by 2

y=(x+9)÷(x-3)
Find the value of y when x=5​

Answers

Answer:y=7

solution,

X=5

[tex]y = \frac{x + 9}{x - 3} \\ = \frac{5 + 9}{5 - 3} \\ = \frac{14}{2} \\ = 7[/tex]

hope this helps...

Good luck on your assignment..

Answer:

When x=5

Y=(5+9)÷(5-3)

= 14 ÷2

= 7

Mrs. Brown has 11 more boys than girls in her class and has a total of 28 students. Which of the following systems of equations could be used to solve this problem?

Answers

Answer:

g=number of girls in the class b=number of boy in the class

g+b=28

g=11+b

slove all of it please 100 points

Answers

Answer:

Step-by-step explanation:

5x+y-7=0 isolate y

y=-5x+7 (m=-5,b=7)

9x+7y-14=0

7y=14-9x ( divide both sides by 7)

y=-9x/7 +14/7

y=-9/7 + 2  (m=-9/7, b=2)

x+y=1000

4x+3y=3600 ( multiply the first equation by 3 to eliminate y)

3x+3y=3000

4x+3y=3600 ( subtract the two equations)

3x+3y-(4x+3y)=3000-3600

3x+3y-4x-3y=-600

-x=-600

x=600 ( substitute x in the equation)

x+y=1000

600+y=1000

y=1000-600=400

check : x+y=1000 , (600+400)=1000

check : 4x+3y=3600 = (4(600)+3(400))=2400+1200=3600

how many tickets are sold :

adults x=600/4=150

kids (y)=400/3=133 tickets+1 dollars left

unless( x represent kids then x=200, y represent adult = 100)

Answer:

[tex]\boxed{\mathrm{view \: explanation}}[/tex]

Step-by-step explanation:

Question 1:

[tex]5x+y-7=0[/tex]

Write in slope intercept form.

[tex]y=-5x+7 \\m=-5,b=7\\9x+7y-14=0[/tex]

Write in slope intercept form.

[tex]7y=14-9x\\y=-9x/7 +14/7\\y=-9/7 + 2\\m=-9/7, b=2[/tex]

Question 2:

[tex]x+y=1000\\4x+3y=3600[/tex]

[tex]3x+3y=3000\\4x+3y=3600\\3x+3y-(4x+3y) = 3000-3600\\3x+3y-4x-3y=-600\\-x=-600\\x=600[/tex]

[tex]x+y=1000\\600+y=1000\\y=1000-600=400[/tex]

Tickets sold:

Adults:

[tex]x=600[/tex]

Kids:

[tex]y=400[/tex]


Which of the following is the equation of a line that passes through the point
(3.2) and is parallel to the yaxis?

Answers

Answer:

y=2 is the correct ans.

here, tge equn of st line passing through the point (3,2) and is also parallel to y axis.

we have, equn of st line parallel to y xaus is y= b

so , the equn of st line passing through the point (3,2) is y= 2 (where 2 is likely to b).

The answer to your question is y=2

Through any 2 points there is exaclty_____line.

Answers

Answer:

One

Step-by-step explanation:

Through any 2 points, there is exactly one line.

Answer:

ONE

Step-by-step explanation:

Through any 2 points there is exaclty ONE line.

find a18 of the arithmetic sequence 2, -5, -12, -19

Answers

Answer:

The 18th term of the sequence is -117.

Step-by-step explanation:

The given sequence is 2,-5,-12,-19

From this AP,

First term, a = 2

Common difference, d = -5-2 = -7

It is required to find the 18th term of the sequence. The nth term of an AP is given by :

[tex]a_n=a+(n-a)d\\\\a_{18}=a+17d\\\\a_{18}=2+17\times (-7)\\\\a_{18}=-117[/tex]

So, the 18th term of the sequence is -117.

Which expression is equivalent to.......


See pictures

Answers

Answer:

[tex] \sqrt{ {2}^{5} } [/tex]

Step-by-step explanation:

[tex]\huge \bigg( {2}^{ \frac{1}{2} }. {2}^{ \frac{3}{4}} \bigg)^{2} \\ \\ \huge = {2}^{ \frac{1}{2} \times 2 }. {2}^{ \frac{3}{4} \times 2} \\ \\ \huge = 2 \times {2}^{ \frac{3}{2} } \\ \\ \huge = {2}^{ \frac{3}{2} + 1 } \\ \\ \huge = {2}^{ \frac{3 + 2}{2} } \\ \\ \huge = {2}^{ \frac{5}{2} } \\ \\ \huge = \sqrt{ {2}^{5} } [/tex]

A grasshopper makes jumps that are either 17 or 19 cm in length, in either direction (forwards or backwards). Is it possible for the grasshopper to cover a distance of 101 cm in 100 jumps?

Answers

Answer:  No. The grasshopper cannot cover exactly 101 cm in exactly 100 jumps.

Step-by-step explanation:  

If the grasshopper makes 50 forward jumps of 19 cm and 50 backward jumps of 17 cm (in any order) the jumps total 950-850 for a net result of 100.

Changing to any other amount just gets farther away from the goal.

A system of equations yields no solution of integers.

x + y ==100

19x - 17y =101

You can try it, but the result has a decimal. This grasshopper cannot make partial jumps!

what number decreased by 6 equals 3 times the number

Answers

Answer:

-3

Step-by-step explanation:

x-6=3x

2x=-6

x=-3

The required number is -3 decreased by 6 equals 3 times.

A number to be determine when decreased by 6 equals 3 times the number.

What is arithmetic?

it explores the numbers of operations according to the statements.

Let the number be x,
Now,
x-6=3x
x= -3

Thus, the required number is -3 decreased by 6 equals 3 times.

Learn more about arithmetic here:

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A 7-column table with 2 rows. Column 1 is labeled Sample with entries catfish, all fish. Column 2 is labeled 1 with entries 3, 20. Column 3 is labeled 2 with entries 5, 20. Column 4 is labeled 3 with entries 7, 20. Column 5 is labeled 4 with entries 5, 20. Column 6 is labeled 5 with entries 6, 20. Column 7 is labeled 6 with entries 8, 20. The mean number of catfish in all 6 samples is approximately 5.7. If 200 fish are in the pond, which proportion can be used to predict the number of catfish in the population? StartFraction 5.7 over 20 EndFraction = StartFraction x over 200 EndFraction StartFraction 5.7 over 20 EndFraction = StartFraction 200 over x EndFraction StartFraction 34 over 20 EndFraction = StartFraction x over 200 EndFraction StartFraction 8 over 20 EndFraction = StartFraction 20 over x EndFraction

Answers

Answer: The correct option is 5.7/20 = x/200

Step-by-step explanation: Please refer to the diagram attached for more details.

From the 7-column by 2-row table drawn, you can determine that the mean number of catfish as given in the question is derived as follows;

Mean = Summation of observed data / Number of observations

Mean  = (3 + 5 + 7 + 5 + 6 + 8)/6

Mean = 34/6

Mean = 5.6667

Mean ≈ 5.7

Also the mean number of all fish is derived as follows;

Mean = Summation of observed data / Number of observations

Mean = (20 + 20 + 20 + 20 + 20 + 20)/6

Mean = 120/6

Mean = 20

Using relative frequency, we can confidently predict the number of catfish population in the pond. This simply means, if the mean number of catfish is 5.7 and the mean number of all fish is 20, then the relative frequency would be 5.7 over 20 of the total fish population.

Hence, if there is a total of 200 fish in the pond then to predict the proportion which would be catfish can be expressed as follows;

StartFraction 5.7 over 20 EndFraction = StartFraction x over 200 EndFraction.

OR better expressed as;

5.7/20 = x/200

Answer:

5.7/20 = x/200

Step-by-step explanation:

The play director spent 190190190190 hours preparing for a play. That time included attending 35353535 rehearsals that took varying amounts of time and spending 933493 \dfrac{3}{4}9343​93, start fraction, 3, divided by, 4, end fraction hours on other responsibilities related to the play. What question does the equation 35x+9334=19035x+93\dfrac{3}{4}=19035x+9343​=19035, x, plus, 93, start fraction, 3, divided by, 4, end fraction, equals, 190 help answer?

Answers

Answer:

The equation above represents the total time the play director spent preparing for a play.

Step-by-step explanation:

The time spent by the play director for preparing for a play is, 190 hours.

Of these 190 hours, the director spent varying amounts of time attending 35 rehearsals for the play.

Let the varying amounts of time be denoted by, x.

The director also spent 3/4th of an hour, i.e. 45 minutes, on other responsibilities related to the play.

The equation provided is:

[tex]35x+\frac{3}{4}=190[/tex]

The equation above represents the total time the play director spent preparing for a play.

Which equation represents a graph with a vertex at (-1,6)?

Answers

Answer:

B. [tex]y = 3x^2 -6x -3[/tex]

Step-by-step explanation:

Well, we can use the following formula to find the x coordianate of the vertex  -b / 2a.

So let’s start with a)

-6 / 6

-1

A. is wrong because its vertex starts with -1.

b)

6 / 6

1

now that we have our x coordinate we can plug it into the equation to get our y.

3 - 6 - 3

So the y coordinate is -6.

Hence, the answer choice B. [tex]y = 3x^2 -6x -3[/tex]

look at the image below.

which term of the AP:3,15,27, 39,.....will be 132 more than its 54th term​

Answers

Answer:

n=65th term

Step-by-step explanation:

AP:3,15,27,39......

From the AP

a=3

a+d=15

a+2d=27

3+d=15 (1)

3+2d=27 (2)

Subtract (1) from (2)

We have,

2d-d=27-15

d=12

54th term=a+(n-1)d

=3+(54-1)12

=3+(53)12

=3+636

=639

The term is 132 more than the 54th term

132+54th term

=132+639

=771

Find the term

771=a+(n-1)d

771=3+(n-1)12

771-3=12n-12

768=12n-12

768+12=12n

780=12n

n=780/12

=65

n=12

The term which is 132 more than the 54th term is the 65th term

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