The sum of 28 consecutive odd positive integers is a perfect cube. Determine the smallest possible set? What is the first and last terms in the sequence. Plz helppp!

Answers

Answer 1

Answer:

71 + 73 + ..... + 125 = 2,744 = [tex]14^{3}[/tex].

Step-by-step explanation:

The smallest set starts at 71.  The last term is 125.

The total is 2,744, which is [tex]14^{3}[/tex].

Answer 2

The smallest possible set is 71,73,75,....125. The first and last terms in the sequence is 71 and 125 respectively.

What is airthmatic sequence?

Geometric sequence is the sequence in which the next term is obtained by adding or substracting the previous term with the same number for the whole series.

The sumation of airthmatic sequence is find out using the following formula.

[tex]S=\dfrac{n}{2}(a+l)[/tex]

Here, (a) is the first term of the sequence, (l) is the last term and (n) is the number of terms in sequence.

Let x is the first and the smallest term of the set.  This set consists 28 consecutive odd positive integers. Thus, the sum of this set will be,

[tex]\sum=x+(x+2)+(x+4)+...+(x+54)\\\sum=28x+(2+4+6+....+54)\\\sum=28x+[\dfrac{27}{2}(2+54)]\\\sum=28x+756\\\sum=28(x+27)\\\sum=2\times2\times7(x+27)[/tex]

Now here 7 is prime number. The value of (x+27) should be perfect square of 7 and 2 to make it perfect cube. thus,

[tex]x+27=7^2\times2\\x=98-27\\x=71[/tex]

Put this value to find the sequence as,

[tex]71,71+2,71+4......,71+34\\71,73,75,.......125[/tex]

The first term in this set is 71 and last term is 125.

Hence, the smallest possible set is 71,73,75,....125. The first and last terms in the sequence is 71 and 125 respectively.

Learn more about the airthmatic sequence here;

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Related Questions

Hi My Name Is Christine I am New on here and I need help on math I'm usually good at it but I need help please
Also before I put the question I need a Boy Named Scott They always seem to be smart So if your name is Scott HELP
5x-3x+58=?

Answers

Answer: 2x+58

Step-by-step explanation:Combine Like Terms:

=5x+−3x+58

=(5x+−3x)+(58)

=2x+58  

What is the density of an object that has a mass of 20 grams and has a length of 8cm and a width of 2cm and a height of 5cm????

Answers

Answer:

Volume is the amount of space an object occupies. To determine the volume of any rectangular object, multiply the measurements of length, width, and height.

Volume = Length × Width × Height

Calculate the volume of this rectangular object.

Length = 3 cm

Width = 3 cm

Height = 12 cm

Volume = l × w × h

Volume = 3 cm × 3 cm × 12 cm

Volume = 108 cm3

Notice that the units for volume are cubic centimeters (cm3).

So 8 ÷ 25 = 0.32 and the units would be g/ cm3 . Other units of density could be g/L or g/ml or mg/ cm3 or kg/ m3 and the list could go on and on. Any unit of mass divided by any unit of volume.

Step-by-step explanation:

hope this helpa

please hurry!!!! look at screenshot!!

Answers

Answer:

BCD= 15

Step-by-step explanation:

3x-15+?=180

3x=180

x=60

x=60

3(60)-15=180

180-15=165

What number must be placed in the box in the equation below to produce an equation that has more than one solution: 5u+3(4u-6)=-3u-27+20u+ ▢

Answers

Answer: the number must be placed in the box is 9

suppose: the number must be placed in the box is x

have:

5u + 3(4u - 6) = -3u -27 + 20u + x

⇔ 5u + 12u - 18 = -3u - 27 + 20u +x

⇔ 17u + 3u - 20u = -27 + 18 + x

⇔ 0 = x - 9

⇔ x = 9

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

Simplifying both sides gives 

17u - 18 = 17u - 27 + ▢.

Subtracting 17u from both sides gives

-18 = -27 + ▢. 

If the number in the box is anything but 9, then the equation cannot be true, and the original equation has no solutions. If the number in the box is 9, then the two sides of the original equation are equivalent, and all values of u are solutions to the equation.

Simple stuff
5+5=______

Answers

Answer:

10?

Step-by-step explanation:

Which equation represents the line with a slope of
5
6
that passes through the point
(

2
,
1
)
?

Answers

Can you re write The Question?

r numbers 13 - 17, use f(x) =
3x – 9
1+1
13) Where is the y-intercept?
A. (0-9)
B. (0,-1)
C. (0, -3)
D. (0,9)

Answers

Answer:

A is correct

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

13-17=-4

f(3x-9)=6xwhere you f=6x-4=

Solve.

-11 2/3 x (-4 1/5)=

A.44 2/15

B.-44 2/15

C.49

D.-49

Answers

C: 49

To get this answer first you want to covert the mixed number into an improper fraction and you will get -35/3 x (-21/5). Next you reduce the numbers with the greatest common factor and you should get 7x7. Then finally you multiply and get your answer 49.

Mia has $50 on a gift card to her favorite coffee shop. Each time she visits the coffee shops she spends $3.75 on her favorite drink. Choose the equation that represents the relationship between x, the number of times she visits the coffee shop, and y, the total amount on her gift card.

Answers

Given:

Value of Gift card = $50

Each time she visits the coffee shops she spends $3.75 on her favorite drink.

To find:

The equation for the given situation.

Solution:

Let x be the number of times she visits the coffee shop, and y be the total amount on her gift card.

Cost of her favorite drink for one time = $3.75

Cost of her favorite drink for x times = $3.75x

Value of gift card is $50. So,

Amount on her gift card = 50 - Cost of her favorite drink for x times

[tex]y=50-3.75x[/tex]

Therefore, the required equation is [tex]y=50-3.75x[/tex].

Brady went on a field trip to the water park. The cost of the trip was $19.99 to get into the park. He bought a hot dog for $3.50 and spent $2.10 on gas money. How much money did Brady spend?

Answers

Given:

Cost of the trip to get into the park = $19.99

Brady bought a hot dog for $3.50 and spent $2.10 on gas money.

To find:

The total money Brady spend.

Solution:

It is clear that,

Total money he spend = Cost of the trip to get into the park + Cost of a hot dog + Amount he spent on gas money

On substituting the values, we get

Total money he spend = $19.99 + $3.50 + $2.10

                                      = $25.59

Therefore, the total money Brady spend is $25.59.

Which of the following numbers ordered from least go gratest?


0.5, 5/8, 65%, 3/5.

Answers

Answer:

0.5 3/5 5/8 65%

Step-by-step explanation:

Answer:

Your answer is 0.5, 3/5, 5/8, 65%.

Step-by-step explanation:

Convert all numbers to decimals:

0.5 = 0.5

5/8 = 0.625

65% = 0.65

3/5 = 0.6

Arrange the numbers accordingly: 0.5, 0.6, 0.625, 0.65. Hence, your answer is 0.5, 3/5, 5/8, 65%.

shala bought a pen on sale. she saved 17 percent of the original price of 29$. about how much money did she save?
A.1$
B.5$
C.10$
E.20$

Answers

Answer:

B or E im not sure

Step-by-step explanation:

$4.93

Step-by-step explanation

That's the exact answer but going of your answers it'll be 5$

Discount:

(29 x 17)/100 = $4.93

Final Price:

29 - 4.93 = $24.07

Answer:

the answer for edge 2021 is 5

Step-by-step explanation:

Please mark brainliest

PLEASE HELP FAST!!!!
factor completely: 5x^3+40x^2-2x-16

Answers

Answer:

(x+8)(5x2−2)

Step-by-step explanation:

Hope this helps have a nice day :)

what is 3 times piy time 53 divided by 72

Answers

Answer:

6.93768377668

Step-by-step explanation:

confusion

Shean has a piece of string 7/8 meter long. He uses 1/5 of he piece of string to tie a package and cuts the rest into 5 equal parts. What is the length of the pieces.

Answers

Answer:

7/50 meter

Step-by-step explanation:

Total piece of string = 7/8 meter

Used string = 1/5 of the piece of string

Used string =

1/5 of 7/8 meter

= 1/5 × 7/8

= 7/40 meter

Balance = Total string - used string

= 7/8 - 7/40

= 35-7/40

= 28/40

Balance = 28/40 meter

cuts the rest into 5 equal parts. What is the length of the pieces.

28/40 ÷ 5

= 28/40 × 1/5

= 28 / 200

= 7/50 meter

Length of each piece = 7/50 meter

a figure has reflected symmetry across line a. line a passes through the figure. which statement is not true about the figure.

Answers

Answer:

hard stuff i can't answer

AnswerAnswerAnswerAnswerAnswerAnswer

Solve the equation: 3(x - 5) = x + 21
( please help me )

Answers

Answer:x=18

Step-by-step explanation:

3(x-5)=x+21

Distribute the 3

3x-15=x+21

Add 15 to each side

3x=x+36

Subtract x from each side

2x=36

Divide each side by 2

x=18

Ken's heart rate went from 74 beats per minute while resting to 148 while exercising what is the percent increase in his heart rate​

Answers

Answer:

Subtract the original from the new to find the difference:

It was a 200% increase.

Step-by-step explanation:

Subtract the original from the new to find the difference:

148 - 74 = 74

Now divide the new by the difference:

148 / 74 = 2

Multiply that by 100 to get the percentage:

2 x 100 = 200%

an architect is designing a commemorative steel arch in the shape of a parabola. its axis is vertical and its feet are 300 yd. apart. If the focus of the parabolic arch is to be 80 yd. above the ground, how high must the arch be?

Answers

Answer:

125yd

option b is correct

The height of the arch from the ground will be 125 yards.

Given information:

An architect is designing a commemorative steel arch in the shape of a parabola.

Parabola is vertically placed and its legs are 300 yards apart.

The focus of the parabola is 80 yards above the ground.

Let a be the distance of focus from the vertex of the parabolic arch.

So, the equation of parabola will be,

[tex]x^2=-4ay[/tex]

Assume the origin is placed on the vertex of the parabola.

So, the coordinates of the legs will be,

(-150, -(80+a)) and (150, -(80+a))

Satisfy the above point with the equation of parabola as,

[tex]x^2=-4ay\\150^2=4a(80+a)\\a^2+80a-5625=0[/tex]

Solve the above quadratic equation as,

[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\a=\dfrac{-80\pm\sqrt{80^2+4\times 1\times5625}}{2}\\a=\dfrac{-80\pm170}{2}\\a=-125, 45[/tex]

The value of a can't be negative. So, [tex]a=45[/tex].

So, the height of arch will be,

[tex]80+a=80+45\\=125\rm\;yd[/tex]

Therefore, the height of the arch from the ground will be 125 yards.

For more details, refer to the link:

https://brainly.com/question/4443998

HELP!
A submarine dlves 630 feet every 6 minutes and 4,200 feet every 40 minutes.
Find the constant rate at which the submarine dives. Enter your answer in feet per minute and feet per
hour.
The submarine dives
feet per minute.
The submarine dives
feet per hour.

Answers

105 feet per minute and 6300 feet per hour

If 260 is 20% what is the number for 80%

Answers

0.8
I think this is the answer :’D

math shi someone help me. ​

Answers

do you need help with both or is it one question

A polynomial function has a root of –3 with multiplicity 2, a root of 0 with multiplicity 1, a root of 1 with multiplicity 1, and a root of 3 with multiplicity 2. If the function has a positive leading coefficient and is of even degree, which could be the graph of the function?​

Answers

We are given a polynomial function has :
A root of –3 (multiplicity 2).
Therefore, one factor would be (x+3)^2
A root of 0 with multiplicity 1.
Therefore another factor is x.
A root of 1 with multiplicity 1.
Therefore another factor is (x-1).
A root of 3 with multiplicity 2.
Therefore, another factor would be (x-3)^2
Therefore, polynomial function would

Peter shot 40 free throws. He made 80% of his shots. What fraction is equivalent to 80%? Pleas answer im trying to get my work done over here. Im in math honors and im really not feeling it today so someone please!

Answers

Answer:

32 free throws.

Step-by-step explanation:

It is given that,

Peter shot 40 free throws. He made 80% of his shots.

We need to find the fraction that is equivalent to 80%.

It means we have to find 80% of 40. It can be calculated as follows :

[tex]F=\dfrac{80}{100}\times 40\\\\=32[/tex]

80% of 40 is equivalent to 32 free throws.

Please Complete the question.

Answers

Answer:

0.0174 is the answer you are looking for

Seven friends shared a Two-thirds pound bag of pistachios. If each person had the same amount of nuts, how many pounds did each person eat?
StartFraction 2 Over 21 EndFraction
StartFraction 3 Over 14 end Fraction
4 and two-thirds
10 and one-half

Answers

Answer:

3 over 14.

Step-by-step explanation:

Maria borrowed $3,000 at a simple interest rate of 4% per year. How much did she have to repay after 4 years?
$3480
$480
$7800
$4800

Answers

Answer:

$3480

Step-by-step explanation:

Simplify the ratio 5:20

Answers

answer 1:4

explanation:Simplify Ratio 5:20

To simplify the ratio 5:20, we find the greatest common divisor of 5 and 20, and then we divide 5 and 20 by the greatest common divisor.

The greatest common divisor that you can use to simplify 5:20 is 5. Which means the answer to ratio 5:20 simplified is:

1:4

In a sequence, each number after the first number is obtained by adding 4 to the previous number. If the first number in the sequence is 7, which of the following expressions represents the nth number in the sequence?


A 7+4n
B 7+(4n−1)
C 7+4(n−1)
D 7+4(n+1)

Answers

The answer to this question is C

Expression (C) [7 + 4(n - 1)] represents the nth number in the given arithmetic sequence.

What is an arithmetic sequence?A series of numbers called an arithmetic progression or arithmetic sequence has a constant difference between the terms. An arithmetic progression with a common difference of 2 is found, for instance, in the numbers 5, 7, 9, 11, 13, and 15. Starting with a number and repeatedly adding a fixed constant (d) to it is an easy technique to create a series.

So, in the arithmetic sequence, there is a formula to find the nth term in the series.

Formula for aₙ term is: aₙ = a₁ + d(n - 1)Where d is the common difference and n is the number of terms.Here, d is 4 and a₁ is 7.

Then, For aₙ term:

aₙ = a₁ + d(n - 1)aₙ = 7 + 4(n - 1)

Therefore, expression (C) [7 + 4(n - 1)] represents the nth number in the given arithmetic sequence.

Know more about arithmetic sequence here:

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#SPJ2

need help asap (mathmatics.)

Answers

Answer:B

Step-by-step explanation:

Answer: the correct answer is B (3,0)

Step-by-step explanation: HOPE THIS HELPS HAVE A GOOD DAY

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