a series of 1125 consecutive integers has a sum which is a perfect cube find the smallest possible positive sum for this series?
please show your work :)

Answers

Answer 1
The smallest possible sum for the series is 91125

If zero is considered to be positive, the answer is zero (0).

otherwise

562 negative consecutive integers, then 0, then 562 positive consecutive integers has a sum of zero (0).

Moving the start, the smallest integer up 1 adds 1125 to the sum.

1125 = 9 * 125

1125 = 9 * 5³

= 9³ * 5³ is the smallest sum

= 45³

= 91125

Therefore the smallest  possible sum is 91125

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Related Questions

Marlee has to find the point that divides the line segment between the points P(-6, 10) and R(2, -4) exactly in half. Marlee states: "the answer is M(-2, 3). Since a midpoint divides a line segment into 2 equal parts, I used the midpoint formula." Is this a logical argument?

Please choose one of these choices.:

A. Yes; using the midpoint formula will determine the middle point of a line segment.
B. No; she should have used the distance formula.
C. No; she should have used the quadratic formula.
D. No; she should have used the slope-intercept formula y = mx + b.

Answers

Answer:

A.

Step-by-step explanation:

If you use the points P(-6,10) and R(2,-4) and put them it the midpoint formula you would get (-2,3) therefore it would be logical to use it

Find the next two numbers in the pattern -96, 48, -24, 12,...​

Answers

[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]

The given sequence is a geometric ~

let's find the common ratio (r) first ~

[tex] \dfrac{48}{ - 96} [/tex]

[tex] - \dfrac{1}{ 2} [/tex]

And the first term (a1) of the sequence is ~ -96

let's find the 5th and 6th term.

The value of 5th term is ~

[tex]a_1{(r )}^{n - 1} [/tex]

[tex] - 96{ \bigg( - \dfrac{1}{2} \bigg) }^{5 - 1} [/tex]

[tex] - 96 { \bigg( - \dfrac{ 1}{2} \bigg) }^{4} [/tex]

[tex] - 96 \times \dfrac{1}{16} [/tex]

[tex] - 6[/tex]

The value of 6th term is ~

[tex]a_1{(r )}^{n - 1} [/tex]

[tex]- 96{ \bigg( - \dfrac{1}{2} \bigg) }^{6 - 1} [/tex]

[tex]- 96{ \bigg( - \dfrac{1}{2} \bigg) }^{5 } [/tex]

[tex] - 96 \times - \dfrac{1}{32} [/tex]

[tex]3[/tex]

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!9

Answers

Answer:

think its a

Step-by-step explanation:

the slope is 2/1 but both y int are different

help will reward brainly

Answers

Answer: Positive but I might be wrong I haven't done slopes in a while

Step-by-step explanation:

Positive because from left to right it goes up

If it were negative, it would go the opposite way

2. Kyle owes his sister 24. He gives his sister $15 that he earned mowing
lawns. Write and simplify an addition expression to find how much Kyle
still owes his sister. (leton 2)

Answers

ok so he is owing his sister 24 and he gives her 15

so 24-15=9

but as an addition expression it will be

x+15=24

x=24-15

x=9

The temperature of one furnace is 1,200°C and cools at a rate of 15°C per minute. The temperature of another furnace is 900°C and is heated at a rate of 5°C per minute. After how many minutes will the furnaces be the same temperature? Write the answer as a whole number or decimal. __ minute(s)

Answers

Step-by-step explanation:

how many cups of water do you need to fill fill one jar

Write a simplified expression for the perimeter of the triangle.
6x - 1, 5x + 6, 9
Perimeter : __ Units

Answers

Answer:

6973 t u 6hud3w. don't knoow

Answer:

the answer is 11x+14

Step-by-step explanation:

 (h[tex]2[/tex] b[tex]\2[/tex])/2

Please help! I also don’t understand a). My friend did it for me when I wasn’t looking so if you could explain that too, that’s be great

Answers

Answer:

a) 45

b) No. AD and BC arent parallel.

Step-by-step explanation:

a)

3x + 2x + x + 90 = 360

6x = 270

x = 45

Hope you could understand.

If you have any query, feel free to ask.

Calcula lo solicitado para una persona que gana un salario de $980.000 mensuales:
auxilio de transporte: $106.454
18 dias de trabajo: sueldo /30 * los dias que le quiero pagar
auxilio de transporte: aux tras/30* los dias que le quiero pagar
EPS: 4% sueldo
total a pagar:
ayudaaa porfa es para hoy mismo

Answers

Yes baby of course totaln yess

3/4 ÷ 1/2 +1 ddgngadgaekyfyuktyjrthrgefwretrytjyktuli;obpnML"NKP?boliykujhtgrfedw

Answers

Answer:

5/2

Step-by-step explanation:

alternative = 2 1/2 , 2.5

Evaluate -24=(-6)-(-18).

Answers

Answer:

−24= 12

Step-by-step explanation:

Answer:

-2=1

Step-by-step explanation:

-24=(-6)-(-18)

-24=(-6)+18

-24=12

-24/12 = 12/12

-2=1

(2 negatives make a positive)

give the intersection points of y=x^5 and y=x^7

Answers

Step-by-step explanation:

that means both functions deliver the same result for the same x.

therefore

x⁵ = x⁷

one solution is of course, x = 0.

the other(s) we get for x<>0 by dividing both sides by x⁵ :

1 = x²

that means we have 2 more solutions (a quadratic equation has 2 solutions, a cubic equation has 3 solutions,...) :

x = 1

x = -1

so, the intersection points are

for x = 0, we get y = 0⁵ (or 0⁷) = 0

for x = 1, we get y = 1⁵ (or 1⁷) = 1

for x = -1, we get y = (-1)⁵ or (-1)⁷ = -1

(-1, -1)

(0, 0)

(1, 1)

The intersection points of the function y = x⁵ and y = x⁷ are (0, 0) , (1, 1) and (-1 , -1).

What is Intersection point?

The intersection point is the point at which the two lines are cuts to each other.

Given that;

The equations are,

⇒  y = x⁵

⇒ y = x⁷

Now, Solve for intersection point as;

The equations are,

⇒  y = x⁵

⇒ y = x⁷

Equate both equation to each other, we get;

⇒ x⁷ = x⁵

Subtract x⁵ both sides , we get;

⇒ x⁷ - x⁵ = x⁵ - x⁵

⇒ x⁷ - x⁵ = 0

⇒ x⁵ (x² - 1) = 0

This gives two conditions;

⇒ x⁵ = 0

or, ⇒ x² - 1  = 0

Solve both the equations as;

⇒ x⁵ = 0  

⇒ x = 0

And,  x² - 1  = 0

( x - 1 ) (x + 1) = 0

x = 1 or x = -1

Thus, The values of x are 0 , 1 and -1.

So, The intersection points are;

For x = 0; y =  x⁵ = 0

For x = 1; y =  x⁵ = 1

For x = -1; y =  x⁵ = -1

Thus, The intersection points of the function y = x⁵ and y = x⁷ are (0, 0) , (1, 1) and (-1 , -1).

Learn more about the intersection point visit:

https://brainly.com/question/15074194

#SPJ2

what is equivalent to |14-20|

Answers

Answer:

7/10

Step-by-step explanation:

Find the median of the first 13 natural numbers

Answers

Answer

116.4k+ views

Hint: We will write the first ten odd natural numbers and then add them to find their sum. We will then substitute the values in the formula of arithmetic mean , a1+a2...+ann, where n is the number of terms and a1,a2,..an are n observations.

Complete step-by-step answer:

We have to find the arithmetic mean of first ten odd natural numbers .

Natural numbers are counting numbers and starts from 1.

Odd numbers are not multiples of 2.

The first ten odd natural numbers are 1,3,5,7,9,11,13,15,17,19.

Arithmetic mean is calculated by adding all the observations by the total number of observations.

Arithmetic mean is given by a1+a2...+ann, where n is the number of terms and a1,a2,..an are n observations.

Therefore, we will calculate the sum of the first ten odd natural numbers.

⇒1+3+5+7+9+11+13+15+17+19⇒100

Now, we will divide this by 10 as there are a total 10 numbers.

10010=10

Hence, the arithmetic mean of first ten odd natural numbers is 10.

Note: Arithmetic mean is also known as average or simply mean. Odd numbers are not divisible by 2. The sum of n odd natural numbers is also given by n2

you eat 3/10 of a packet
of donuts. your friend eats 1/5 of
the pack of donuts. How much of
the pack do you and your friend
eat?

Answers

Answer:

5/10 or 1/2 is the answer I think

Pleaseee helpppp me!!!!!!!!!!!!! ​

Answers

Answer:

The graph is linear and increasing from x = -6 to x = -2.

The graph is nonlinear and decreasing from x = -2 to x = 0.

Step-by-step explanation:

Linear means it has a constant slope, or a constant rate of change. That makes a straight line on a graph. On the given graph, you can see the straight line increasing from x = -6 to x = -2.

Non-linear is just anything that isn't a constant slope, and makes a curve on a graph. On the given graph, the curve decreases from x = -2 until x = 0, where it reaches its lowest point and starts heading upwards again.

which statement is correctly written as a conditional statement ​

Answers

Answer:

a shape has four sides,or it is a quadrilateral

Which fraction is equivalent to 9/12

Answers

Answer:   Choice B)  15/20

=========================================================

Explanation:

Let's check to see if 9/12 is the same as 16/24.

Set them equal to one another, and then use cross multiplication like so

9/12 = 16/24

9*24 = 12*16

216 = 192

Both sides aren't the same value after simplifying everything. The third equation being false leads to the first equation being false as well.

Therefore, 9/12 is not the same as 16/24. We can rule out choice A.

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

Let's check choice B

9/12 = 15/20

9*20 = 12*15

180 = 180

We have a match, so 9/12 is the same as 15/20

Notice how:

9/12 = 0.7515/20 = 0.75

Both fractions lead to the same exact terminating decimal, which is more evidence that the two fractions are equivalent.

Choice B is the final answer.

It is normal for some newborn babies to lose weight in their first week of life. Baby Todd's birth weight was 10 pounds. One week after being born, he is 10% lighter. What is Todd's current weight? pounds Submit

Answers

Answer:

9 pounds

Step-by-step explanation:

100% - 10% = 90%

90% -> .9

[Solving] 10 * .9 = 9

Have a nice day!

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

Answer:

9 pounds

Step-by-step explanation:

10% of 10 pounds is 1 pound so baby Todd's current weight is 9 pounds.

The remainder obtained when x⁴ +15x³ +6x² - 12x + 3 is divided by (x+2) is____.​

Answers

Answer:

-53

Step-by-step explanation:

(x+2)

x^4 =       -2^4 = 16

15x^3 =     15* (-2)^3 = -120

6x^2 =       6(-2^2) = 24

12x =        12*(-2) = -24

substitute into equation:

x^4 + 15x^3 + 6x^2 - 12x + 3 = 16+ (-120) + 24 - (-24) + 3 = -53

Given Polynomial is x^4 +15x^3 +6x^2 - 12x +3

Divisor = x+2

We know that

Remainder Theorem:

Let P(x) be a polynomial of the degree is greater than or equal to 1 and (x-a) is another linear polynomial,If P(x) is divided by (x-a) then remainder is P(a).

So, P(x) is divided by (x+2) then the remainder is P(-2).

P(-2) =

⇛(-2)^4+15(-2)^3+6(-2)^2-12(-6)+3

⇛ 16+15(-8)+6(4)+72+3

⇛16-120+24+72+3

⇛ 67-120

⇛ -53

P(-2) = -53

Answer:- The remainder is -53.

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The remainder obtained when x^4 + 3x^2 - 2x + 2 is divided by (x + b) is the square of the remainder obtained when x^2 – 3 is divided by (x + b...

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(7,1) and (-5,1)
Find the slope of the line that passes through the 2 points.

Answers

☆Answer : (X1, Y1) = (7, 1) (X2, Y2) = (-5, 1)

m = (Y2 - Y1)/(X2 - X1)

m = (1 - 1)/(-5 - 7)

m = 0/(-12)

m = 0

help pls ! i need to do this and i cannot figure this out

Answers

I think it’s 8 too!!!
With them being similar I noticed the bigger triangle is 18 and the second is 12. So the smaller triangle was shrink by 1/3 which give 1he 12 for the bigger triangle you take 1/3 away in which your left with 8.

Simplify 2y+4x=16x +6y ​

Answers

The Answer would be y=-3x

If f(1)=3f(1)=3 and f(n)=f(n-1)^2-3f(n)=f(n−1) 2 −3 whatsthe value of f(4)f(4)

Answers

Answer:

Step-by-step explanation:

So you can do that for me and you have a lot to say I don’t want you have a lot

Can someone pls help me!

Answers

Answer:

x is -3

Step-by-step explanation:

three fifths of the children in a school are boys seven eighths of the girls in the school are right handed. What fractions of the children in the school are left handed girls?

Answers

Answer:

Step-by-step explanation:

Firstly, we need to get the fraction that are girls

What we have to do is to subtract the three-fifths from the total fraction of 1

Mathematically,that would be :

1- 3/5=2/5

We have it that seven-eigths of the girls are left-handed. This mean one-eight of the girls are left handed

To get the fraction of the school that are left handed, we multiply the fraction of girls by the fraction of left-handed girls

We have this as:

1/8 x 2/5=1/20

We have it that 1/20 of the children are left-handed girls

Last year at a certain high school, there were 60 boys on the honor roll and 100 girls on the honor roll. This year, the number of boys on the honor roll increased by 10% and the number of girls on the honor roll increased by 25%. By what percentage did the total number of students on the honor roll increase? Round your answer to the nearest tenth (if necessary).

Answers

Answer:

19.3%

Step-by-step explanation:

There were 10% * 60 = 6 more boys, and 25% * 100 = 25 more girls, so in total 31 more students got on the honor roll. From 160 to 191, the percentage is 31/160 = 0.19375  

0.19375 = 19.3%

The amount of oil it takes to cover the bottom of a frying pan.

Answers

Answer:

about 1 cup maybe less

Step-by-step explanation:

List the sides from shortest to longest in ABC. A 630 50° с B O A. AB,BC , AC о B. BC , AC , AB C. D. AC , BC, AB not enough information O
Help Please!​

Answers

Answer:

  A.  AB, BC, AC

Step-by-step explanation:

The side lengths have the same order (smallest to largest) that their opposite angles have.

Angle B = 180° -50° -63° = 67°

The angles, smallest to largest, are C = 50°, A = 63°, B = 67°.

Their opposite sides (shortest to longest) are AB, BC, AC. (matches choice A)

Kristen and Marina are making prisms out of cardboard using the designs shown below.



Whose design uses more cardboard, and by how many square inches? Show how you determined your answer.

Answers

Answer:

kristen

Step-by-step explanation:

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