If the sum of 4040 consecutive integer numbers is 2020, find out the absolute difference between the first number and the last number.

Answers

Answer 1

Let [tex]x[/tex] be the smallest of the consecutive integers summing to 2020. Then the largest integer in the sum is [tex]x+4039,[/tex] so our answer is [tex]\boxed{4039}.[/tex]

For completeness, though, let's solve for the value of [tex]x[/tex] that satisfies the conditions of the problem. Recall that the sum of an arithmetic series with first term [tex]a_1,[/tex] last term [tex]a_n,[/tex] and [tex]n[/tex] terms, is [tex]\frac{n(a_1+a_n)}{2}.[/tex] Plugging in our known values gives us the equation [tex]\frac{4040(2x+4039)}{2}=2020,[/tex] which simplifies to [tex]2x+4039=1.[/tex] Thus, [tex]x=-2019,[/tex] so the 4040 consecutive integers are [tex]-2019,-2018,\dots,-1,0,1,\dots,2018,2019,2020.[/tex] Notice how everything except the [tex]2020[/tex] cancels out!


Related Questions

Line segments AB and BC are tangents to Circle P. What is the value of x?
a.117
b.73
c.107
d.146

Answers

Answer:

c. 107°

Step-by-step explanation:

In the figure attached, Circle P, segments AB and BC, and angle x are shown.

From circumscribed angle theorem, we know that angle ABC and angle x are supplementary, then:

x + 73° = 180°

x = 180° - 73°

x = 107°

6 cm
4 cm
3 cm
12 cm
What’s the purple? Areas

Answers

Answer:

36 cm

Step-by-step explanation:

A = b1 + b2 x h / 1/2

A = 12 + 6 x 4 / 1/2

1. What side in the second trapezoid corresponds to CD?
choices:
RU
ST
TU
RS

2. What angle in the second trapezoid corresponds to B?

choices:
T
S
U
R



Answers

Answer:

1...ut

2..s

Step-by-step explanation:

you can see that the trapezium ABCD is talented than you are St trapezium so then from the ABCD trapezium Appa what then you can see a De is parallel to you are and ab is parallel to AC and DC is parallel parallel to T s and a De is parallel to ur

Answer:

1. UT

2. S

Step-by-step explanation:

1. parallel sides of the first trapezoid are DC and AB, the last being the longest

so the answer is

UT, which is shorter base

2. B is the right angle

so S is the one on the second trapezoid

The figure below shows the quotient of Fraction 3 over 4 divided by Fraction 3 over 8 .

Rectangle divided into eight equal parts, where the first three-part is shaded dark representing three-eighths, the next three parts are shaded light to complete the three-fourths, and the last two parts are not shaded

The quotient is ____.

Answers

3/4 divided by 3/8 is 2
The correct answer is 2

Aisha is playing a game in which she can gain or lose points on each turn. The table below
shows the points she scores on each of four turns in the game.
Aisha states that her highest score is on Turn 3, because 16 is greater than 3, 10, or 9. Use the
drop-down menus to explain Aisha's mistake.

Answers

Answer:

A score of -16 represents the lowest of points for these four turns.

The number for Aisha's highest score will be turn 2 on the number line.

That number is 10.  

Step-by-step explanation:

Since the options of the drop down menu are not included, you should choose any option similar to lowest.

Aisha's highest score was obtained in turn 2 and that is 10.

Aisha is comparing absolute terms, that is why she believes that -16 represents a good score, while in reality is the worst she got.

Below is the graph of a trigonometric function. It has a minimum point at (- 10.4, - 9.8) and a maximum point at (- 3.6, - 1.2) . What is the period of the function?

Answers

Answer:

13.6

Step-by-step explanation:

The period is double of the distance (on the x-axis) between the maximum and the minimum. In this case, the x-coordinate of the minimum is -10.4, the x-coordinate of the maximum is -3.6, the distance is -3.6 - (-10.4) = 6.8, and the period is 2*6.8 = 13.6

Answer:

Step-by-step explanation:

4.3 unit from by khan academy

A mayor wants to determine if the people in his city think that he is doing a good job. Which choice BEST represents the population? A) Voters age 21 to 35. B) All the local business owners. C) The people who voted for him. D) All the residents of the city. Eliminate

Answers

Answer:

D

Step-by-step explanation:

D is the best choice. A excludes voters age 18-20 and 36+. B excludes everyone who doesn't own a business, and C excludes those who didn't vote for him. For the most honest results, D - everyone - is the best choice.

When 50 pounds of a compound are produced, the manufacturing cost is described by x
and the selling price is described by x^2 + 8x - 20.
What is ratio of the cost to the selling price when x = 50?

Answers

Answer:

45

Step-by-step explanation:

y

The answer is 45 hope this helps buddy

(x+4)−(x−1)
HELPPPP
5edrfytguyhidiftougyih;fygvjbmncifyykgvjb mnr6o7ftuglh.bjnhugiyfltudkrysi6d7tfugiy;h/junk;lk

Answers

Answer:

There is no plug-in for x.

X=0.

(0+4) - (0-1) = [(4 - (-1)] = 5.

Answer:

5

Step-by-step explanation:

(x+4) -x +1

x - x = 0

5

−8⋅f(0)+4⋅g(−8)=
Please help

Answers

Answer:

-32

Step-by-step explanation:

Look at the attachment

Functions can be represented as equations and graphs.

The value of [tex]\mathbf{-8\cdot f(0)+4\cdot g(-8)}[/tex] is -32

From the graph, we have the following values.

[tex]\mathbf{f(0)= 1}[/tex]

[tex]\mathbf{g(-8)= -6}[/tex]

So, we have:

[tex]\mathbf{-8\cdot f(0)+4\cdot g(-8)= -8 \times 1 + 4 \times -6}[/tex]

Simplify

[tex]\mathbf{-8\cdot f(0)+4\cdot g(-8)= -8 -24 }[/tex]

[tex]\mathbf{-8\cdot f(0)+4\cdot g(-8)= -32 }[/tex]

Hence, the value of [tex]\mathbf{-8\cdot f(0)+4\cdot g(-8)}[/tex] is -32

Read more about functions and equations at:

https://brainly.com/question/3468890

PLS HELP!!!!!! In a survey of 4530 U.S. adults, 87% said that they would like to donate more to charity. What is the margin of error for the survey? Round to the nearest tenth of a percent

Answers

Answer:

Margin of Error = 1.0% to the nearest tenth of a percent.

Step-by-step explanation:

Margin of Error is the width of the confidence interval about the mean.

It is given mathematically as,

Margin of Error = (Critical value) × (standard Error)

Critical value is obtained from the z-tables at the popular confidence level of 95% and z-tables is used because the sample size, 4530, is large enough to approximate the population properties.

Critical value = 1.960

Standard error = σₓ = √[p(1-p)/n]

p = 87% = 0.87

n = sample size = 4530

σₓ = √[0.87×0.13)/4530]

= 0.0049966876

Margin of Error = 1.96 × 0.0049966876 = 0.0097935078 = 0.00979 = 0.979% = 1.0% to the nearest tenth of a percent.

Hope this Helps!!!

What is the solution to the equation below? Round your answer to two
decimal places
e^x = 5.9

Answers

Answer:.1.77

Step-by-step explanation:

e^x = 5.9

Take the natural logarithm of both sides

x = ln (59/10)

x = 1.77

Answer: x=1.77

Step-by-step explanation:

A P E X

answer with work pls!!

Answers

The reflected coordinates will be ( 15,7)

Ming took a cab across town. His fare was $22, and he leaves an 18%tip.
What is the total amount Ming pays the cab driver?

Answers

He payed a total of 25.96 because the tip was 3.96

Answer:

$25.96

Step-by-step explanation:

take 18% of 22, which is 3.96. Add it to 22 and that's the amount Ming payed!

Solve the problem in the image above

Answers

Answer:

Step-by-step explanation:

3[tex]x^{4}[/tex]

Answer: 9 √(3^x6)

Step-by-step explanation:

Jared makes $133 per hour, but he loses 20% of his pay for a day if his boss catches him on the internet. If Jared works for 8 hours a day for 5 days, and his boss only catches him on the internet once how much money will he make in the five days?

Answers

Answer:

$5107.20

Step-by-step explanation:

His pay after he was caught once

133x 8=1064

1064x 20% = 212.8

1064-212.8=851.2

1064x 4= 4256

4256+ 851.2=5107.2

What is the output or waste of the cellular respiration cycle?

Answers

Answer: The outputs, or products, of cellular respiration are water and carbon dioxide

Explanation: The inputs, or reactants, of cellular respiration are glucose and oxygen. The outputs, or products, of cellular respiration are water, carbon dioxide

What is the distance between (6, 2) and (-3,-2)?
09
03
O V97
05

Answers

The answer is (9, 4)

Answer:

√ 97

Decimal Form:

9.84885780 …

which one isn’t a function ?

Answers

Answer:

D isn't a function because points intersect vertically on the graph

Step-by-step explanation:

Todd has created the following diagram to prove the Pythagorean theorem. He drew (triangle)ABC with leg lengths a and b and hypotenuse length c. Then he drew altitude CZ to the hypotenuse. He determines that c/a=a/z and c/b=b/y. Then he determines that cx=a^2 and cy=b^2. What is the next step in proving the theorem?

Answers

Answer:

cx + cy = a² + b²

Step-by-step explanation:

Next step is adding up cx and cy:

cx + cy = a² + b²

Then followed by:

c(x+y) =  a² + b²c² =  a² + b²

Answer: cx + cy = a² + b²

Step-by-step explanation:

1 gal 3 c= _fl oz

Convert the unit of capacity

Answers

Answer:

152 fluid ounces

Step-by-step explanation:

there are 128 fluid ounces in 1 gallon. there are 24 fluid ounces in 3 cups. 128+24 is 152. :)

Suzy is shopping at a book sale. The table shows prices for paperbacks.

A two-column table with 3 rows. Column 1 is labeled Books (x) with entries 4, 6, 8. Column 2 is labeled Cost (y) with entries 6, 9, 12.

These points are graphed. Notice the pattern of the points. What is the rate?

The cost is $
for every 2 books.

Answers

Answer:

3 bucks

Step-by-step explanation:

The rate of change is 2 and the cost of two books is $3.

What are lines and their slopes?

We know lines have various types of equations, the general type is

Ax + By + C = 0, and the equation of a line in slope-intercept form is

y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

Given, Suzy is shopping at a book sale. The table shows prices for paperbacks.

The points are, (4, 6), (6, 8), and (8, 12).

Slope(m) = (12 - 8)/(8 - 6).

Slope(m) = 4/2.

Slope(m) = 2.

Now, 4 books cost $6, hence 2 books cost $3.

learn more about lines and slopes here :

https://brainly.com/question/3605446

#SPJ3

If you answer can you write how you solved it?

Answers

Answer:

[tex]145.3in^2[/tex]

Step-by-step explanation:

[tex]A_{L} =2\pi rh=2*\pi *2.5*9.25\\=145.3in^2[/tex]

Which figure has an orthocenter outside the triangle? A triangle has angle measures of 30, 75, and 75 degrees. A triangle has angle measures of 54, 56, and 74 degrees. A triangle has angle measures of 45, 110, and 25 degrees. A triangle has angle measures of 90, 48, and 42 degrees. plzzzz help

Answers

Answer:

A triangle has angle measures of 45, 110, and 25 degrees would has an orthocenter outside the triangle.

Hope this helps!

:)

Answer:

The Third option is correct.

Step-by-step explanation: just got it right on edge

A right angle is equal to how many angles

Answers

Answer:

90 degrees

A right angle is equal to 90 degrees. A line segment (AB) drawn so that it forms right angles with a line (CD).

Step-by-step explanation:

Answer:

3 angles

Step-by-step explanation:

there are 3 angles, one a right angle (90 degrees), and the other two are acute angles (45 degrees)

What is the surface area of a cone with a radius of 3 meters and a slant of 4

Answers

Answer:

A≈65.97m²

Step-by-step explanation:

A=πrl+πr2=π·3·4+π·32≈65.97345m

Which is the angle measure represented by 2 rotations counterclockwise?
a. -1080°
C. 1080°
b. -720°
d. 720°

Answers

-720 because counter clockwise it would be 720 which is 360 times 2 but since it is backwards it’s -720.
I think it is a

Explanation is counterclockwise means going bakwards so that might be right

A blueberry bush was 13 inches tall. One year later, the bush was 25 inches tall.
Which number sentence shows how many inches the bush grew in one year?

Answers

Answer:

12 inches

Step-by-step explanation:

25-13=12

(How much it grew in the last year.)

Answer:
12 inches

Expression:
25-13

Estimate a 15% tip on a dinner bill of $81.66 by first rounding the bill amount to the nearest ten dollars.​

Answers

Answer:

12 dollars

Step-by-step explanation:

Round the bill to the nearest ten dollars

81.66 rounds to 80 dollars

80 * 15%

80 *.15

12

The tip is 12 dollars

Answer:

81.66/100*115 = 93.909 rounding down to $90

Step-by-step explanation:

which of the following are properties of the circumference of a triangle

Answers

Answer:

angle, length height

Step-by-step explanation:

The circumference of a triangle are the lengths of all three sides added together. If you ask yourself what are the properties you need to measre the lengths of a side.

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