1 + 2 + 3 + ... + 98 + 99 + 100

Answers

Answer 1

Answer:

101 + 102 + 103 + ... + 998 + 999 + 1000

Step-by-step explanation:

Answer 2
Answer:     5050

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

Explanation:

This series is arithmetic since the common difference is 1. In other words, we're adding 1 to each term to get the next one.

The quickest way to find the sum is to use the formula below

S = (n/2)*(a+b)

where n is the number of terms, 'a' is the first term, and b is the last (or nth) term. This formula only works for arithmetic series.

We can see that n = 100, a = 1 and b = 100, so....

S = (n/2)*(a+b)

S = (100/2)*(1+100)

S = 50*101

S = 5050

-----------

This can be confirmed by noticing that we have 100/2 = 50 pairs of terms. Pair up the terms such that 1 goes with 100, 2 goes with 99, 3 goes with 98, and so on.

We have these fifty sums

1+100 = 101

2+99 = 101

3+98 = 101

....

48+53 = 101

49+52 = 101

50+51 = 101

We have 50 copies of 101 being added, which leads to 50*101 = 5050

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

The slowest and most tedious way to confirm this is to type 1+2+3+...+98+99+100 into your calculator. The result should say 5050. Using a spreadsheet would be a better option instead of using a handheld calculator. I don't recommend this unless you need more proof that we end up with 5050 as the final answer.


Related Questions

Find the equation of a vertical line passing through the point B(2,-1)

Answers

Answer:

x = 2

Step-by-step explanation:

In a vertical line, all x-coordinates are the same.

x = 2

Answer:

x =2

Step-by-step explanation:

A vertical line means the x value remains constant

The x value is 2

x =2

HELPPPPPPPPPPPPPPPPPPP ASAP!!!!!!

Answers

Answer:

there is 8 quadrilateral shapes

Jeremy uses 2 feet 3 inches of board for each birdhouse he builds. How many inches of board does he need to make 6 birdhouses? Use a number line to solve?

Answers

Answer:

The length of board required is 13 feet 6 inches .

Step-by-step explanation:

Board required to make one bird house = 2 feet 3 inches

= 2 x 12 + 3 = 27 inches

Number of bird houses = 6

So, the board required  

= 6 x 27 = 162 inches

13.5 feet = 13 feet 6 inches

Which expression is the result of factoring the expression below by taking out its greatest common factor?
4x^2+16x-4=?
Choose 1 answer:
A. 2x(2x^2+8x−2)
B. 2(2x^2+8x−2)
C. 4x(x^2+4x−1)
D. 4(x^2+4x−1)

Answers

Answer:

4(x^2 +4x-1)

Step-by-step explanation:

4x^2+16x-4

Factor out a 4

4(x^2 +4x-1)

Answer:

D. 4 ( x² + 4 x - 1 )

Step-by-step explanation:

4 x ² + 16 x - 4

Taking out common factor = 4

4 ( x² + 4 x - 1 )

For which set of numbers is the number 4 a common multiple?
A
B.
C.
D.
4.8 and 16
2.4 and 8
1, 2 and 4
0 and 4
ОА​

Answers

Answer:

A is the answer

Step-by-step explain

Answer:

Hello There!!

Step-by-step explanation:

I believe the answer is O A.4.8 and 16.

hope this helps,have a great day!!

~Pinky~

How do you solve this?

Answers

Answer:  Choice D.  (2,6)

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

Explanation:

If we plugged (x,y) = (0,8) into the first inequality, then we get

y < x^2+6

8 < 0^2+6

8 < 0+6

8 < 6

which is false. So we can rule out choice A.

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

Trying choice B leads us to

y < x^2+6

2 < 4^2+6

2 < 16+6

2 < 22

That last statement is true, so the first inequality is true for (x,y) = (4,2)

Let's try the other inequality

y > x^2-4

2 > 4^2-4

2 > 16-4

2 > 12

That's false. Since one of the inequalities is false (it doesn't matter which one), this means the entire system is false. We cross choice B off the list.

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

Now onto choice C

You should find that y < x^2+6 becomes -4 < 10 after plugging in (x,y) = (-2,-4). Since -4 < 10 is true, we move onto the next inequality.

The inequality y > x^2-4 becomes -4 > 0 after plugging in those mentioned x,y values. The inequality -4 > 0 is false.

We cross choice C off the list.

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

The only thing left is choice D. It has to be the answer.

Let's find out if we get true inequalities when plugging in (x,y) = (2,6)

y < x^2+6

6 < 2^2+6

6 < 10 ... true

and

y > x^2-4

6 > 2^2-4

6 > 4-4

6 > 0 .... also true

Both inequalities are true, so the entire system is true. Therefore, (x,y) = (2,6) is one of the infinitely many solutions to this system.

Choice D is confirmed as the answer

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

Refer to the diagram below. I've graphed the two dashed boundary curves and the shaded region between. This region is above the y = x^2-4 curve, and below the y = x^2+6 curve. So we're ignoring the stuff above the y = x^2+6 curve.

Points A through D represent the four answer choices in the order given. We see that point D is the only point in the shaded region, so that visually confirms we have the correct answer.

Note: points on the dashed boundaries do not count as solutions.

Find the perimeter of the figure. SOMEONE PLS HELP ME IVE ASKED THIS QUESTION 3 TIMES NOW

Answers

Answer:

Step-by-step explanation:

The lengths of the tangents drawn from an external point tot he circle are equal.

RA = RB = 12.2

QA = QC = 5.9

PC = PQ - QC = 27.4 - 5.9 = 21.5

PC = PB = 21.5

QR = QA + RA = 5.9 + 12.2 = 18.1

PR = PB + RB = 21.5 + 12.2 = 33.7

Perimeter = PQ  +  QR + PR

                 = 27.4 +  18.1 + 33.7

                 = 79.2

Suppose y varies directly with x, and y = 65 when x = 13. What direct variation equation relates x and y?

Answers

Answer:

y = 5x

Step-by-step explanation:

y = kx

65 = k (13)

65/13 = k

k = 5

~~~~~~~~~~~~

y = 5x

will mark brainliest
show workings​

Answers

Answer:

a) 20 km away fro the starting point.

b) The bearing from P to R is 80°.

c) Q is 60 km North P.

d) Q is - 60 km west of P

Step-by-step explanation:

Stating Facts in the Question:

P to Q is 80 km and bearing 330°

It turned around, Q to R is 60 km and bearing 250°.

a) Picture a number line (Look at the first image)

You go 80 to the right. You turn around and go 60 to the left.

80 - 60 = 20

20 km away fro the starting point

b) Picture a number line (Look at the second image)

P to Q is bearing 330°

Q to R is 60 km is bearing 250°

P to Q is red

Q to R is blue

330° - 250° = 80°

The bearing from P to R is 80°

c) P to Q is 60 km

The plane went forward or North so the answer is 60 km.

Q is 60 km North P.

d) Q to P is 60 km

Q is not to the west of P

Q is - 60 km west of P

Mr. Theorem writes the expression 6^2 Divided bye 23 on the board. What is the value

Answers

Answer:

[tex]1\frac{13}{23}[/tex]

Step-by-step explanation:

6² ÷ 23

36 ÷ 23

[tex]1\frac{13}{23}[/tex]

Place the following linear equation in slope intercept form: 6x - 4y = 9

Answers

Answer:

y = 3/2 x - 9/4

Step-by-step explanation:

bring all the y's to one side.

4y = 6x-9

divide by 4 to isolate the y

y = 6/4x - 9/4

simplify

y = 3/2 x - 9/4

Answer:

y = (3/2)x - 9/4

Step-by-step explanation:

Slope intercept form is

y = mx + b

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

6x - 4y = 9

subtract 6x from both sides

-4y = -6x + 9

Divide both sides by -4

y = (3/2)x - 9/4

In the decimal expansion of the fraction 1/13, what digit is in the 2021st decimal place?

please answer correctly (full answers)

Answers

Answer:

2

Step-by-step explanation:

1/13 = 0.07692307692307

1/13 has a 6 place repeating decimal

076923   076923

2021/6 = 336 5/6

There will be 336 complete sets and then

2021 will be the 5th place of 076923

how many zeroes are there​

Answers

Answer:

infinity zeros are there

Step-by-step explanation:

please make me brainlsit answer

This figure is known as a triangular prism. Find the surface area in square feet.
10 ft
3 ft
7 ft
8 ft

Answers

Step-by- step explanation : Perimeter of the triangular base=10+10 + 16 =36 ft Height of the prism n = 15ft Base area = Area of the triangle = 1 2 (Base)(Height ) = 1 2 (16)(6); =48 square ft Surface area of the triangular ism = 2(base area) + (perimeter * heig ) =2(48); + 36 * (15) = 96 + 540 =636


FIND THE TOTAL NUMBER OF COMBINATIONS
How many ways could a 3 topping pizza be selected if you have 10 toppings
to choose from?
A 720
B 120
60
D 30

Answers

Answer:

B.120 i took the test and got it right.

Answer:

Its letter B.

Step-by-step explanation:

hopefully i got it right loll

PLEASE SOMEONE HELP ME I WILL GIVE BRAINLIEST

Answers

20 a: x = 5

20 b: x = 12

17 c: 30

Solve 3n – 5p + 2n = 10p for n.

Answers

Answer:

n = 3p

Step-by-step explanation:

3n−5p+2n=10p

5n−5p+5p=10p+5p

5n=15p

5n/5 = 15p/5

n = 3p

Answer:

3n+2n=10p+5p

5n=15p

Divide both sides by 5

n=3p

(-6)(4) preform indicated operation

Answers

Answer:

-24

Step-by-step explanation:

(-6)(4)

The indicated operation is multiplication

-24

Answer:

-24

Step-by-step explanation:

Multiply -6 and 4

For the function f(x)= |x+2| -3 , explain the difference between f(2x) and 2f(x). Comparing the y-intercept , x-intercepts

Answers

Answer:

For a function f(x), the y-intercept is the value of f(0), while the x-intercepts are the values of x such that:

f(x) = 0.

Here we can also start with some information about dilations.

For a function f(x), a vertical dilation of scale factor k is written as:

g(x) = k*f(x)

While, again, for a function f(x), an horizontal dilation of scale factor k is written as:

g(x) = f(x/k)

So when here they ask us the difference between f(2x) and 2f(x)

We can say that the first one is a horizontal dilation of scale factor 1/2, while the second is a vertical dilation of scale factor 2.

Now let's analyze the intercepts for each case.

if f(x) = |x + 2| - 3

2*f(x) = 2*(|x + 2| - 3)

        = 2*|x + 2| - 6

The y-intercept is:

2*f(0) = 2*|0 + 2| - 6 = 4 - 6 = -2

and the x-intercepts are given by:

2*f(x) = 0 = 2*|x + 2| - 6

           6 = 2*|x + 2|

         6/2 = |x + 2|

           3 = |x + 2|

Here we have two solutions for x,

x = 1:             3 = |1 + 2| = |3| = 3

x = -5:           3 = |-5 + 2| = |-3| = 3

Now for the other transformation, we have:

f(2*x) = |2*x + 2| - 3

the y-intercept is:

f(2*0) = |2*0 + 2| - 3

         = |2| - 3 = -1

(So the y-intercept is different)

And the x-intercepts are given by:

f(2*x) = 0 =  |2*x + 2| - 3

           3 = |2*x + 2|

           3 = 2*|x + 1|

           3/2 = |x + 1|

Here the two solutions are:

x = 1/2

x = -5/2

So the x-intercepts are also differents.

This happens because in one case, we affect the function horizontally and in the other case vertically, so one could expect that the resulting functions are different (thus, have different intercepts)

Find the area of a quadrilateral wxyz with wx =24m, xy= 50m, yz = 40m, zw = 30m and diagonal being 50m

Answers

Answer:

The area of the quadrilateral is 1,182.46 m2.

Step-by-step explanation:

In order to find the area of a quadrilateral WXYZ, with WX=24m, XY=50m, YZ=40m, ZW=30m and the diagonal being 50m, the following calculation has to be done:

X = 0,5 24 × 30 × sen 24 + 0,5 × 50 × 40 × sen 40

X = 1,182.46 m2

If P = (-3,5), find the image
of P under the following rotation.
90° counterclockwise about the origin
([?], [
[]
Enter the number that belongs in
the green box

Answers

Answer:

(-5 , -3)

Step-by-step explanation:

use formula of 90 degree counterclockwise rotation about the origin

formula:

(x , y) = (-y , x)

(-3 , 5) = (-5 , -3)

The required coordinate of the point after 90° clockwise rotation is (-5, -3).

What does it mean by rotation?

A shape or item is rotated when it is spun around a certain point (center) without being moved in any other way. Size and shape are unaffected by rotation.

The given coordinate of the point is (-5, -3).

Counterclockwise rotation about the origin is given as,

(x , y) = (-y , x)

(-3, 5) = (-5 , -3)

Thus, the required coordinate of the point after 90° clockwise rotation is (-5, -3).

Learn more about rotation here:
https://brainly.com/question/1571997
#SPJ2


According to exponent rules, when we divide the expressions we
exponents.

Answers

The quotient rule for exponents states that if we divide exponents with the same base, then we can subtract the exponents and keep the base unchanged.

HELP, I don’t understand as this is due today!!!!

Answers

Answer:

in orange you cost 5.52

in apple you cost 3.9

Step-by-step explanation:

1 1/2=2×1+1=3

so multiplied the 3 in the price per pound

so in orange you got this solution

3×1.84=5.52

and in apple you got this solution

3×1.30=3.9

#CARRY ON LEARNING

#MARK ME AS BRAINLIEST

#100% SURE

CAN I GET THE REAL ANSWER I NEED THIS 100% MY MOM IS GOING WHOOP ME TILL I GOT 10 STAINS ON MY BUTT AND LEGS PLEASE HELP

Answers

Answer:

Haha sure mate! Its 116 :) Your thing is wrong but I would select 106 because it seems like a more reasonable mistake

Step-by-step explanation:

Give me braiest answer if I saved you a whooping

Answer:

The answer to your question is 244 degrees

Step-by-step explanation:

Simply add 60, 90, 82, and 12 to get 244 degrees.

Two tangents are drawn to a circle from an external point. If the measure of the major arc is 260º, what is the measure, in degrees, of the angle formed by the two tangents?

Answers

Answer:

80degrees

Step-by-step explanation:

Using the expression to get the minor arc;

minor arc + major arc = 360degrees

minor arc + 260 = 360

minor arc = 360 - 260

minor arc = 100degrees (central angle)

Note that the central angle and that formed from the intersection of the tangents (X) are supplementary. Hence;

100 + X = 180

X = 180 - 100

X = 80degrees

REAL ANSWER FOR BOTH OF THEM PLEASE THERES MORE POINTS ON THIS ONE

Answers

The first question is 83

The second is 235

hope this helps!

Answer:

the answer to your first question is 235 degrees or B

the answer to your second question is 83 degrees

Step-by-step explanation:

for the first question simply add all of the angles

for the second question a straight line/angle is 180 degrees so simply subtract 97 from 180 to get 83 degrees

Given the inequality -8<2, explain what happens when you multiply or divide both sides by 2 and what happens when you multiply or divide both sides by -2.

Answers

You get a side lol idek

Answer:

When you multiply or divide both sides by 2, the result is going to be a negative number.

When you multiply or divide both sides by -2, the results are going to be positive.

Step-by-step explanation:

When you multiply or divide a negative and a negative, it's going to be a positive.

When you multiply or divide a negative and a positive, it's going to be a negative.

The cost of a High Definition television now averages $700, but the cost is decreasing about 15% per year. In how many years will the cost be under $200?

Answers

Answer: 7.7 years

Step-by-step explanation:

Given

The cost of HD TV is $700 and it is decreasing at the rate of 15% per year

After one year it becomes

[tex]\Rightarrow 700-700\times 15\%\\\Rightarrow 700(1-0.15)[/tex]

after 2 year it becomes

[tex]\Rightarrow 700(1-0.15)-700(1-0.15)\times 15\%\\\Rightarrow 700(1-0.15)(1-0.15)\\\Rightarrow 700(1-0.15)^2[/tex]

Suppose, after x years it becomes $200

[tex]\Rightarrow 200=700(1-0.15)^x\\\\\Rightarrow \dfrac{2}{7}=0.85^x\\\\\text{Taking log both sides}\\\\\Rightarrow x=\dfrac{\ln (\frac{2}{7})}{\ln (0.85)}\\\\\Rightarrow x=7.7\ \text{years}[/tex]

Thus, it takes 7.7 years for the cost to come under $200.

the sum of two integers is 310. if one of them is - 52. find the other​

Answers

Answer:

Integer = 362

Step-by-step explanation:

Let the two integers be x and y

Sum of two integers, x + y = 310 ------(1)

Given one of the integer, Let x = -52

Substitute x = -52 in (1) ,

                                      -52 + y = 310

                                              y = 310 + 52

                                              y = 362

A TV has a listed price of $695.95 before tax. If the sales tax rate is 7.75%, find the total cost of the TV with sales tax included. Round your answer to the nearest cent, if necessary.

Answers

Answer:

$749.89

Step-by-step explanation:

TV price = 100% = 695.95

Sales TAX = 7.75% = x

Total price = 107.75% = x dollars

1.0775 * 685.95 = 749.886125 ≈ 749.89

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

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