I need a step by step explanation as well as work

If x is an integer, and

x + (x + 1) + … + 2020 + 2021 = 2021

then of course

x + (x + 1) + … + 2020 = 0

and we can write the left side as a sum,

[tex]\displaystyle \sum_{k=0}^n (x+k) = 0[/tex]

with n such that x + n = 2020. (Notice that there are n + 1 terms in the sum.) Then x = 2020 - n, so that

[tex]\displaystyle \sum_{k=0}^n (2020 - n + k) = (2020 - n) \sum_{k=0}^n 1 + \sum_{k=0}^n k= 0[/tex]

Recall that

[tex]\displaystyle \sum_{k=1}^n 1 = 1 + 1 + 1 + \cdots + 1 = n[/tex]

[tex]\displaystyle \sum_{k=1}^n 1 = 1 + 2 + 3 +  \cdots + n = \frac{n(n+1)}2[/tex]

Then

[tex]\displaystyle (2020 - n) (n + 1) + \frac{n(n+1)}2= 0[/tex]

Solve for n :

(2020 - n) (n + 1) + n (n + 1) / 2 = 0

4040 + 4039 n - n² = 0

(n - 4040) (n + 1) = 0

⇒   n = 4040   or   n = -1

But we are taking the sum of a positive number of terms, so n = 4040.

Then since x + n = 2020, it follows that x = 2020 - 4040 = -2020.

Answer:

56

Step-by-step explanation:

cross multiply

0.06z - 0.36 = 3

0.06z = 3.36

z = 56

Answer:

I'm guessing 401 tickets. lol

Number of tickets Alicia sold is equals to 401 .

" Linear equation is defined as the algebraic expression with one or more variables with highest power of the variable equals to one."

According to the question,

x represents the number of tickets Alicia sold

As per the data given,

Number of tickets Jenna and Matt sold together = 282 + 178

                                                                                 = 460 tickets

Substitute the given values in the condition we get linear equation,

   x + 59 = 460

⇒ x = 460 - 59

⇒ x = 401 tickets

Hence, number of tickets Alicia sold is equals to 401 .

Learn more about linear equation here

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#SPJ2

Answer:

f(3) = g(6)

Step-by-step explanation:

Answer:

lol wat r u doing .........

Answer:

805.98

Step-by-step explanation:

671.65x.20=134.33

134.33+671.65=805.98

Answer:

Here is a generic way to set up this type of algebra problem.

d = total amount of dirt at the site (tons)

r = rate or removal (tons/hr)

t = time it takes to remove all of the dirt (hr)

d = rt

The total amount of dirt equals the removal rate times hours spent removing all the dirt.

Since you want to solve for t, divide both sides by r

t = d/r

Answer:

linear

Step-by-step explanation:

Answer:

Linear slope of 5/1

Step-by-step explanation:

The rate is constant.

Hope that helps

Answer:

Step-by-step explanation:

x=0

Answer:

8

Step-by-step explanation:

18×4 = 72

And 72 ÷ 9 = 8

So 9×8 would be 72

Answer:

27

Step-by-step explanation:

let th original number=x

x+108=5x

5x-x=108

4x=108

x=108/4=27

Answer:17/23

Step-by-step explanation:

Answer:  17/40 of the students are girls.

Step-by-step explanation:

First, to find the number of girls in the class, we can subtract the number of boys (23) from the total number of students (40) to get:

40 - 23 = 17

There are 17 girls in the class.

Finally, to get the fraction of the girl students of the class, we can divide the number of girls (17) by the total number of students (40) to get:

17 ÷ 40 = [tex]\frac{17}{40}[/tex]

Since the fraction [tex]\frac{17}{40}[/tex] is already simplified, the final answer comes out to be [tex]\frac{17}{40}[/tex].

Answer:

Yes, 8.5 is greater than 0.85

Step-by-step explanation:

In counting from 0 to the highest possible positive number in steps of 0.01, we come across 0.85 before 8.5. This means that 8.5 is greater than 0.85

Answer:

HLO Mate here is ur answer

Answer: The value of 5/6 is 5 and the value 7/11 is 7.

Step-by-step explanation:

Answer:

y+1=3(x+8)

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(5-(-1))/(-6-(-8))

m=(5+1)/(-6+8)

m=6/2

m=3

y-y1=m(x-x1)

y-(-1)=3(x-(-8))

y+1=3(x+8)

Answer:

80

Step-by-step explanation:

3.5*2*2*2*2*5=280

The value of x if the side length of Terrarium A is four times the side length of Terrarium B is 3.6

Since we are both given the required length, we can assume the side length of Terrarium A and B and solve it in a general way.

Let;

If the side length of Terrarium A is four times the side length of Terrarium B, then;

x - 6 = 4(x + 3)

x - 6 = 4x + 12

x + 4x = 12 + 6

5x = 18

x = 3.6

Hence the value of x if the side length of Terrarium A is four times the side length of Terrarium B is 3.6

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Answer:

D (bottom right)

Step-by-step explanation:

Using the vertical line test, only D passes.

Hope that helps

Answer:

5

Step-by-step explanation:

3a+5=20 -5

3a=15 /3

a=5

Answer:

Step-by-step explanation:

Mean: 56.95

Median: 64

Mode: 65

Range: 93

15 plates = $1000 + 8(15) = $1120

75 plates = $1000 + 8(75) = $1600

150 plates = $1000 + 8(150) = $2200

Answer:

Step-by-step explanation:

a) The current term number is added to the previous term to get the current term.

__

b) Using n = 2, 3, 4 in the given formula, we have ...

  a2 = a1 +2 = 1 +2 = 3

  a3 = a2 +3 = 3 +3 = 6

  a4 = a3 +4 = 6 +4 = 10

The value of the current term is the sum of all positive integers up to the term number, that is, term n is the n-th "triangle number."

Answer: 4509

8,140-3,631

= 4509

The number of possible outcomes for both Billy and Karen = 32 possible outcomes.

A coin has head and tail and thus;

Number of possible outcomes of a coin toss = 2

Now, for the for the spinner, since there are 8 equal regions;

The number of possible outcomes of the spinner = 8

Now, since they are playing a game;

Number of possible outcomes for Billy for one toss of coin and one time of spinning the spinner = 8 × 2 = 16

Similarly;

Number of possible outcomes for Karen for one toss of coin and one time of spinning the spinner = 8 × 2 = 16

Therefore;

Total possible outcomes for both Karen and Billy = 16 + 16 = 32 possible outcomes.

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Answer:

-2g

Step-by-step explanation:

Distribute G to -2

In simple words multiply G and -2