an arithmetic series begins 29+25+21+...
find the maximum value that the series could have

Answers

Answer 1

The series' value is maximized if the sum only consists of positive terms. Notice that each term in the sum takes the form 4n + 1 for integer n. This means the smallest positive integer that the sum can involve is 1, so the maximum value is

S = 29 + 25 + 21 + … + 9 + 5 + 1

Reversing the order of terms gives the same sum,

S = 1 + 5 + 9 + … + 21 + 25 + 29

Adding terms in the same positions gives us twice this sum,

2S = (29 + 1) + (25 + 5) + (21 + 9) + … + (1 + 29)

Notice how each grouped sum adds to 30. There are 8 terms in the sum, since 4n + 1 = 29 when n = 8. So

2S = 8 × 30 = 240   ===>   S = 120


Related Questions

Simplify.
Rewrite the expression in the form b".
6^-2/6^4

Answers

Answer:

Step-by-step explanation:

[tex]\dfrac{a^{m}}{a^{n}}=a^{m-n}\\\\\\\dfrac{6^{-2}}{6^{4}}=a^{-2-4}=6^{-6}[/tex]

x+ y + z=1
3x - y- z=7
2x - 2y - 4z = 52

Answers

https://core.ac.uk/download/pdf/48393503.pdf

What is the value of x in the equation x − 7 = 11?

Answers

Answer: x = 18

explanation: By adding 11 and 7 you get 18

Answer:

18

Step-by-step explanation:

x - 7 = 11x = 11 + 7x = 18

[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]

|2-x|>|2x-1|


tolong sertakan cara pertidaksamaan nilai mutlak kak​

Answers

Answer:

a

Step-by-step explanation:

PLEASE HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

Step-by-step explanation:

Answer:

xwvy

Step-by-step explanation:

seven pints of water are needed to water each square foot of lawn. At least how many gallons of water are needed to water a lawn 12 feet by 16 feet.

Answers

Find total area: 12 x 16 = 192 square feet.

7 pints are needed for each square foot , multiply total square feet by 7 pints to find total pints needed:

192 x 7 = 1,344 total pints.

1 gallon = 8 pints.

Divide total pints needed by 8 to get gallons:

1,344 / 8 = 168

168 gallons are needed

X ÷ 0.25 = 0 um... Ya pls help...

Answers

Answer:

X = 0

Step-by-step explanation:

If AB = 4x+4, BC = x - 5 and AC = 19
find x, ab, and bc

Answers

Answer:

AB=x+3;

BC=2x;

AC=4x−5

AB+BC=AC

x+3+2x=4x−5

3x+3=4x−5

x=8.

Step-by-step explanation:

I don’t understand what the rule is fit this and how to get it.

Answers

It’s like some type of math form or sum

Which expression is equivalent to the given expression?
-2.12 + 80 - 9 + 4r + 712 + 2
A.-912 – 12r + 11
B. 5x2 + 12r-7
C. -9x2 + 4x – 7
D. -5.2 + 4x + 11

Answers

Answer:

912-12r+11

don't worry

A total of 592 tickets were sold for the school play. They were either adult tickets or student tickets. There were 58 fewer student tickets sold than adult tickets. How many adult tickets were sold?

Answers

Answer:

 148 adult tickets

Step-by-step explanation:

The number of adult tickets sold is 1/4 of the total:

 (1/4)×592 = 148 . . . adult tickets sold

Write the ratio of cats to dogs 3
different ways if there are 5 cats and
9 dogs.

Answers

Answer:

5 cats to 9 dogs

5 : 9

5 / 9

Step-by-step explanation:

hope this helps!

Answer:

Ratio of cats to dogs :

5 to 9

5:9

5/9

Hope it helps :)

Joshua has $500 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax.
He buys a new bicycle for $306.11.
He buys 4 bicycle reflectors for $7.06 each and a pair of bike gloves for $17.67.
He plans to spend some or all of the money he has left to buy new biking outfits for $42.28 each.

Write and solve an inequality which can be used to determine oo, the number of outfits Joshua can purchase while staying within his budget.

Answers

Answer: 12

Step-by-step explanation:

Answer:

Inequality: 42.28o + 352.02 ≤ 500

Answer: o ≤ 3.5

Step-by-step explanation:

Have a good day :)

Solve for x. -3(x+n)=x

Answers

Answer:

x = 3/4 n

Step-by-step explanation:

-3(x+n)=x

Distribute

-3x-3n = x

Add 3x to each side

-3x-3n+3x= x+3x

3n = 4x

Divide by 4

3/4n = 3x/3

3/4 n = x

Làm ơn hãy giúp tôi
(a+b)²
(a-b)²

Answers

Answer:

[tex](a + b) ^{2} = {a}^{2} + 2ab + {b}^{2} \\ (a - b) ^{2} = {a {}^{2} - 2ab + {b}}^{2} [/tex]

Step-by-step explanation:

hopethe answer helped you :)

Answer:

(a+b)² = a²+2ab+b²

(a-b)² = a²-2ab+b²

Step-by-step explanation:

find the missing endpoint endpoint h (-1,0) midpoint p(0,-1)​

Answers

Answer:

Step-by-step explanation:

Let the other end point be (a,b)

Then the midpoint p(0,-1) is between the two end points (-1,0) and (a,b)

So

(0,-1) = ( (-1+a)/2 , (0+b)/2)

So we have

0 = (-1 +a) /2

0 = -1 + a

a =1

and

-1 = (0+b)/2

-2 = 0+b

b = -2

So the other end point is ( 1, -2)

can someone help me with this please

Answers

Answer:

7.5

plss mark brainliestt

Step-by-step explanation:

5×1.5=7.5

if u dilate or enlarge something by a scale factor bigger than 1,then it gets larger

If you worked 40 hours a week at a minimum wage job in
Oregon, how much would you make in one week before tores
and other deductions?

Answers

Answer:

450+120w

will be the expression

Equation: 450+120w = x

How are arithmetic and geometric sequences similar.

Answers

Answer:

The similarities between arithmetic and geometric sequences is that they both follow a certain term pattern that can't be broken.

brainliest is appreciated

Step-by-step explanation:

An arithmetic sequence is a sequence of numbers that is calculated by subtracting or adding a fixed term to/from the previous term. However, a geometric sequence is a sequence of numbers where each new number is calculated by multiplying the previous number by a fixed and non-zero number.

HELP FAST PLEASE (First answer gets brainliest!!!)
Solve for x:

Answers

Hello here's ur answer ⤴️

Step-by-step explanation:

hope it helps

Answer:

x = 0.4

Step-by-step explanation:

[tex] \frac{2}{3} + \frac{1}{3} x = 2x \\ = > \frac{2}{3} + \frac{x}{3} = 2x \\ = > \frac{2 + x}{3} = 2x \\ = > 2 + x = 2x \times 3 \\ = > 2 + x = 6x \\ = > 2 = 6x - x \\ = > 2 = 5x \\ = > \frac{2}{5} = x \\ = > 0.4 = x[/tex]

(hi, help please.) You are on the ski trip with BPM, it is your very first time trying out this new skiing thing. Nerd Dawg is there.

Top Elevation: 2,200 feet above sea level
Bottom Elevation: 500 feet above sea level

Questions

1) Nerd Dawg starts at an elevation of 2,150.67 feet and he falls down at an elevation of 1,440.34 feet. What number shows his change in elevation?

2) Ms. Moody starts out on the ski lift at 500 ft. When she gets off of the ski lift, she is at 2,190 ft. What is her change in elevation?

Answers

Answer:

1,440.34 ft OR 710.33 ft and 1690 ft

Step-by-step explanation:

1)

He starts at 2,150.67 feet and ends up in 1,440.34 feet.

If you're asking what number shows his change in elevation, it's obviously 1,440.34.

OR if they are asking for the difference, the answer is 710.33

2)

She starts ar 500 ft. When she gets off, it's 2,190 ft. If you subtract those 2 numbers, it should be 1690 ft.

What is the inverse function of f(x) = x/x—2

Answers

Answer:

[tex]y = \frac{2x}{x - 1} [/tex]

Step-by-step explanation:

find the inverse of the function

 

To find the inverse function, swap x and y, and solve the resulting equation for x.

If the initial function is not one-to-one, then there will be more than one inverse.

So, swap the variables

[tex]y = \frac{x}{x - 2} [/tex]

becomes

[tex]x = \frac{y}{y - 2} [/tex]

Now, solve the equation 

[tex]x = \frac{y}{y - 2} [/tex]

 for y.

[tex]y = \frac{2x}{x - 1} [/tex]

PLEASE HELP I WILL GIVE BRAINLIEST TO RIGHT ANSWER
Cameron has $720 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax.
He buys a new bicycle for $200.75.
He buys 4 bicycle reflectors for $12.29 each and a pair of bike gloves for $20.49.
He plans to spend some or all of the money he has left to buy new biking outfits for $70.25 each.

Write and solve an inequality which can be used to determine xx, the number of outfits Cameron can purchase while staying within his budget.

Answers

The inequality which can be used to determine x, the number of outfits Cameron can purchase while staying within his budget is 720 ≤ 270.4 + 70.25x

Given:

Amount with Cameron = $720

Cost of new bicycles = $200.75

Cost of 4 bicycle reflectors = $12.29 × 4

= $49.16

Cost of bike gloves = $20.49

Cost of new banking outfit = $70.25

let

number of outfits = x

The inequality:

720 ≤ 200.75 + 49.16 + 20.49 + (70.25 × x)

720 ≤ 270.4 + 70.25x

720 - 270.4 ≤ 70.25x

449.6 ≤ 70.25x

x ≤ 449.6 / 70.25

x ≤ 6.4

He can only purchase a whole value of outfits, not a decimal number

Therefore, the number of outfits Cameron can purchase is 6 pairs

Read more:

https://brainly.com/question/15816805

example: The sum of 2x and 9 = (2x + 9)

1) The sum of three times a number, x, and 12

2) The sum of 5z and a number, n.

3) The sum of 5z and a number n, decreased by 35.

4) The sum of a number x, and 4, and 7

5) The sum of a number z, and 9 and 18

Answers

Answer:

Step-by-step explanation:

1) 3x  + 12

2) 5z + n

3) 5z + (n-35)

4) x + 4 + 7

5) z + 9 + 18

-19 = x - 19

heyyy i need some help again :)

Answers

Answer:

[tex] - 19 = x - 19 \\ x = - 19 + 19 \\ x = 0 \\ thank \: you[/tex]

Answer:

x = 0

Step-by-step explanation:

-19 = x - 19

Add 19 to both 19’s

0 = x

x = 0

What are the repeating digits in a small scoop of repeating digits in the decimal equivalent of the fraction shown below 1111/999

Answers

Let x = 1111/999. Then

999x = 1111

1000x - x = 1111

Clearly 1 < x < 2, and x must have a repeating pattern of 3 digits immediately after the decimal point. So we can write

x = 1.abcabcabc

Then

1000x = 1abc.abcabcabc

and

1000x - x = 1abc.abcabcabc… - 1.abcabcabc

999x = 1abc - 1

x = (1abc - 1)/999

Now,

1abc - 1 = 1000 + 100a + 10b + c - 1

and

1111 = 1000 + 100 + 10 + 1

which means a = b = 1 and c = 2.

So we have

1111/999 = 1.112112112…

13x - 2 (8 + 5x) = 12 - 11x

A) -4/7
B) 28/29
C) 2
D) 4

Answers

Answer:

[tex]13 x - 2(8 + 5x) = 12 - 11x \\ 13x - 16 - 10x = 12 - 11x \\ x \: terms \: togather \\ 13x + 11x - 10x = 12 + 16 \\ 14x = 28 \\ x = \frac{28}{14} = 2 \\ thank \: you[/tex]

Answer:

x=2

option c.

Step-by-step explanation:

13x - 2 (8 + 5x) = 12 - 11x13x-16-10x=12-11x13x-10x-16=12-11x3x-16=12-11x3x+11x=12+1614x=28x=28/14x=2

Hence, option c. is the correct answer

juantia spent 3/4 of he allowance at the mall. Of the money spent at the mall 1/2 was spent on new earphones. what part of her allowance did juantia spend on earphones.

Answers

Answer:

3/8

Step-by-step explanation:

Juanita spent 3/4 of her allowance at the mall. Of the money spent at the mall, 1/2 was spent on new earphones. What part of her allowance did Juanita spend on earphones?

Correct Answer: 3/8

Help please asap.. I don’t understand..

Answers

Answer:

5.5

Step-by-step explanation:

Subtraction with Real Numbers (I need the equation on how to solve the answer)

-3-(-8)=

Answers

Answer:

5

Step-by-step explanation:

Given:

- 3 - (- 8)

Remember two subsequent negatives turn to positive:

- 3 + 8 = 8 - 3 = 5

Answer:

5

Step-by-step explanation:

[tex] - 3 - ( - 8)[/tex]

Remove the parentheses:

[tex] - 3 + 8[/tex]

= 5

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