X, 2X + 11 and 4X - 3 are consecutive terms of an arithmetic sequence. Find the constant difference between terms. Give a formula for finding the nth term of the sequence. Use your formula to find the 27th term of this sequence.

Answer:

10.9

Step-by-step explanation:

[tex]a^2+b^2=c^2[/tex]

[tex]9.1^2+6^2=c^2[/tex]

[tex]82.81+36=c^2[/tex]

[tex]c^2=118.81[/tex]

[tex]c=\sqrt{118.81} =10.9[/tex]

Answer:

2.592 x 10^5

Step-by-step explanation:

1st step: Calculate for 1 day.

if 1 hour = 3.6 X 10³

24 hrs = (3.6 x 10³) X (2.4 x 10¹)

= 3.6 x 2.4 X 10⁴

= 8.64 x 10⁴

2nd Step: Calculate for 3 days;

if 1 day = 8.64 x 10⁴

3 days = (8.64 x 10⁴) X (0.3 x 10¹)

= 8.64 x 0.3 x 10^5

= 2.592 x 10^5

-4 ≤ x ≤ 6

x ≥ -4

3x ≥ -12

3x + 12 ≥ 0

3x + 14 ≥ 2

6 ≥ x

6 - x ≥ 0

1 - x ≥ -5

A. 3x + 14 ≥ 2 and 1 - x ≥ -5

9514 1404 393

Answer:

  5√13 m

Step-by-step explanation:

The length of the space diagonal is the "Pythagorean sum" of the lengths of the edges of the cuboid.

  AC = √(8² +6² +15²) = √325 = √(13·25)

  AC = 5√13 . . . meters

__

AB is the hypotenuse of the right triangle with legs 6 and 8, so is 10 units. AC is the hypotenuse of right triangle ABC, so is ...

  AC = √(AB² +BC²) = √(10² +15²)

Answer:

Y=Srt(12xs^2/z^2)

Step-by-step explanation:

Firstly

We multiply both sides with 1/x^2

We get

Y^2=12/z^2*1/x^2

Y^2=12x^2/z^2

Next: introduce a srt root

We have

Y=srt(12x^2/z^2)

Answer:

Here are a few examples.

(30/2 + 1)/2

(26/2 + 3)/2

(28/2 + 2)/2

9514 1404 393

Answer:

Step-by-step explanation:

Dilation about the origin multiplies each coordinate value by the dilation factor.

  A' = 2A = 2(-1, -2) = (-2, -4)

  B' = 2B = 2(-1, 3) = (-2, 6)

 C' = 2C = 2(4, 3) = (8, 6)

  D' = 2D = 2(4, -2) = (8, -4)

Answer:

100000

Step-by-step explanation:

100000x80=8m

He spent $22.5 on the student discount card.

This question is solved using proportions.

The cost of each card is of $1.50.

Paul bought 15 passes, that is, 15 cards.

Considering that he bought 15 cards, each for $1.50, his spending was of:

He spent $22.5 on the student discount card.

Answer:

True

Step-by-step explanation:

Both happened in different times and are seprate events

Answer:

Step-by-step explanation:

Answer:

6x+36=180

6x=144

x=24

Step-by-step explanation:

this is the correct answer

Answer:

The answer is 20

Step-by-step explanation:

3 times 2 is 6, and 120 divided by six is 20%.

please mark this answer as brainlist

Answer:

353 tickets.

Step-by-step explanation:

Let's say that there are s student tickets and n nonstudent tickets.

s + n = 669

5s + 8n = 4293

Multiply -5 by the entire first equation to get...

-5s - 5n = -3345

Combine the two equations.

5s - 5s + 8n - 5n = 4293 - 3345

3n = 948

n = 316

Now, put the number of nonstudent tickets sold back into the first equation.

s + 316 = 669

s = 353 tickets.

Hope this helps!

Answer:

32

Step-by-step explanation:

Step 1: change 22 - ( -  10) into 22 + 10

Step 2: solve it like normal

z = 3i / (-1 - i )

z = 3i / (-1 - i ) × (-1 + i ) / (-1 + i )

z = (3i × (-1 + i )) / ((-1)² - i ²)

z = (-3i + 3i ²) / ((-1)² - i ²)

z = (-3 - 3i ) / (1 - (-1))

z = (-3 - 3i ) / 2

Note that this number lies in the third quadrant of the complex plane, where both Re(z) and Im(z) are negative. But arctan only returns angles between -π/2 and π/2. So we have

arg(z) = arctan((-3/2)/(-3/2)) - π

arg(z) = arctan(1) - π

arg(z) = π/4 - π

arg(z) = -3π/4

where I'm taking arg(z) to have a range of -π < arg(z) ≤ π.

Answer:

1, 2, 3, 4, 6, and 12

Step-by-step explanation:

Answer:

1,2,3,4,6,12

Step-by-step explanation:

because they divide the numbers without any remainder.

Answer:

$480

Step-by-step explanation:

Let original price be x

{Original price - discount amount = sale price}

So, x - (x * 35/100) = 312

x - 35x/100 = 312

100x - 35x / 100 = 312

65x/100 = 312

65x = 31200

x = 31200/65

x = $480

So I think the original price of desk was $480

The original price of the desk is $480.

A discount is the reduction of either the monetary amount or a percentage of the normal selling price of a product or service.

Given that, a desk is being sold for $312.

Let the original price of the desk be x.

Here, x-35% of x =312

x- 35/100 ×x=312

x-0.35x=312

0.65x=312

x=312/0.65

x=480

Therefore, the original price of the desk is $480.

To learn more about the discount visit:

https://brainly.com/question/3541148.

#SPJ2

Lets do

[tex]\\ \sf\longmapsto K=\dfrac{AB}{A+B}[/tex]

[tex]\\ \sf\longmapsto \dfrac{1}{K}=\dfrac{A+B}{AB}[/tex]

[tex]\\ \sf\longmapsto \dfrac{1}{K}=\dfrac{1}{A}+\dfrac{1}{B}[/tex]

[tex]\\ \sf\longmapsto \dfrac{1}{B}=\dfrac{1}{K}-\dfrac{1}{A}[/tex]

[tex]\\ \sf\longmapsto \dfrac{1}{B}=\dfrac{K-A}{AK}[/tex]

[tex]\\ \sf\longmapsto B=\dfrac{AK}{K-A}[/tex]

Step-by-step explanation:

0.09w + 1.8 = 0

0.09w = 0 - 1.8

0.09w = - 1.8

0.09w ÷ 0.09 = - 1.8/ 0.09

w = - 20

Answer:

OD) 16 cubic centimeters

Answer:

failure to correctly define the problem

Step-by-step explanation:

He changes the menu without identify that the real problem was the service.

Answer:

Drawing 4 - 1/10

Drawing odd number - 1/2

Not drawing 3- 9/10

Drawing 5 or 6 -  1/5

Drawing a number greater than 9 - 0

Let me know if this helps!

Answer:

207m

Step-by-step explanation:

(17+5)*6=132

(15*5)=75

132+75=207

I assume A ∆ B denotes the symmetric difference of A and B, i.e.

A ∆ B = (B - A) U (A - B)

where - denotes the set difference or relative complement, e.g.

B - A = {b ∈ B : b ∉ A}

It can be established that

A ∆ B = (A U B) - (A ∩ B)

so that

n(A ∆ B) = n(A U B) - n(A ∩ B) = 10 - 3 = 7

Not sure what you mean by p(A ∆ B), though... Probability?

Answer:

first one is correct bro

The correct factorization of x³ - 27 is  (x - 3)(x² + 3x + 9).

a³ + b³ = (a + b)(a² -ab + b²) and a³ - b³ = (a - b)(a² + ab + b²).

If we know the formula of these two we can conclude by observing that

the second option x³ - 27 = (x - 3)(x² + 3x +9) is correct.

As x³ - 27

= x³ - 3³.

= (x - 3)(x² + 3x + 9).

learn more about algebraic formulas here :

https://brainly.com/question/14583646

#SPJ2

The following information related to irrigation is as follows:

The gallons of irrigation water per square foot is [tex]326,700\ gallons\ per\ square\ foot[/tex]

For determining the gallons of irrigation water we have to multiply the square foot by the number of gallons in a cubic foot.

Given that,

There are 43,560 square feet in an acre i.e. 1 acre = 43,560.

And, there are 7.5 gallons in a cubic foot i.e. 1 cubic foot = 7.5 gallons.

So, the gallons of irrigation water per square foot is

[tex]= 43,560 \times 7.5\ gallons \\\\= 326,700\ gallons\ per\ square\ foot[/tex]

Therefore we can conclude that the gallons per square foot of irrigation water is [tex]326,700\ gallons\ per\ square\ foot[/tex]

Learn more about per square foot here: brainly.com/question/5991264

Answer:

326,700 gallons

Step-by-step explanation:

1 acre = 43,560 square feet

1 acre-foot of irrigation is an acre irrigated 1 foot deep with water.

Since thee are approximately 7.5 gallons in 1 cubic foot,

1 acre-foot of irrigation = 43,560 * 7.5 gallons

1 acre-foot = 326,700 gallons

This is the number of gallons in one acre-foot, not gallons per square foot.

Answer:

272 yd²

Step-by-step explanation:

Surface area = base area + lateral area

= (10×10)+(8.6×10×2)

= 100+172

= 272 yd²

Answers:

The venn diagram is shown below.

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

Explanation:

M = set of people studying math

C = set of people studying chemistry

P = set of people studying physics

Something like the notation n(C) refers to the count of items in set C, aka the number of people who study chemistry. Similar ideas apply to n(M) and n(P) to refer to the counts of math and physics respectively.

Something like n(C and M) is the number of people who study chemistry and math. Same idea applies to something like n(C and P) or n(M and P)

With all that in mind, we have these 7 facts

We'll start with fact 7. This value goes in the very center of the 3 overlapping circles of the venn diagram. Refer to the diagram below.

Since 9 people study all three subjects, and 16 study chemistry and math, this must mean 16-9 = 7 people study chemistry and math without physics involved. We'll write 7 in the region between circles C and M, but outside of circle P.

Since 9 people study all three subjects, and 14 study math and physics, we know that 14-9 = 5 people study only math and physics without chemistry. We'll write 5 in the region between circles M and P, but outside circle C.

Since 9 people study all three subjects, and 18 study chemistry and physics, we know that 18-9 = 9 people study only chemistry and physics without math. We'll write 9 in the region between circles C and P but outside circle M.

If you're lost, then refer the diagram below. So far, we have filled in the very center "9" and the closest three values surrounding it (the 7, 9 and 5).

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

Focus your attention on circle M for now. The values in this circle add to: 7+9+5 = 21

Since n(M) = 41, this must mean the missing value must be 20. This goes in circle M but outside the other two circles.

Note how 7+9+5+20 = 41 when we add everything in circle M. This circle is completely filled out. We'll follow a similar path for the other circles.

Move onto circle C. Adding everything in it so far gets us 9+9+7 = 25. We want to get to n(C) = 48 which means we need to have 48-25 = 23 in circle C but outside the other circles. Circle C is now done.

Lastly, focus on circle P. The values we found so far in this circle add to 9+9+5 = 23. The missing value must be 19 because 42-23 = 19, and n(P) = 42.

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

At this point, all three circles are filled out. The only thing missing is the number outside the circles, but inside the rectangle.

Add up everything in the circles: 23+7+20+9+9+5+19 = 92

This tells us that we have 92 people who studied at least one subject (i.e. one or more subjects). There are 120 people surveyed, meaning that 120-92 = 28 people study neither of these subjects. We write 28 outside the circles.

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

The venn diagram is done by this point. To address the questions, we'll just read from the diagram (and at most do an addition problem).

To find the number of people who study exactly one subject, we will add up the numbers that are in one circle but not in any other circle. Those values are: 23, 20, and 19. So 23+20+19 = 62 people study exactly one subject.

We already found the number of people who study at least one subject, and that was 92 people. This was when we added every number in the circles.

For the last question, we already found this value as well. This answer is 28 people which is found outside all three circles.

The venn diagram is shown below to visually summarize and organize all of the data. Hopefully it clears up any confusion you may have about the previous steps.

Total number of students who exactly one subject is 62

No of students who study at least one subject is 92

No of students who do not study any subject is 28

let us do this problem by set theory.

in the attached figure

three circles have been drawn representing the number of students studying maths, physics and chemistry.

from the diagram

1) Number of students who study exactly one subject=no of students who study maths + number of students who study chemistry+number of students who study physics- 2*[number of students who study both physics and chemistry-number of students who study both physics and maths-number of students who study both maths and chemistry ]+3*number of students who study all three subjects

from the attached figure,

2) Total number of students who exactly one subject = 20+19+23 = 62

3) No of students who study at least one subject will be the sum of each data in the attached figure i.e union of all three sets.

no of students who study at least one subject = 20+7+5+9+19+9+23=92

no of students who do not study any subject = total students- the union of all three sets.

no of students who do not study any subject = 120-92 = 28

therefore,

total number of students who exactly one subject is 62

no of students who study at least one subject is 92

no of students who do not study any subject is 28

to get more about set theory refer to the link,

https://brainly.com/question/13458417