(2x + 23), (8x + 2) and (20x – 52) are three consecutive terms of an arithmetic sequence.
Prove that the common difference of the sequence is 12

Answers

Answer 1

Step-by-step explanation:

Given (2x + 23), (8x + 2) and (20x - 52) are three consecutive terms of an arithmetic sequence.

(8x + 2) - (2x + 23) = (20x - 52) - (8x + 2)

or, 6x - 21 = 12x - 54

or, 12x - 6x = - 21 + 54 = 33

or, 6x = 33

or, 2x = 11

∴ x = 11/2

∴2x + 23 = 2 × 11/2 + 23 = 34

8x + 2 = 8 × 11/2 + 2 = 46 and

20x - 52 = 20 × 11/2 - 52 = 110 - 52 = 58

34, 46 and 58 are three consecutive terms of an arithmetic sequence.

∴ Common difference(d) = 46 - 34 = 58 - 46 = 12, it is proved.

Hence, the common difference of the sequence is 12.


Related Questions

solve similar triangles (advanced)

Answers

Step-by-step explanation:

similar triangles mean that all angles are the same, and the side lengths of one triangle correlate to the corresponding sides of the other triangle by the same factor.

that means that the sides 2 (ED) and x (CB) have the same relation as the 6+4 (AD) and the 6 (AB) sides.

so,

x/2 = 6/(6+4) = 6/10 = 3/5

x = 2 × 3/5 = 6/5 = 1.2

1000000x900=?????????????

Answers

Answer:

The answer is 900000000

Answer:

900000000, or 9.0x 10^8

Step-by-step explanation:

do 1(9)=9

then add the 0's behind.

What is 0.27845 rounded to 3 decimal places

Answers

Answer:

0.278

Step-by-step explanation:

Just gonna attach a picture of the problem so it’s easier

Answers

Answer:

You have to find the intercept hope this helps

Step-by-step explanation:

I didn't pay attention today​

Answers

Answer:

because you was busy and nor interested in paying attention.

What is the value of y in the formula show when x=4/5

Answers

Answer:

there is no way to solve for y, but if your solving for x then x=4/5 and in decimal form it is x=0.8    hope that helps

Step-by-step explanation:

Evaluate the figure below.
Find the value of x.
Formula for area of a rectangle: A = lw

Answers

Answer:

x=9,-7

Step-by-step explanation:

(x+3)(x-5)=48

x^2-2x-15-48=0

x^2-2x-63=0

(x-9)(x+7)=0

x=9,-7

dont use the negative number becuase it would not make sense in this scenario

width = 12

length=4

HELP ASAP 10 POINTS


Which coordinates are the best estimate of the solution to the system of equations?

Hint: Which coordinate is closest to where the lines meet?
Question 4 options:


(6,0)


(0,5)


(1,4)


(1,5)

Answers

Answer:

(1,4)

Step-by-step explanation:

It was either (1,3) or (1,4) but there was no (1,3) so (1,4).

Hopes This Helps :)

When we first learn arithmetic, we focus on working with whole numbers. Then, we extend our understanding to fractions and negative numbers.

In algebra, we transfer these same skills to expressions involving variables. What elementary skills have you used so far in this course, and how have you extended them?

PLESE ANSWER AS FAST AS YOU CAN, IT MEANS ALOT!

Answers

Answer:

I don't think I can remember every skill I was taught through the years but in Kindergarten we used Number Sense so we could understand the meaning of more and less also there's estimation and  PEMDAS. I've also learned how to round up so that the solution is at least around those numbers if the skill is to be applied.

hope that helps

Step-by-step explanation:

Need help quickly please

Answers

Step-by-step explanation:

just want your ponit hahahaHA


A stainless steel gas grill is list priced at $495. The manufacturer offers a series discount of 25/20/10 to wholesalers and a 25/20 series discount to
retailers. What is the difference between the prices?

Answers

Answer:200$

Step-by-step explanation:

Help me plzzzzz
y=__×+__​

Answers

Y=-1/4x-6. There you go

Find the m, b, and write the equation for the following graph:

Answers

Answer:

y=3

Step-by-step explanation:

m=0

b=3

Can someone please help me <3

Answers

Answer:

x = 9

Step-by-step explanation:

10 + x/3 = 13

x/3 = 13 -10

x/3 = 3

x = 3*3 = 9

Answer:

9

Step-by-step explanation:

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS is the order of operations, and stands for:

Parenthesis

Exponents (& Roots)

Multiplications

Divisions

Additions

Subtractions

~

First, subtract 10 from both sides of the equation:

[tex]\frac{x}{3} + 10 = 13\\\\\frac{x}{3} + 10 (-10) = 13 (-10)\\\\\\\frac{x}{3} = 13 - 10\\\\\\\frac{x}{3} = 3[/tex]

Next, isolate the variable, x, by multiplying 3 to both sides of the equations:

[tex](\frac{x}{3}) * 3= (3) * 3\\\\x = 3 * 3\\\\x = 9[/tex]

~

Select the expressions that are equivalent to 12n - 8. Select all that apply.
A. 3n + 4 + 3n + 4 + 4n
B. 11n + 4 + n -12
C. 6(6n - 2)
D. 4(3n – 2)
E. 4n + 22 - 12 + 8n

Answers

A.3n+4+3n+4+4n

=3n+3n+4n+4+4

=10n+8

B.11n+4+n-12

=11n+n+4-12

=12n-8

C.6(6n-2)

=36n-12

D.4(3n-2)

=12n-8

E.4n+22-12+8n

=4n+8n+22-12

=12n+10

so,B and D are the expressions that are equivalent to 12n-8.

The FitnessGram™ Pacer Test is a multistage aerobic capacity test that progressively gets more difficult as it - IM JUST KIDDING I ACTUALLY NEED HELP THO​

Answers

45 degrees. A triangle should add up to 180 degrees. So 76+59+?=180. The ? Is 45 so that is your answer. Another way is to take 180 and subtract 59 and 76 which will leave you with 45.
Following the Triangle Sum Theorem, the three angles in a triangle must sum up to 180°.

Therefore, we can create an equation to find the measure of angle 1, given the two other angles.

76+59+x=180. x=the measure of angle 1 (unknown).

135+x=180. [76+59=135]

135-135+x=180-135 [Isolate x by subtracting 135 from both sides]

x=45.

Therefore, the angle measure of angle 1 = 45°

Each day Jacob records the number of laps and the distance he walks, in miles, on a track. Graph the relation and determine whether the distance that Jacob walks is a function of the number of laps.
{(3, 0.75), (6, 1.5), (9, 2.25), (2, 0.5), (7, 1.75), (10, 2.5), (4, 1)}

Answers

The distance is 6.18 miles that Jacob walks as a function of the number of laps which is represented in the attached graph.

We have been given the relation below:

{(3, 0.75), (6, 1.5), (9, 2.25), (2, 0.5), (7, 1.75), (10, 2.5), (4, 1)}

What is the distance between two points?

The distance between two points is defined as the length of the line segment between two places representing their distance.

The formula of the distance between two points is P(x₁, y₁) and Q(x₂, y₂) is given by: d (P, Q) = √ (x₂ – x₁)² + (y₂ – y₁) ².

The given relation of function is represented in the attached graph.

Take two endpoints (3, 0.75) and (9, 2.25)

x₁ = 3, y₁ = 2.25

x₂ = 4, y₂ = 9

distance = √ (9 – 3)² + (2.25 – 0.75)²

distance = √ (6)² + (1.5)²

distance = √ (36 + 2.25)

distance = √ (38.25)

distance = 6.18 miles

Therefore, the distance is 6.18 miles that Jacob walks is a function of the number of laps.

Learn more about the distance between two points here:

brainly.com/question/15958176

#SPJ5

Line N passes through the points (-1, 4) and (-1, -4).
5
4
3-
2
1
-5 -4 -3 -2 -14
1
2 3 4 5
x
X
اسة.
5
3
ܛܝܝܝ
5
Which is true of line N?

Answers

Answer:

i don't know btw is this eighth grade

Which correlation coefficient indicates the stronger linear relationship between random variables for a fixed sample size?


a

r = 0..8

b

r = 0.5

c

r = -0.2

d

r = -0.9

Answers

Answer:

D) r=-0.9

Step-by-step explanation:

Recall that when [tex]|r|[/tex] is closest to 1, the stronger the correlation between the variables. In this case, while [tex]|0.8|=0.8[/tex], [tex]|-0.9|=0.9[/tex] is actually larger and shows a stronger negative correlation between random variables. Therefore, D is correct.

While In a cave what did Sirius tell Harry and his friends about crouch

Answers

The information that was given to Harry about Crouch was that it was Crouch who gave the order for him to be sent to the wizard prison without a trial.

It should be noted that when Harry went to Hogsmeade, he brought food for Sirius and he was still in his dog form. Sirius then led them to a cave.

In the cave, they saw Buckbeak, the hippogriff. Sirius then turned back to a human being. He then gave Harry the piece of information that Crouch gave the order for him to be sent to Azkaban which was a prison for wizards.

Learn more about Harry on:

https://brainly.com/question/1173893

-0.5x=3.6

F. -72
G. -7.2
H. 7.2
I. 72

Answers

Answer:

G

Step-by-step explanation:

3.6÷-0.5 is -7.2, so it's G

plssssssssssssssssssssssss​

Answers

Y = x^2 -3

y = (x-3)(x+3)

For x-intercepts, y = 0

Therefore (x-3)(x+3) = 0

x intercepts are (3,0) and (-3,0)

The line of symmetry is x = 3+(-3) = 0

Vertex is on the line of symmetry

When x = 0, y = -1

Vertex = (0,-1)

Answer:

The answer is equal to 0

Step-by-step explanation:

Explanation in the picture.

write the equation in slo
pe intercept form -1=-2x+y

Answers

Answer:

y = -2x - 1

Step-by-step explanation:

Put y on the left and everything else on the right

Plz help ToT I'm horrible at math

Answers

Answer:

24 Square Inches

Step-by-step explanation:

Jayden had $43 in his bank account. He wanted to buy a game at GameStop. The game cost $15. He made the purchase.
a) Write an expression to show his purchase activity.

b) How much did he have, after the purchase of the game?

Answers

Answer:

a) 43 - 15

b) 28

43 represents the money he has the game costs $15, subtract 15 from 43 and get $28. After the purchase he now has $28

compare the following number :-

▪︎ 3 × 10¹² and 4 × 10¹¹

I need a well explained solution,
pls not from any other websites

thx for answering~~​

Answers

Answer:

[tex] {10}^{12} = 1000000000000[/tex]

Then ,

[tex]3 \times {10}^{12} = 3000000000000[/tex]

And

[tex] {10}^{11} = 100000000000[/tex]

Then ,

[tex]4 \times {10}^{11} = 400000000000[/tex]

Step-by-step explanation:

• Hence , 3 x 10 to the power 12 is greater .

The value of 3 × 10¹² is greater than 4 × 10¹¹

The standard scientific expression is given as A * 10^n

Given the scientific values 3 × 10¹² and 4 × 10¹¹, we need to compare the values.

The value of their powers will determine which of the values is greater or less.

For the notation 3 × 10¹², we can see that the power is 12 while for the notation  4 × 10¹¹, the power is 11. Since 12 is greater than 11, hence the value of 3 × 10¹² is greater than 4 × 10¹¹

Learn more on scientific values here: https://brainly.com/question/1522308

What is the distance between (7, 1) and (-4, -5)?

Answers

Answer:

The distance between [tex](7,1)[/tex] and [tex](-4,-5)[/tex] is [tex]\sqrt{157}[/tex] units

Step-by-step explanation:

Use the distance formula [tex]d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex] where [tex]d[/tex] is the positive distance between [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]:

[tex]d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]

[tex]d=\sqrt{(-5-1)^2+(-4-7)^2}[/tex]

[tex]d=\sqrt{(-6)^2+(-11)^2}[/tex]

[tex]d=\sqrt{36+121}[/tex]

[tex]d=\sqrt{157}[/tex]

Therefore, the distance between [tex](7,1)[/tex] and [tex](-4,-5)[/tex] is [tex]\sqrt{157}[/tex] units

Answer: The distance between (7,1), and (-4, -5) is 12.53.

A *bank* is a regular quadrilateral with four equal sides and four equal angles.
HELP PLEASE QUICK

Answers

Answer:

square

Step-by-step explanation:

question: A _____ is a regular quadrilateral with four equal sides and four equal angles.

first we have that it is a regular quadrilateral.

regular shapes are shapes that have equal side lengths, and equal interior angle measures.

a quadrilateral means it has 4 sides

if there are 4 sides, and all the angles are equal then each angle will be 90 degrees/ a right angle.

therefore you get a shape with:

4 congruent (equal) sides

4 right angles

this describes a square!

What is the equation of a line that is perpendicular to the line y = - 1/2 x + 1 and passes through the point (8, - 1)? A y = −1/2 x + 8 B y = 2x - 17 C y = −1/2 x − 2 D y = 2x - 1

Answers

Answer is B y = 2x - 17

First find the negative reciprocal of the gradient for y = -1/2 x + 1 to find the perpendicular line gradient.

-1/2 = 2

Gradient of perpendicular line = 2

Perpendicular line is y=2x + c

Substitute (8,-1) into the line to find the y-intercept (c).

-1 = 2(8) + c
-1 = 16 + c
c = -17

Therefore, the perpendicular line is y = 2x - 17.

what would be the resulting difference if the line transition: width 2s, height 2s; was removed from the first css rule?

Answers

Answer:

ages would no longer get larger as the mouse hovers over them. The transition would happen over 10s, since this is the default duration.

Step-by-step explanation:

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