(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

8) The height of a stack of CD cases is Proportional to the number of CD’s in the stack. A stack of 6 CD’s is 66mm high.* Find the unit rate**

a) How high is a stack of 10 CD’s?


b) Write an equation that relates the height (y) of a stack of CD’s and the number of CD cases(x) in the stack.

Answers

Step-by-step explanation:

well, when 6 CD cases are 66 mm high, then 1 CD case is 66/6 = 11 mm high.

a)

therefore, 10 CD cases are 11×10 = 110 mm high.

b)

y = 11x

Name all points collinear with point E.

Answers

Answer:

n,c,b

Step-by-step explanation:

Consider the numbers 54.162 and 5,416.2. Which statements accurately reflect the relationship between the "6" in each number?
Select two (2) that apply.
The 6 in 54.162 has a greater value than the 6 in 5,416.2
The 6 in 54.162 has a smaller value than the 6 in 5,416.2.
a
The value of the 6 in 5,416.2 is 10 times greater than the value of the 6 in 54.162.
The value of the 6 in 54.162 is 10 times greater than the value of the 6 in 5, 416.2.
The value of the 6 in 5,416.2 is 100 times greater than the value of the 6 in 54.162.
The value of the 6 in 54.162 is 100 times greater than the value of the 6 in 5,416.2.

Answers

Answer:

1) The value of the 6 in 5,416.2 is 100 times greater than the value of the 6 in 54.162.

2) The 6 in 54.162 has a smaller value than the 6 in 5,416.2.

Step-by-step explanation:

1) 0.06 times 100 equals 6

2) 0.06 < 6

From his eye, which stands 1.61 meters above the ground, Jacob measures the angle
of elevation to the top of a prominent skyscraper to be 25°. If he is standing at a
horizontal distance of 281 meters from the base of the skyscraper, what is the height
of the skyscraper? Round your answer to the nearest tenth of a meter if necessary.

Answers

Step-by-step explanation:

we have a right-angled triangle, that is "hovering" 1.61 m above the ground.

the Hypotenuse (the side opposite of the 90 degree angle) is the line of sight from the eye to the top of the skyscraper.

one leg is the height of the skyscraper (minus the 1.61 m).

the other leg is the ground distance from Jacob to the skyscraper (281 m).

we know already 2 angles : the 90° angle between the ground distance and the skyscraper height. and the 25° between the ground distance and the line of sight.

and as we know that the sum of all angles in a triangle is always 180°, we know that the third angle (between the line of sight and the skyscraper height) is

180 - 90 - 25 = 65°

now we can use the law of sines

a/sin(A) = b/sin(B) = c/sin(C)

(the ratio between a side and its opposing angle)

to get all missing side lengths.

the 25° angle is opposite of the skyscraper height, and the 65° angle is opposite of the ground distance (the only side length we know so far).

so,

height/sin(25) = 281/sin(65)

height = 281 × sin(25)/sin(65) = 131.0324519... m

to get the full height of the skyscraper, we need to add the 1.61 m that the described triangle was "hovering" above ground.

therefore, the height of the skyscraper is

131.0324519... + 1.61 = 132.6424519... ≈ 132.6 m

Help me plzzzz

Graph y = -3x + 7.​

Answers

Answer:

This is the graph. Hope the pic loads.

19. The passing marks in an examination is 40%. If Seema gets 130 marks, she fails by ups 2 marks. Find the total marks.​

Answers

Given :-

Passing marks in an exam is 40% .Seema gets 130 marks and fails by 2 marks.

To find :-

The maximum marks for the exam .

Solution :-

According to the Question ,

[tex]\dashrightarrow[/tex] Passing marks = 40% .

[tex]\dashrightarrow[/tex] Seema's marks = 130 .

Let us take the maximum marks be x . Then ,

[tex]\dashrightarrow[/tex] Passing marks = 130 + 2

[tex]\dashrightarrow[/tex] Passing marks = 132

And , by question ,

[tex]\dashrightarrow[/tex] 40x/100 = 132

[tex]\dashrightarrow[/tex] x = 132 * 100/40

[tex]\dashrightarrow[/tex] x = 330

Hence the maximum marks for the exam is 330.

Given :

Passing marks in the examination = 40% .

Marks obtained by Seema = 130 .

So, Let us assume the maximum marks as x .

Also,

Passing marks = 132 [ ∵ Seema got 130 marks and she failed by 2 marks ]

According to the question :

[tex] \\ \tt : \implies\dfrac{40x}{100} = 132 \\ \\ \tt : \implies\dfrac{4 \cancel{0}x}{10 \cancel{0}} = 132 \\ \\ \: \: \: \tt \: : \implies 4x = 132 \times 10 \\ \\ \tt : \implies \: 4x = 1320 \\ \\ \tt : \implies \: x = \frac{1320}{4} \\ \\ \tt : \implies \: x = 330 \: \: \\ [/tex]

Hence, The total marks is 330 .

a video game system was on sale for $350. if the discount was 10% off, how much money did they take off the price?

Answers

Answer:

they took off 35$

Step-by-step explanation:

hope this helps

Answer:

$35

Step-by-step explanation:

10 divided by 350 = $35

9 13 / 16 + 10 3 / 8 =

Answers

It equals 20 3/16, or 20.1875

Solve: x ÷ 0.6 = 8.9



5.34



9.5



8.3



0.07

Answers

Answer:

5.34

Step-by-step explanation:

x = 8.9 X 0.6

x = 5.34

Your welcome :)

Identify the terms and like terms in the expression.3n+7−n−3

Answers

Answer:

n

Step-by-step explanation:

In algebra, like terms are terms that have the same variables and powers.

Help help help on marhswatch please help!!

Answers

7x-35<2x-10 distribut it

7x-2x<-10+35 collect like them

5x<25 divide both side by 5

x<5

Perform the operation. (-4x^2-2x-6)-(-7x^2-2x-2)

Answers

Answer:

3x²-4

Step-by-step explanation:

1 distribute

(-4x²-2x-6)+7x²+2x+2

2 eliminate redudant parentheses

-4x² -2x - 6+7x² +2x+2

3 Add the numbers

-4x²-2x-4+7x²+2x

4 Combine like terms

3x²-2x-4+2x

5 Combine like terms

3x²-4

Answer:

[tex]3x^{2} -4[/tex]

Step-by-step explanation:

Before solving this you have to know that,

( - ) × ( - ) = ( + )

( + ) × ( + ) = ( + )

( - ) × ( + ) = ( - )

Let us solve now.

[tex](-4x^2-2x-6)-(-7x^2-2x-2)[/tex]

[tex](-4x^2-2x-6)+7x^{2} +2x+2[/tex]

[tex]-4x^2-2x-6+7x^{2} +2x+2[/tex]

Now combine like terms

[tex]-4x^{2}+7x^{2} -2x+2x-6+2[/tex]

[tex]3x^{2} -4[/tex]

Hope this helps you .

Let me know if you have any other questions :-)

Is the figure a right triangle?


A yes, the relationship of the sides follows Pythagorean theorem

B no, the relationship of the sides DOSE NOT follow Pythagorean theorem

C no, the relationship of the sides follows Pythagorean theorem

D Yes, the relationship of the sides DOSE NOT follow Pythagorean theorem

Answers

Answer:

c will correct..

like

h² = p² + b²

14² = 74 + 122

196 = 196

The answer is B
Hope this helps

Which form most quickly reveals the zeros (or "roots") of the function?
Choose 1 answer:
f(2)=3(x+6)2 - 75
B
f(x) = 3x2 + 36x +33
f(x) = 3(x + 1)(x +11)
Write one of the zeros.
T =

Answers

Answer:

c

Step-by-step explanation:

Maggie's brother is 5 years younger than three times her
age. The sum of their ages IS 43.
How old is Maggie?

Answers

Answer:

Step-by-step explanation:

Let Maggie's age = x

The brother's age = 3x - 5

x + 3x - 5 = 43

4x - 5 = 43              Add 5 to both sides

4x - 5 + 5 = 43+5

4x = 48                  Divide by 4

4x/4 = 48/4

x = 12

Maggie = 12

Brother = 3*12 - 5

Brother = 36 - 5

Brother = 31

PLEASE I NEED HELP, ILL MARK AS BRAINLIEST!!

Raul  is filling a 55 gallon fish tank with water. There are 18.5 gallons of water in the take 2.5 gallons of water flows from the hose each minute how many gallons of water are in the fish tank after 12 minutes

Answers

Answer:

All you do is multiply 2.5 x 12

Step-by-step explanation:

multiplying both numbers gets you a toltal of 24.60 or 24.6

ok i rly need help w this PLZ HELPPP

1. 2(x−4 1/2)=−6.
2. 3(p+2.55)=9 3/4

Answers

Answer:

1)x=1.5

2) p=0.7

Step-by-step explanation:

please try looking at the picture :(( i’m really struggling so much!!

Answers

Answer:

4- true

5-true

6-false

7-false

8-true

9-true

Step-by-step explanation:

Follow the letters and the sign of congruence

Marissa bought 3 chocolate bars each week. How many chocolate bars will Marissa buy after 3 weeks?

Answers

all you have to do is multiply 3 by 3, and your answer would be 9.
Hello! If Marissa buys 3 chocolate bars each week, than over three weeks she would have 9 chocolate bars.

3 is the chocolate bars each week.
Three weeks.
3x3=9
9 chocolate bars after three weeks.

Iqbal and Sachin have bookshelves of the same size and holding books of the same sizes. Iqbal's shelf is 7/8 full and Sachin's shelf is 12/15 full. If 351 more books of the same size are distributed among them, then they can fill their shelves completely. How many books does Sachin have now?
a)
864

b)
865

c)
800

d)
850

Answers

Answer:

540 books

Step-by-step explanation:

It is given that Iqbal's shelf is 7/8 full ..

→ That Means we can say that, iqbal's shelf is (1 - 7/8) = 1/8 is Empty .....

Similarly,

Sachin's shelf is 12/15 full.

→ That Means we can say that, sachin's shelf is (1 - 12/15) = 3/15 is Empty.....

→ Both total Empty = (1/8 + 3/15)

Taking LCM of denominator ,

→ (15+24 /120)

→ 39/120

→ 13/40 part is Empty in both .

Now, it has been said that, when 351 more books are distributed among them , both shelves filled completely .

So, we can say that :----

→ 13/40 part ---------------- 351

→ 1 part ---------------------- 351*40/13 = 1080 = Total Books in Both Selves .

__________________

Now, since bookshelves of the same size and holding books of the same sizes ,,

→ Both have Books in Each = 1080/2 = 540 books .

HELP PLZZZZZZZ with #1

Answers

Answer:

Option A, 300 - 20w

Step-by-step explanation:

In a week, she withdraws $20

in w weeks, she will withdraw ; w × 20

= 20w

Balance = Initial amount - Amount withdrawn

= 300 - 20w

Please help me :) triangles, and i need help Brainliest to correct answers!!! NO LINKS

Answers

Answer:

Step-by-step explanation:

ur mom

PLS HELP!!!! Mrs Gonzalez decides to write an algorithm that her employees follow when they open her store each day. What should be the first step of Mrs. Gonzalez process?


A. Check errors


B. Write a list of steps


C. Be sure that she understands every part of the situation


D. Think about what other situations could use an algorithm

Answers

The answer is C
I think

Answer:

Write a list of steps

Step-by-step explanation:

Pls mark me brainliest! Tnx

Work out m and c for the line: 2 y + 3 x = − 5

Answers

Answer:

m is -3/2

c is -5/2

Step-by-step explanation:

The standard linear equation is given by;

[tex]{ \tt{y = mx + c}}[/tex]

» m is the slope and c is the y-intercept

Then, our slope is;

[tex] { \tt{2y + 3x = - 5 }} \\ \\ { \tt{2y = - 3x- 5}} \\ \\ { \tt{y = - \frac{3}{2}x - \frac{5}{2} }}[/tex]

Make y the subject of the formula
5y - 4h = 18

Answers

Answer:

[tex]\displaystyle \large{y=\frac{18+4h}{5} }\\[/tex]

Alternatively, you can use [tex]\displaystyle \large{y=\frac{18}{5}+\frac{4h}{5} }\\[/tex] as an answer.

Step-by-step explanation:

To make y as the subject of equation, we have to find a way to isolate y-variable.

First, add 4h both sides of equation which we obtain:

[tex]\displaystyle \large{5y-4h+4h=18+4h} \\\displaystyle \large{5y=18+4h}[/tex]

Next, we divide both sides by 5 so we can finally have y-isolated equation and thus it becomes the new subject of equation.

[tex]\displaystyle \large{\frac{5y}{5} =\frac{18+4h}{5} }\\\displaystyle \large{y=\frac{18+4h}{5} }[/tex]

Thus the answer is y = (18+4h)/5

Alternatively for solution, you can separate the fraction which we obtain a valid alternative solution.

[tex]\displaystyle \large{y =\frac{18}{5} +\frac{4h}{5} }\\[/tex]

Either one of these solutions work.

_______________

Let me know in the comment if you have any questions.

The question is in the picture pls help!!!!!

Answers

Answer:

I believe its (B.)

To qualify for a scholarship, a student must score at least 90% on a written test. The test is 64 questions. Using this metric, what is the greatest number a student can miss and still qualify for the scholarship?

Answers

Answer:

6 questions

Step-by-step explanation:

First, you divide the total score of 100 by the 64 questions to get 1.5625 points per question. Next, you divide the lowest score to qualify of 90 by the 1.5625 to get 57.6 questions correct to qualify. Then, you round 57.6 questions correct up to 58 questions correct because a fraction of a question correct doesn't make sense. Finally, you subtract the total number of questions (64) by the required correct answers (58) to get 6 questions you can miss to still qualify for the scholarship.

12
66 77 84 | 3
'
43
mZ1 =
m22 =
m23 =
-

Answers

Answer:

30; 41 69 :):):):):):):):)')'))'):):):):):):)):):):

Can someone please help me with this question.

How can you tell whether two sets of data, ordered pairs, vary directly?

Answers

Answer:

graph them

Step-by-step explanation:

you can tell if you graph them

Find f(x) and g(x) so that the function can be described as y = f(g(x)). (5 points) y = (2/x^2) + (9)

Answers

Answer:

f(x) = x+9

g(x) = 2/x^2

Step-by-step explanation:

I just thought at a simple function for f(x). It could have been just f(x) = x and g(x) = 2/x^2 + 9. Nothing would have changed.

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