Mathematics College

Let [tex]\sf a+b,a-b,ab,\dfrac{a}{b}[/tex] form an arithmetic sequence. What is the sixth term of this sequence?​

Answers

Answer 1

Answer:

171/40 or 4 11/40

Step-by-step explanation:

AP givena + b, a - b,  ab, a/bTo find6th termSolution

Common difference

Difference of first two

d = (a -b) - (a + b) = -2b

Difference of second two

d= ab - (a - b)

Difference of last two

d = a/b - ab

Now comparing d:

-2b = ab - (a - b)ab - a = - 3ba(1 - b) = 3ba = 3b/(1 - b)

and

a/b - ab = -2ba(1/b - b) = -2ba = 2b²/(b² - 1)

Eliminating a:

2b²/(b² - 1) = 3b/(1 - b)2b/(b+1) = -32b = -3b - 35b = - 3b = -3/5

Finding a:

a = 3b/(1 - b) = 3*(-3/5) *1/(1 - (-3/5)) = -9/5*5/8 =-9/8

So the first term is:

a + b = -3/5 - 9/8 = -24/40 - 45/40 = - 69/40

Common difference:

d = -2b = -2(-3/5) = 6/5

The 6th term:

a₆ = a₁ + 5d =-69/40 + 5*6/5 = -69/40 + 240/40 =171/40 = 4 11/40

Related Questions

You are purchasing a car for $12,465.00 plus 5.65% sales tax. You make a $1,300.00 down payment and have a fair credit score. If you improved your credit score to good and paid $1,500 on your purchase, how much interest could you save in the first month?

Secured Unsecured
Credit APR (%) APR (%)
Excellent 4.75. 5.50
Good 5.00 5.90
Average 5.85 6.75
Fair 6.40 7.25
Poor 7.50 8.40



$13.25


$14.68


$21.74


$25.69

Answers

Answer:

21.74

Step-by-step explanation:

HELP PLEASE
Determine the length of a chord whose central angle is 65° in a circle with a radius of 9 feet.
Question 5 options:


1)
4.84 feet


2)
9 feet


3)
9.67 feet


4)
8.16 feet

Answers

Answer:

3)

9.67 feet

Step-by-step explanation:

The length of the chord is approximately 8.16 feet. The correct option is 4.

What is the length of the chord of the circle?

A line segment connecting two points on a circle is referred to as a circle's chord in geometry. The circle's center is traversed by the longest segment that can be drawn between any two points on the circle.

To get the chord's length, we can utilize the formula for a circle's chord length. The equation is:

Length of chord = 2r sin(θ/2)

where r is the circle's radius, is its radian central angle, and sin is the sine function.

First, we need to convert the central angle from degrees to radians:

θ = 65° = (65/180)π = 1.14 radians

Now we can plug in the values:

Length of chord = 2(9 feet) sin(1.14/2) ≈ 8.16 feet

Therefore, the length of the chord is approximately 8.16 feet.

To know more about the chord of a circle follow

https://brainly.com/question/8937665

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Graph 16x−4y=2.Please answer I will make you the brainlist and rate you 5 stars if good.And report if bad.

Answers

Answer:

First one is the graph second one is the equation

Step-by-step explanation:

Hope this helps :)

Answer:

Step-by-step explanation:

as graphed

which expression is equivalent to 15+8x+3+2x​

Answers

Answer:

10x + 18

Step-by-step explanation:

First, we need to add like terms. Like terms are terms that are alike. For instance 8x and 2x are like terms. 15 and 3 are also like terms.

So, we have to add 8x plus 2x and 15 plus 3. That’s comes out to 10x plus 18.

Therefore, this expression is equivalent to 10x + 18.

A rectangle has a length of 3x + 7 and a width of 2x. If the perimeter of the
rectangle is 94 units, what is the length of the rectangle.

Answers

Answer:

The length of the rectangle is 31.

Step-by-step explanation:

We have that the length (L) and width (W) are:

[tex] L = 3x + 7 [/tex]

[tex] W = 2x [/tex]

The perimeter of the rectangle is given by:

[tex] P = 2W + 2L [/tex]

[tex] 94 = 2(2x + 3x + 7) [/tex]

[tex] 94 = 10x + 14 [/tex]

[tex] x = 8 [/tex]

Now, we can calculate the length of the rectangle:

[tex] L = 3x + 7 = 3*8 + 7 = 31 [/tex]        

         

Therefore, the length of the rectangle is 31 units.

I hope it helps you!                

Nada is making square coasters with sides of 3 inches. On each coaster is a circular design. What is the radius of the largest circle that fits on one of the coasters?

Answers

Answer:

1.5

Step-by-step explanation:

diameter is half the length of the circle so if it is 1.5 the full length will be 3 inches which is the full length of the coaster

What’s is 9 divided by 3/10

Answers

Answer:

30

Step-by-step explanation:

9/(3/10)=9*(10/3)=30

On Wednesday, farmer bell wants to take an inventory of his mango trees He planted 7 rows of mango trees. There are 42 mango trees in each row. How many mango trees does he have altogether?

Answers

7•42= 294 mango trees

Р
D
Which of the statements describe the transformation on
the left? Check all that apply.
NOPQR-N'O'P'Q'R'
ONOPQR-→ NOPQR
O QRNOP → R'N'O'P'Q'
NOPQR maps to N'O'P'Q'R'
O QPONR maps to Q'P'O'N'R'
N
R
N
R

Answers

The statements which describe the transformation on the left are:

NOPQR → N'O'P'Q'RNOPQR maps to N'O'P'Q'R'QPONR maps to Q'P'O'N'R'

What is a transformation?

A transformation refers to the movement of a point from its original position to a new location. Hence, when an object is transformed, all of its points would also be transformed.

Based on the image of these geometric figures (see attachment), we can infer and logically deduce that the following statements describe the transformation on the left:

NOPQR → N'O'P'Q'RNOPQR maps to N'O'P'Q'R'QPONR maps to Q'P'O'N'R'

Read more on transformation here: https://brainly.com/question/12040896

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Answer: a,b,d that´s the answer

Step-by-step explanation

A ladder 5 m long, leaning against a vertical wall makes
an angle of 65° with the ground. How far up the wall is
the top of the ladder?

Answers

The height of the top of the ladder from the ground is 4.53 m

Step-by-step explanation:

Given:

length of ladder =5 m

Angle formed = 65°

Let h be the Height of the top of the ladder from the ground

Required:

Height of the top of the ladder from the ground

Equation:

SOH-CAH-TOA

Since the hypotenuse side is given and what we are to solve is the opposite side, use SOH

[tex]sinθ\:=\: \frac{opposite}{hypotenuse}[/tex]

[tex]sin(65°)\:=\: \frac{opposite}{5\: m}[/tex]

[tex]opposite\:=\:(5 \:m )\:sin(65°)[/tex]

[tex]opposite\:=\:4.53 \:m[/tex]

Final Answer:The height of the top of the ladder from the ground is 4.53 m

Please refer to the photo for the illustration

Write a linear model for the amount of boxes, b, as a function of the number of hours since they opened, h. Use your model to predict the number of boxes in stock at the end of an 8 hour shift.

Answers

Question:

A company produces boxes of DVDs at a rate of 52 boxes per hour they begin to produce boxes when they first opened for the day and after 3 hours have 400 boxes in stock.

- How many boxes were in stock when they opened?

- Write a linear model for the amount of boxes, b, as a function of the number of hours since they opened, h.

- Use your model to predict the number of boxes in stock at the end of an 8 hour shift.

Answer:

1. [tex]Initial = 244[/tex]

2. [tex]b = 244 + 52h[/tex]

3. 660 boxes

Step-by-step explanation:

Given

[tex]Rate = 52\ per\ hour[/tex]

[tex]Total\ boxes\ in\ 3\ hours = 400[/tex]

Solving (a): Initial Number of boxes

First, we calculate the number of boxes made in 3 hours

[tex]Boxes = Rate * Hours[/tex]

[tex]Boxes = 52 * 3[/tex]

[tex]Boxes = 156[/tex]

If they had 400 boxes at the 3rd hour.

Then, the number of boxes when they opened is:

[tex]Initial = 400 - 156[/tex]

[tex]Initial = 244[/tex]

Solving (b): Linear function

[tex]b = boxes[/tex]

[tex]h = hours[/tex]

Since, we have the rate and the initial number of boxes.

The linear function is:

[tex]Boxes = Initial + Rate * Hours[/tex]

i.e.

[tex]b = 244 + 52 * h[/tex]

[tex]b = 244 + 52h[/tex]

Solving (c): Boxes at the end of the 8th hour

We have:

[tex]b = 244 + 52h[/tex]

In this case:

[tex]h = 8[/tex]

Substitute 8 for h

[tex]b = 244 + 52 * 8[/tex]

[tex]b = 244 + 416[/tex]

[tex]b = 660[/tex]

Hence, there are 660 boxes at the end of the 8th hour

Andrea earns $32.25 a day. After 9 days , about how much will she have earned?

ESTIMATE

Answers

270? not completely sure.

HELP ME FAST PLEASE I NEED THIS VERY SOON!!! you’d be a lifesaver omg

There are 600 seats in the auditorium. This is 112 less than the number of seats in the gymnasium. How many seats are in the gymnasium?



Answers

712 is the answer of this question

The answer would be 712

Explanation:

600

+

112

———

712

8+3(p-9)
Pleaseeee helppp

Answers

Answer:

3p - 19

Step-by-step explanation:

8 + 3(p - 9)

Distribute;

8 + 3p - 27

Collect like terms;

-19 + 3p

3p-19 by using addition and the distributive property

Hello! :)
Please help me solve this + explain your answer :)

I will indeed give you Brainlst <3

Answers

The answer B makes the most sense out of all because s and b are congruent and that’s the only two there
The answer is b make sense

Ed spent 25% of his savings on lunch, which cost $5.25. How much did he have in savings before lunch?

Answers

Step-by-step explanation:

I think 21 dollars is the answer

Roberto wants to display 18 sports cards in an album. Some pages hold 2 cards and others hold 3 cards. How many different ways can Roberto display his figures?


Answers

Answer: The answer is 2.

HOPE IT HELPS!!

What is the value of 9(4x - 4) when x = 5

Answers

Answer:

144

Step-by-step explanation:

plug in 5 where you see the x.

that gives us 9(4(5)-4)

multiply the 4 and the 5 first to get 9(20-4)

and by PEMDAS, we solve the parentheses first so now we have 9(16)

so now just multiply 9x16 to get 144

Step-by-step explanation:

9((4×5)-4)

9(20-4)

9(16)

144

What is the value of q?
52 589
9

Answers

I believe the answer is 55

Solve for x.
-1+4x5= 3

Answers

Answer:

[tex]x = 0.2 \: or \: \frac{1}{5} [/tex]

Step-by-step explanation:

[tex] - 1 + 4x.5 = 3[/tex]

[tex] = > 20x - 1 = 3[/tex]

[tex] = > 20x = 3 + 1 = 4[/tex]

[tex] = > x = \frac{4}{20} = \frac{1}{5} = 0.2[/tex]

Which is the percent for 1.67

Answers

The percent is 167% have a good day

Answer:

167%

i thank that is the anserr.

Step-by-step explanation:

The sum of 1 and a number x

Answers

9515 1404 393

Answer:

  1 + x

Step-by-step explanation:

A sum is found by adding terms. Here, you are told the terms to add are 1 and x. We use the plus sign (+) to signify addition. Your sum is ...

  1 + x

In which direction must the graph of f(x) = |x| be shifted to produce the graph of g(x) = |x − 3|?

A.
left
B.
down
C.
up
D.
right

Answers

Answer:

In which direction must the graph of f(x) = |x| be shifted to produce the graph of g(x) = |x − 3|?

A. left

B. down

C. up

✓D. right

Right is the right answer.

Answer:

Down

Step-by-step explanation:

I took the test and got it right

Based on the table, which function represents the same relationship? The x column has 0, 1, 2, 3. The y column has 0.0625, 0.25, 1, and 4.
Answer
A g(x) = (0.25)
B g(x) = 256(0.25)
C92) = 0.0625(4)"
D g(x) = 0.5(4)"

Answers

The answer is c. I hope u get it right

Answer: C 92) = 0.0625(4)

Step-by-step explanation:

it iz

Please help me if u know

Answers

Lol I’m lookin for the same answer

3.2 - 5.1n - 3n + 5= n +8.2 can someone tell me what goes in the blank

Answers

The answer for (n) is 0

How many solutions exist for the given equation?
x+12) = 4x-1
EEEE
O zero
O one
two
O infinitely many

Answers

Answer:

One answer exists for this equation.

Which statement describes data that is normally distributed?

A.
The majority of the data is to the left of the mean.

B.
The majority of the data is to the right of the mean.

C.
The majority of the data is in the center with the mean.

D.
The majority of the data is split to the right and left of the mean.

Please explain and no answering just for points.

Answers

Answer: D.) The majority of the data is split to the right and left of the mean

A store pays $13 for a bicycle helmet and marks up the price by 40% what is the amount of the mark-up?

Answers

Answer:

Step-by-step explanation:

the amount of mark up is

13*(40/100)=5.20

--6x = 48 (solving equations)

Answers

if your solving for X your answer will be -8 im glad to help! have a nice day~
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