1. You are given the 3rd and 5th term of an arithmetic sequence. Describe in words how to determine the general term.

2. You are given the 3rd and 5th term of an geometric sequence. Describe how to determine the 10th term without finding the general term.

Answers

Answer 1

Step-by-step explanation:

1. In an arithmetic sequence, the general term can be written as

xₙ = y + d(a-1), where xₐ represents the ath term, y is the first value, and d is the common difference.

Given the third term and the fifth term, and knowing that the difference between each term is d, we can say that the 4th term is x₃+d and the fifth term is the fourth term plus d, or (x₃+d)+d =

x₃+2d. =x₅ Given x₃ and x₅, we can subtract x₃ from both sides to get

x₅-x₃ = 2d

divide by 2 to isolate d

(x₅-x₃)/2 = d

This lets us solve for d. Given d, we can say that

x₃ = y+d(2)

subtract 2*d from both sides to isolate the y

x₃ -2*d = y

Therefore, because we know x₃ and d at this point, we can solve for y, letting us plug y and d into our original equation of

xₙ = y + d(a-1)

2.

Given the third and fifth term, with a common ratio of r, we can say that the fourth term is x₃ * r. Then, the fifth term is

x₃* r * r

= x₃*r² = x₅

divide both sides by x₃ to isolate the r²

x₅/x₃ = r²

square root both sides

√(x₅/x₃) = ±r

One thing that is important to note is that we don't know whether r is positive or negative. For example, if x₃ = 4 and x₅ = 16, regardless of whether r is equal to 2 or -2, 4*r² = 16. I will be assuming that r is positive for this question.

Given the common ratio, we can find x₆ as x₅ * r, x₇ as x₅*r², and all the way up to x₁₀ = x₅*r⁵. We don't know the general term, but can still find the tenth term of the sequence


Related Questions

The sum of two integers is -360. One of them is 60, then the other integer is

Answers

2
CNN can. Nxkxmcidnxixnxksnxixnxixmficocc

PLEASE HELP! much appreciated :D

Find the value of x.

Answers

Answer:

a

Step-by-step explanation:

give me examples of equivalent expressions of square root 54 with a radican of 3

Answers

Try this answer 3√54

Which expression is equivalent to 7√x^2/5√y^3? Assume y≠0

Answers

Answer:

Step-by-step explanation:

If the √y³ term is in the denominator, then the expression needs to be written with parentheses:  7√x²/(5√y³)

find the solution to this system of equations x+y=1
2x-y+z=1
x+2y+z=8/3

Answers

9514 1404 393

Answer:

  (x, y, z) = (1/3, 2/3, 1)

Step-by-step explanation:

We can use the first equation to write an expression for x that can be substituted into the other equations.

  x = 1 -y

  2(1 -y) -y +z = 1   ⇒   -3y +z = -1

  (1 -y) +2y +z = 8/3   ⇒   y +z = 5/3

Subtracting the first of these equations from the second gives ...

  (y +z) -(-3y +z) = (5/3) -(-1)

  4y = 8/3

  y = 2/3

  z = 5/3 -y = 1

  x = 1 -y = 1/3

The solution is (x, y, z) = (1/3, 2/3, 1).

8 and 1/3divided by 3 and 4/7

Answers

Answer:

7/3

Step-by-step explanation:

8 1/3 divided by 3 4/7

Let’s start by 8 1/3

Multiply 3 x 8 and then add 1

3 x 8 = 24 + 1 = 25

Add the denominator back

25/3

3 4/7

Multiply 7 x 3 and then add 4

7 x 3 = 21 + 4 = 25

Add the denominator back

25/7

Final Results: 25/3 & 25/7

Now we’re ready to divide!

Multiply 7 by 25

7 x 25 = 175

Multiply 3 by 25

3 x 25 = 75

Answer: 175/75

Finally Simplify

175/75 = 7/3

Final Answer: 7/3

in a class, 64 offers mathematics while 94 offers chemistry , How many will offer the both course?

Answers

Answer:

30

Step-by-step explanation:

94-64=30 will offer the same course because the chemistry offers ocerride the mathematics offers

Ravi bought 50kg rice at the rate of tk.40 per kg and sold it at the rate of tk.44 per kg. What is the percentage of profit

Answers

He paid 0.40 x 50 = 20

He sold it for 0.44 x 50 = 22

His profit was 22-20 = 2

Percentage was 2/20 = 0.10 = 10 %

Answer 10 %

Singh's house the weekly consumption of milk is 6.5 liters what is their daily consumption of milk if they consume same quantity of milk every day

Answers

Answer:

Their daily consumption of milk is of 0.93 liters.

Step-by-step explanation:

Weekly consumption:

6.5 liters.

Daily consumption:

A week has 7 days.

Each day the amount consumed is the same, so the daily consumption is:

6.5/7 = 0.93

Their daily consumption of milk is of 0.93 liters.

Is the relationship shown by the data linear? If so, model the data with an equation.

Answers

Yes it is linear, you go up my fours in the y side and go down by two on the x side. The equation is y=2x+19

Look at the numbers below. −9.8 −5.4 1.0 14.8 Which shows the best way to add these numbers using the Commutative and Associative Properties? A. (–9.8 + 1.0) + (–5.4 + 14.8) B. (–9.8 + 14.8) + (–5.4 + 1.0) C. (1.0 + 14.8) + (–9.8 + (–5.4)) D. (1.0 + (–9.8)) + (14.8 + (–5.4)

Answers

Answer:

B

Step-by-step explanation:

i did the test and it was correct, ur welcome

in a small town in New York, we initiated a cohort study and followed 5,900 people for a mean follow-up of 2 years. At the end of the 2nd year, none of the participants was lost to follow-up. During this follow-up, we identified 600 cases of malaria. What was the cumulative incidence?
a. 10.1%
b. 10.1 per 1,000
c. 50.8%
d. 10 cases

Answers

Answer:

Option A

Step-by-step explanation:

From the question we are told that:

Sample size n=5900

Number of newly developed cases No.C=600

Generally the equation for Cumulative Incidence is mathematically given by

[tex]CI=\frac{No.C}{n}[/tex]

[tex]CI=\frac{600}{5900}[/tex]

[tex]CI=0.101[/tex]

[tex]CI= 10.1%[/tex]

Option A

Proving the Single Opposite Side Pair Theorem
Given: AD = BC and AD || BC
Prove: ABCD is a parallelogram.
Angles Segments Triangles Statements Reasons
ZBCA
ZDAC
А
Statements
Reasons
B
D
с
Assemble the proof by dragging tiles to
the Statements and Reasons columns.

Answers

9514 1404 393

Explanation:

1. AD ≅ BC, AD ║ BC . . . . given

2. ∠DAC ≅ ∠BCA . . . . alternate interior angles theorem

3. AC ≅AC . . . . reflexive property

4. ΔDAC ≅ ΔBCA . . . . SAS postulate

5. AB ≅ CD, ∠BAC ≅ ∠DCA . . . . CPCTC

6. AB ║ CD . . . . converse of alternate interior angles theorem

7. ABCD is a parallelogram . . . . definition of a parallelogram (has 2 pairs of parallel & congruent sides)

_____

We don't know what your tiles/choices are for statements or reasons. We have shown the triangles are congruent, so their corresponding parts (sides/angles) are congruent. That lets us claim opposite sides are congruent and  parallel. YMMV

Answer:

Picture Down Below

Step-by-step explanation:

find the product using suitable product 854×102 step by step explanation​

Answers

Answer:

87108

Step-by-step explanation:

854 x 102

= 854 x ( 100 + 2 )

= 854 ( 100 ) + 854 ( 2 )

= 85400 + 1708

= 87108

87108

854
102 x
——-

87108

What is the remainder of 119 divided by 4

Answers

The remainder is three. 4 can go into 119 29 times with a remainder of three.

Hope this helps! Please make me the brainliest, it’s not necessary but appreciated, I put a lot of effort and research into my answers. Have a good day, stay safe and stay healthy.

The remainder when dividing 119 by 4 is 3.

We have,

To find the remainder when dividing 119 by 4, we perform the division and observe the remainder.

When we divide 119 by 4, we get:

119 ÷ 4 = 29 remainder 3

The quotient is 29, which means that 4 goes into 119 twenty-nine times without any remainder.

However, there is a remainder of 3.

Therefore,

The remainder when dividing 119 by 4 is 3.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ6

Which sets of ordered pairs show equivalent ratios? Use the grid to help you.

Check all that apply.

A: (1, 2), (2, 3), (4, 7)

B: (2, 2), (4, 4), (6, 6)

C: (3, 1), (4, 1), (5, 1)

D: (4, 1), (8, 2), (12, 3)

E: (2, 1), (4, 3), (5, 4)

Answers

Answer:

B and D

Step-by-step explanation:

in B the ratio of x/y = 1 for all pairs.

in D the ratio of x/y = 4 for all pairs.

in all other sets there are different ratios inside the set.

Answer:

The pairs (2, 2), (4, 4), and (6, 6) have ratios of 1 and the pairs (4, 1), (4, 1),      (8, 2), and (12, 3) have ratios of 4. The other pairs do not have similar ratios.

Step-by-step explanation:

Step 1; In order to pair up the pairs with equivalent rations, we first need to calculate the ratios for all the pairs by dividing the first value with the second value. The same procedure must be followed throughout to be able to pair them up.

Step 2; By dividing the values, the ratios are;

For (1, 2), the ratio is  = 0.5,

For (2, 3), the ratio is  = 0.6666,

For (4, 7), the ratio is  = 0.5714,

For (2, 2), the ratio is  = 1,

For (4, 4), the ratio is  = 1,

For (6, 6), the ratio is  = 1,

For (3, 1), the ratio is  = 3,

For (4, 1), the ratio is  = 4,

For (5, 1), the ratio is  = 5,

For (4, 1), the ratio is  = 4,

For (8, 2), the ratio is  = 4,

For (12, 3), the ratio is  = 4,

For (2, 1), the ratio is  = 2,

For (4, 3), the ratio is  = 1.333,

For (5, 4), the ratio is  = 1.25.

Step 3; Now we pair up the sets with the same ratios, out of these 15 pairs. The pairs (2, 2), (4, 4), and (6, 6) have ratios of 1 and the pairs (4, 1), (4, 1),      (8, 2), and (12, 3) have ratios of 4. The other pairs do not have similar ratios.

I hope this is right and it helps you !!!!!!!!!!

An investor puts $800 into an account that pays 7.5% interest compounded annually. The total amount A in the account after t years is given by which function below?
A = 800(1.75) ^t
A = 800(1.075) t
A = 800(1.075)^ t
A = 800 + (1.075)^ t

Answers

Answer:

A = 800( 1.075)^(t)

Step-by-step explanation:

The equation for interest is

A = p (1+r/n) ^ nt   where p is the principle, r is the interest rate, n is the number of times per year  and t is the years

A = 800( 1+ .075/1)^(1*t)

A = 800( 1.075)^(t)

Let's see

[tex]\\ \tt\leadsto A=P(1+r/n)^{nt}[/tex]

n is 1

[tex]\\ \tt\leadsto A=P(1+r)^t[/tex]

[tex]\\ \tt\leadsto A=800(1+0.075)^t[/tex]

[tex]\\ \tt\leadsto A=800(1.075)^t[/tex]

Option C

A baseball is projected upward at 64 feet per second. It can be approximated by the equation -16t^2+64t. The baseball reaches it maximum height at the vertex. That can be gotten from x= −/2a . How long until the baseball reaches its full height? Note a quadratic equation can be written as ax^2+bx+c

Answers

Answer:

f(t) = -16t²+64t

t = number of secondsf(t) = height (in feet)

The x-coordinate(t) of the vertex can be found using formula [tex]\frac{-b}{2a}[/tex], where:

a = -16b = 64

Therefore the t-value of the vertex is:

[tex]\frac{-64}{2(-16)} =\frac{-64}{-32} =2[/tex]

The baseball will reach its maximum height after two seconds.

Ophelia is making homemade spaghetti sauce by combining 48 oz of tomato paste with 6 cups of water.how many cups of water are needed for every ounces of tooth paste

Answers

1 cup per 8 oz

48/6 = 8

every 1 cup of water 8 oz of tomato paste.

1 cup per 8 oz
explained : there are 48 oz of tomato paste and 6 cups of water 48 over 6 is 8 therefore per every 1 cup of water there are 8 oz of tomato paste



Draw the image of the rotation of quadrilateral SORT by 270° about the origin.

I need visual help, not a number answer please :)

Answers

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

A rotation 270° CCW is the same as a rotation 90° CW. To see what the figure looks like in its new location, make a copy on a semi-transparent medium, then align the +x axis on the copy with the -y axis on the original graph, keeping the origin in the same place.*

Algebraically, the transformation is ...

  (x, y) ⇒ (y, -x)

For example, ...

  S(7, -6) ⇒ S'(-6, -7)

In the attachment, the rotated figure is in red.

_____

* The exercise of physically doing this on paper or with transparencies can give you the insight you need to learn to do it mentally.

⬆⬆⬆⬆⬆⬆⬆⬆⬆⬆⬆⬆⬆

THAT IS THE RIGHT ANSWER

The price of a car was decreased from $13,000 to $11,830. The price is decreased by what percentage?

Answers

Answer:

It is decreased by 9%

Step-by-step explanation:

First, find out how much money is decreased. To do this, subtract 13,000-11,830=1170. Finally, figure out how much percent 1170 is of the original price of $13,000.

The answer is 7%.

Hope this helps :)

What is the least possible degree of a polynomial that has the root -3 + 2i, and repeated root -2 that occurs twice?

4
3
2
5

Answers

Answer:

4

Step-by-step explanation:

complex roots always occur in pairs.

so roots are -3+2i,-3-2i ,-2,-2

number of roots=4

solve for "X" where x±4=12​

Answers

Answer:

x = 8, 16

Step-by-step explanation:

x + 4 = 12

x = 12- 4

x = 8

x - 4 = 12

x = 12 + 4

x = 16

I hope this can help you

Which of the following choices shows the complete factorization of 50?
52 • 5
2 • 25
52 • 2
None of these choices are correct.

Answers

Answer: None of these choices are correct

Explanation

The factorization of 50 is 2*5^2

None is correct

Which expression is equivalent to 7x , if b > 0?

Answers

Answer:  Choice C

Work Shown:

[tex]7x^2*\sqrt{2x^4}*6\sqrt{2x^{12}}\\\\7*6x^2*\sqrt{2x^4*2x^{12}}\\\\42x^2*\sqrt{4x^{4+12}}\\\\42x^2*\sqrt{4x^{16}}\\\\42x^2*\sqrt{(2x^8)^2}\\\\42x^2*(2x^8)\\\\42*2x^{2+8}\\\\84x^{10}\\\\[/tex]

So that's why the answer is choice C

The requirement that x is nonzero isn't technically necessary. The original expression simplifies to choice C even when x = 0 is the case. Also, we don't have issues such as division by zero errors that could arise. It's a bit curious why your teacher put in that condition.

Answer:

C.

Step-by-step explanation:

7x²×sqrt(2x⁴)×6×sqrt(2x¹²)

we see right away that as constant multiplication factor we have 7×6 = 42.

and then we get from each sqrt expression a sqrt(2), which leads to sqrt²(2) = 2 and therefore 42×2=84.

the only answer option with 84 is C.

now, to be completely sure, and to get some practice, let's look at the other parts :

sqrt(2x⁴) = sqrt(2)×sqrt(x⁴) = sqrt(2)×x²

sqrt(2x¹²) = sqrt(2)×sqrt(x¹²) = sqrt(2)×x⁶

=>

7x²×sqrt(2)×x²×6×sqrt(2)×x⁶ =7×6×2×x²×x²×x⁶ = 84x¹⁰

perfect. C is confirmed.

A tennis coach divides her 9-player squad into three 3-player groups with each player in only one group. How many different sets of three groups can be made?

Answers

Answer:

84

9 choose 3

Step-by-step explanation:

What is the different of (5-3x) and (5x-10)

a. 8x-5

b. 15-8x

c. 8x + 15

d. none of the above

Answers

Answer:

15 - 8x

Step-by-step explanation:

Remark

This all depends on how you read the question. In other words, which comes first 5 - 3x or 5x - 10. It's not clear.

If you do the first one first, you get

5 - 3x - (5x - 10)         Remove the brackets.

5 - 3x - 5x + 10          Collect like terms

15 - 8x                       So that makes the middle one correct.

Now do it the other way.

5x - 10 - (5 - 3x)

5x - 10 - 5 + 3x

8x - 15

That answer isn't available here. So ..

The answer is 15 - 8x

X^2 + bx + 49 is a perfect squad trinomial what is one possible value of b? & I need help with the others also due soon!

Answers

20. (2) 14

A perfect square trinomial will factor into two expressions that are the same, for example: x^2 + 6x + 9 = (x + 3)(x + 3). Since this problem has a C value of 49, it will factor into (x + 7)(x + 7). 7 doubled is 14, therefore one possible value of B is 7.

21. (4) 2, -12

x^2 + 10x + 25 = 24 + 25

(x + 5)^2 = 49

x + 5 = +/- 7

x = 2, -12

22. (3) 3 + sqrt(17)

x^2 - 6x = 8

Complete the Square

x^2 - 6x + 9 = 8 + 9

(x - 3)^2 = 17

x - 3 = +/- sqrt(17)

x = 3 + sqrt(17), 3 - sqrt(17)

23. (1) 1, -5

x^2 + 4x - 5 = 0

x^2 + 4x = 5

x^2 + 4x + 4 = 5 + 4

(x + 2)^2 = 9

x + 2 = +/- 3

x = 1, -5

Hope this helps!

Hello can anyone answer this question please I need help

Answers

9514 1404 393

Answer:

maximum: 40(8/3, 8/3)

Step-by-step explanation:

The graph shows the relevant vertex of the feasible region is ...

  (x, y) = (8/3, 8/3).

The value of z there is ...

  z = 11(8/3) +4(8/3) = (88 +32)/3

  z = 40

Find the value of x on this triangle

Answers

Answer:

33

a2+b2 =c2

a2+ 33 squared = 55 squared

a + 1936 = 3025

3025-1936=1089

square root of 1089 is 33

pleeeaaasssseeee mark as brainliest

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