The 8th and 20th terms of an arithmetic sequence are 20 and 56 respectively. ​What is the 1st term of the sequence.

Answers

Answer 1

Answer:

            a₁ = -1

Step-by-step explanation:

[tex]a_n=a_1+d(n-1)\\\\a_8=a_1+d\cdot7\\\\a_{20}=a_1+d\cdot19\\\\a_{20}-a_8=a_1+19d-(a_1+7d)=12d\\\\56-20=2d\\\\12d=36\\\\d=3\\\\\\ a_1+3\cdot7=20\\\\a_1=20-21=-1[/tex]

Answer 2

If the 8th and 20th terms of an arithmetic sequence are 20 and 56 respectively, then the 1st term of the sequence is -1

The nth term of an arithmetic sequence is given by the formula:

[tex]a_n=a+(n-1)d[/tex]

The 8th term of the arithmetic sequence is 20

[tex]a_8 = 20\\\\a_8=a+(8-1)d\\\\a+7d=20.......................(1)[/tex]

The 20th term of the arithmetic sequence is 56

[tex]a_{20} = 56\\\\a_{20}=a+(20-1)56\\\\a+19d=56.......................(2)[/tex]

Subtract equation (1) from equation (2)

12d  =  36

d  =  36/12

d  =  3

Substitute d = 3 into equation (1)

a  +  7d  =  20

a  +  7(3)  =  20

a  +  21  =  20

a   =  20  -  21

a  =  -1

The first term of the arithmetic sequence is -1

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Related Questions

Zevel overheard Bradley say he got a 66% on the last test. If Zevel only got one-third what
Bradley got, what is Zevel's score?

Answers

Answer:

22

Step-by-step explanation:

66 ÷3=22

3= one third

i believe it’s 1.98 because if you divide 60% by 1/3 You get 1.98

Triangle ABC will be dilated according to the rule

[tex]D_{F, 0.25} (x,y)[/tex], where point F is the center of dilation.

What will be the coordinates of vertex A' of the image?


a. (-8,-4)

b. (-2,-1)

c. (0, 0)

d. (1, 0)


The answer is (1,0), but could someone explain how you get it, please?

Answers

Usually dilations have a center of dilation at the origin (0,0). When this occurs all we need to do is multiply each coordinate by the dilation scale. Unfortunately things get a little more complicated when the center of dilation is not at the origin.

In this case the center of dilation is located at F: (3,1)

The first step we must take is to find how many units point F is from vertex A.

In this case, F is 4 unit up and 8 units right of vertex A. (Reference the first image below to see how I found this)

Now we must multiply these dimensions (4 units and 8 units) by the factor of dilation (0.25)

4 * 0.25 = 1

8 * 0.25 = 2

This shows us how many dimensions away point [tex]A^{1}[/tex] is from point F:

1 unit vertically

2 units horizontally

Now how do we know if [tex]A^{1}[/tex] is above or below, left or right from point F? Easy! There has been no translations so the directions will be the same as the original:

Point F: (3, 1) ---> (3-2, 1-1) ---> (1, 0)

Reference the second image to see this

Hopefully this helps and makes sense. Let me know if you need further explanation or clarification.

~Just a girl in love with Shawn Mendes

Answer:

D 1,0

Step-by-step explanation:

credit to the one up above

Ambrose and Kaitlin are volunteering at a food bank. They both start at the same time. Kaitlin takes 13 minutes to pack a box with donated food. Ambrose takes 7 minutes to pack a box. After how many minutes will they finish packing boxes at the same time?

Answers

Answer:

They will finish packing boxes at the same time after 91 minutes.

Step-by-step explanation:

From the question,

Kaitlin takes 13 minutes to pack a box while Ambrose takes 7 minutes to pack a box. That is,

Kaitlin will finish packing a box after every 13 minutes and Ambrose will finish packing a box after every 7 minutes.

To determine when they will finish packing boxes at the same time, we will list the times they will finish packing boxes

For Kaitlin, she will finish packing box(es) at the following times:

13th minute, 26th minute, 39th minute, 52nd minute, 65th minute, 78th minute, 91st minute, 104th minute etc.

For Ambrose, he will finish packing box(es) at the following times:

7th minute, 14th minute, 21st minute, 28th minute, 35th minute, 42nd minute, 49th minute, 56th minute, 63rd minute, 70th minute, 77th minute, 84th minute, 91st minute, 98th minute, 105th minute etc.

From above, we can observe that, Ambrose and Kaitlin will finish packing boxes at the 91st minute.

Hence, They will finish packing boxes at the same time after 91 minutes.

I'm stumped. Help please

Answers

I believe the answer would be
AEF and CGH

because they intercept through J

Hope this helps

Elizabeth made 80 cookies for the bake sale at school. She sold 35% of the cookies. How many cookies are left to sell tomorrow?

Answers

She has 56 cookies left

1 less than the quotient of a number n and 6

Answers

Answer:

[tex]\frac{n}{6}[/tex] - 1

Step-by-step explanation:

whenever the word than is there (less than, greater than) you have to switch the order so it the words 1 was first or in the beginning of the sentence but since the words less than are there, 1 goes toward the end or after the quotient of a number n and 6.

if 2025 students are arranged in equal number of rows and columns find the number of students in each rows​

Answers

Answer:

45

Step-by-step explanation:

Answer:

45

Step-by-step explanation:

.....

....,..,.....

There are 12 months in a year and 52 weeks in a year. What is the ratio of months to weeks in one year? A 6/27 B 3/13 C. 13/3 D. 27/6​

Answers

Answer:

B.

Step-by-step explanation:

12/52=6/26=3/13

Which one?
A. B. C. or D? ​

Answers

Answer: C

Explanation

Answer: c

Step-by-step explanation: distribute -7p by multiplying it by 8p first, which gives you -56p squared. Then multiply the -7p by -1 which gives you 7p as the two negatives will cancel out.

Find the value of the expression:

4^3·25^3

Answers

The value of the expression is 1000000

HELP ME PLEASE HURRY

Answers

Answer:

x=-2

Step-by-step explanation:

?
Select the correct answer.
No, they only have 1 corresponding equal angle.
Yes, they have 2 corresponding equal angles
No, they are not the same size.
Yes, they are the same shape.
Help

Answers

Answer:

yes they have 2 corresponding equal angles.

Given m|n, find the value of x.
t
m
(9x+23)
(10x+6)°
Someone help?

Answers

Since M is parallel to N that means they would have to equal each other.

if tan A= 1,what is the value of A​

Answers

Answer:

45°

Step-by-step explanation:

Ok, so, there is one thing I need to point out. 45° is the 'main' value if you assume 0°<A<180°. However, sin,  cos, and tan have different periods which means that there are infinite values of A where tanA = 1. The general notation that you could put is A = 45° + (n*180°) where n is just a number. For example, if n = 1, you would get an angle of 225°. If you plug tan225° into the calculator, you get 1. If you did radians, you could write A = [tex]\frac{\pi}{2} + n\pi[/tex]. But ignore that if you haven't. Basically, the answer would be 45° if you are assuming A is between 0° and 180°. Also, you could have just used your calculator and types inverse tan function ([tex]tan^{-1}[/tex]) and plug in 1 to find the primary answer of 45.

NEED YOU GUYS HELP!!! ​

Answers

Answer:

3x and 9x

Step-by-step explanation:

They both are with the variable x

Which one?
A. B. C. or D?

Answers

the answer to this is b
The answer would be b

A scared tarantula was able to go a distance of 20 meters in 6 seconds. What was its
average speed?

Answers

Answer:

3.33 m/s

Step-by-step explanation:

speed = [tex]\frac{meters}{seconds} > \frac{20}{6} = 3.33[/tex]

20 POINTS AND BRAINLIEST
The height (in inches) of a candle, h(t), is modeled by the function h(t) = 8 - t, where t is the amount of time the candle has been burning. What is the meaning of the y-
intercept of the graph of the function?
A. The amount of time the candle has been burning
B. The height of the candle when it starts to burn
C. The maximum amount of time the candle can burn
D. The height of the candle after it is finished

Answers

Answer:B.the height of the candle when it starts to burn

Step-by-step explanation:

The y - intercept is 8. It represents the height of the candle when it starts to burn.

What is the general equation of a Straight line?

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.

We have the height (in inches) of a candle, h(t), is modeled by the function h(t) = 8 - t, where t is the amount of time the candle has been burning.

We have -

h(t) = - t + 8

h(t) = - t + 8

Here, the y - intercept is 8. It represents the height of the candle when it starts to burn.

Therefore, the y - intercept is 8. It represents the height of the candle when it starts to burn.

To solve more questions on straight lines, visit the link below-

brainly.com/question/20400984

#SPJ5

Please help me the picture is above, I’ll mark as brainliest.

Answers

Answer:

function is a straight line, with a y-int of 1, passes VLT and HLT so it is 1:1

Step-by-step explanation:

f(x)= 2x+4

f(-2)= 2(-2)+4 = -4+4 = 0

f(-1)= 2(-1)+4 = -2+4 = 2

f(0)= 2(0)+4 = 0+4 = 4

f(1)= 2(1)+4 = 2+4 = 6

f(2)= 2(2)+4 = 4+4 = 8

idrk the features but i'll guess

Triangle XYZ is rotated to create the image triangle X'Y'Z'.

On a coordinate plane, 2 triangles are shown. The first triangle has points X (negative 2, 2), Y (1, 2), Z (0, 4). The second triangle has points X prime (2, negative 2), Y prime (negative 1, negative 1), Z prime (0, negative 4).
Which rules could describe the rotation? Select two options.

R0, 90°
R0, 180°
R0, 270°
(x, y) → (–y, x)
(x, y) → (–x, –y)

Answers

Answer:

b. e

Step-by-step explanation:

Options B and E are the correct answers.

We need to describe the transformation of triangle XYZ to triangle X'Y'Z'.

What is rotation?

Rotation is the circular movement of an object around an axis of rotation.

Now, from triangle XYZ to triangle X'Y'Z' the angle of rotation is 180°.

The translation is (x, y) → (–x, –y).

Therefore, options B and E are the correct answers.

To learn more about the transformation visit:

https://brainly.com/question/11709244.

#SPJ5

If you have 24 questions how many answers can you miss to have a passing grade

Answers

Answer:

you have to get 15 right so for 60% or above so you can miss 9

Step-by-step explanation:

60% of 24 is 14.4 round it up because if down its below 60% and no longer passing but it rounds to 15

Answer: 7

Step-by-step explanation:

Because if 6 is 75% we can conclude 7 is 71%

can you please help me solve this​

Answers

Answer:

The answer is A because the answer to the equation is x^{2}= -6 and the 7 is negative

Step-by-step explanation:

Hope this helps :)

The value of a machine worth 45,000 rupees is decreasing at the rate of 20% per annum. Find the total reduction after 2 years?

Answers

Answer:

Total reduction after 2 years = [tex]16,200[/tex] rupees

Step-by-step explanation:

Current price of a machine [tex](P_0)[/tex] = 45,000 rupees

Rate of depreciation (r) = 20%

Time (t) = 2 years

Price after 2 years = [tex]P_0(1-\frac{r}{100} )^t[/tex]

[tex]=45000(1-\frac{20}{100})^2 \\=45000(1-\frac{1}{5})^2\\ =45000(\frac{4}{5})^2\\ =45000(\frac{16}{25})[/tex]

[tex]=28800\,\,[/tex] rupees

Total reduction after 2 years = [tex]P-P_0=45,000-28,800=16,200[/tex] rupees

Write an expression for the phrase -4 times the quantity 4 plus w

Answers

-4x+4=-8 is the answer
[tex]\bold{Answer:}[/tex]-4(4+w)


[tex]\bold{Explanation:}[/tex]

does anybody know how to solve this10+|7-5x|= 11

Answers

Answer:

-6/5

Step-by-step explanation:

The first thing that you will do is to remove the absolute value bars. So, it will look like this: 10+7+5x=11

Then, you will combine like terms. So, this is how it will look: 17+5x=11

Next, you will subtract 17 from both sides since it is a positive number, (use the subtraction property of equality) and it will look like: 17-17+5x=11-17

Then you get: 5x=-6

So, from there, you must divide. (use the division property of equality) 5x/5=-6/5

So, your answer is -6/5

Gyyuiyffffddfyuoiuuhhhhj

The last part is function but need help asap

Answers

It would be the top one

Mrs. Deblinsky purchases 850 shares of Cracker Barrell at 45.20 per share. She pays a 1.5% commission to her broker for the transaction. After a year, she sells her holdings for 41.90 a share, using a discount broker who charges $19 per trade. What was her net capital loss?

Answers

Answer: 3362

Step-by-step explanation:

Based on the question, the cost price for the shares will be:

= (850 × 45.20) + 1.5%(850 × 45.20)

= 38420 + 0.015(38420)

= 38420 + 576.3

= 38996.

Selling price will be:

= (850 × 41.9) + 19

= 35615 + 19

= 35634

Net capital loss = 38996 - 35634

= 3362

Accrotime is a manufacturer of quartz crystal watches. Accrotime researchers have shown that the watches have an average life of 26 months before certain electronic components deteriorate, causing the watch to become unreliable. The standard deviation of watch lifetimes is 4 months, and the distribution of lifetimes is normal. A button hyperlink to the SALT program that reads: Use SALT. (a) If Accrotime guarantees a full refund on any defective watch for 2 years after purchase, what percentage of total production will the company expect to replace? (Round your answer to two decimal places.) Incorrect: Your answer is incorrect. % (b) If Accrotime does not want to make refunds on more than 6% of the watches it makes, how long should the guarantee period be (to the nearest month)? months

Answers

Answer:

a

   [tex]P(X <  24 )=  21.186\%  [/tex]  

b

    [tex]x =  19.78 \  months[/tex]

Step-by-step explanation:

From the question we are told that

 The mean is   [tex]\mu  =  26 \  months[/tex]

 The standard deviation is  [tex]\sigma  =  4 \  months[/tex]

 Generally 2 year is  equal to  24 months

Generally the percentage of total production will the company expect to replace is mathematically represented as

      [tex]P(X <  24 )=  P(\frac{X - \mu }{ \sigma} <  \frac{24 - 26}{4}  )[/tex]

Generally  [tex]\frac{X - \mu}{\sigma } =Z (The  \ standardized \  value  \  of  \  X )[/tex]

     [tex]P(X <  24 )=  P(Z <  -0.8  )[/tex]

Generally from the z-table  

       [tex]P(Z <  -0.8) =  0.21186[/tex]

So

       [tex]P(X <  24 )=  0.21186[/tex]

Converting to percentage

      [tex]P(X <  24 )=  0.21186  * 100[/tex]

=>    [tex]P(X <  24 )=  21.186\%  [/tex]  

Generally the duration that should be the guarantee period if  Accrotime does not want to make refunds on more than 6% is mathematically evaluated as

    [tex]P(X <  x) =  P(\frac{X - \mu }{\sigma}  < \frac{x - 26}{4} )= 0.06[/tex]

=> [tex]P(X <  x) =  P(Z < \frac{x - 26}{4} )= 0.06[/tex]

From the normal distribution table the z-score for  0.06 at the lower tail  is

       [tex]z = -1.555[/tex]

So

    [tex]\frac{x - 26}{4} = -1.555[/tex]

=> [tex]x =  19.78 \  months[/tex]  

Can someone please help me with this? I would appreciate it <3

Answers

Answer:

i kinda see its test or not?

Step-by-step explanation:

you have to divided it.

given the definition of f (x) and g(x) below find the value of g(f(-1)).

f(x)=3x²+5x-7

g(x)=2x+13

Answers

Answer:

-29

Step-by-step explanation:

first do the f function which gets you g(-21)

then do the g function

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