PLEASE HELP ME! If an arithmetic sequence has a4 = 107 and a8 = 191, what is a₁? (I need the steps too please). ​

PLEASE HELP ME! If An Arithmetic Sequence Has A4 = 107 And A8 = 191, What Is A? (I Need The Steps Too

Answers

Answer 1

Answer:

[tex]\displaystyle a_1 = 44[/tex]

Step-by-step explanation:

Recall the direct formula for an arithmetic sequence:
[tex]\displaystyle a_n = a_1 + d(n-1)[/tex]

Where d is the common difference.

Therefore, we can write the following two equations:
[tex]\displaystyle \left \{ {a_4 = 107 = a_1 + d(4-1)\atop {a_8 = 191 = a_1 + d(8-1)}} \right.[/tex]

Solve the system. Simplifying yields:
[tex]\displaystyle 107 = a_1 + 3d\text{ and } 191 = a_1 + 7d[/tex]

Subtracting the two equations into each other yields:
[tex]\displaystyle \begin{aligned} (191) - (107) & = (a_1 + 7d) - (a_1 + 3d) \\ \\ 84 & = 4d \\ \\ d & = 21 \end{aligned}[/tex]

Using either equation, solve for the initial term:

[tex]\displaystyle \begin{aligned} 107 & = a_1 + 3(21) \\ \\ a_1 & = 107-63 \\ \\ & = 44\end{aligned}[/tex]

In conclusion, the initial term is 44.

Answer 2

Answer:

[tex]\huge\boxed{\bf\:a_{1} = 44}[/tex]

Step-by-step explanation:

In the given arithmetic series,

[tex]a_{4} = 107[/tex][tex]a_{8} = 191[/tex][tex]a_{1} = ?[/tex]

We know that,

[tex]\boxed{a_{n} = a + (n - 1)d}[/tex]

Therefore,

[tex]a_{4} = a + 3d = 107 -----(1)\\a_{8} = a + 7d = 191 -----(2)[/tex]

By solving the two equations (1) & (2)....

[tex]\:\:\:\:a + 7d = 191 \\-\underline{a + 3d = 107 }\\ \underline{\underline{\:\:\:\:\:\:\:\:\:\:\:\:\:4d = 84\:\:\:\:\:\:\:\:}}\\\\\\\\4d = 84\\d = 84 \div 4\\\boxed{d = 21}[/tex]

Now, we have the value of the common difference (d). To find [tex]a_{1}[/tex] or a, let's substitute the value of 'd' in (1).

[tex]a + 3d =107\\a + 3(21)=107\\a + 63 = 107\\a = 107 - 63\\\boxed{\bf\:a_{1} = 44}[/tex]

[tex]\rule{150pt}{2pt}[/tex]


Related Questions

A shape that has 4 sides and 4 angles.

Answers

Answer:

its called a Quadrilateral

Step-by-step explanation:

Answer:

Quadrilateral, parallelogram

BRAINLIEST please if this helped!

kristin exercises 5 hours each week. Make a dot plot of her hours of exercise
and include the hours her friends exercise. Kristin and her friends' total hours
of exercise are shown in the table. How does Kristin's exercise time compare
with her friends

Answers

The dot plot is made by representing the frequency of the time spent exercising using dots

Kristin spends more time exercising than her friends

How to make the dot plot?

The dataset is given as:

0   6   5   9   5   4   3   5   4   6   4   5   5   4   6

From the dataset, we have the following frequency table:

Time   Frequency

0           1

3           1

4           4

5           5

6          3

9          1

See attachment for the dot plot made from the above frequency table

Interpreting the dot plot

From the dot plot, we can see that Kristin's time of exercise is greater than all of her friend's time of exercise.

Hence, Kristin spends more time exercising than her friends

Read more about dot plots at:

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-15=8z + 7 slove for z

Answers

Answer:

-11/4

Step-by-step explanation:

Answer:

- 2.75 is the answer

Step-by-step explanation:

-8z = 7 + 15

- Z = 22 / 8

- Z = -2.75

Which number is rational?

Answers

Answer:

[tex]\sqrt{16}[/tex]

Step-by-step explanation:

16 has a perfect square, 4.

Answer:

the square root of 16

Step-by-step explanation:

16 is a perfect square so

the square root of 16 is 4

4*4 = 16

just need help with solving for x

Answers

Answer:

13.83431104

Step-by-step explanation:

use sin (opposite/hypotenuse) and solve

How many solutions are there to the equation below?
x = -5
O A. 2
O B. 1
O c. o
D. 25

Answers

We will see that the equation has only one solution, so the correct option is B.

How many solutions an equation has?

For an equation of the form:

p(x) = C

Where p(x) is an expression that depends on x, and C is a constant.

The solutions are all the values of x that make the equality true.

For our case, we have:

x = -5

Notice that there is only one value of x that makes the equality true, if we replace x by -5 we get:

-5 = -5

So that is the only solution for the equation, then we conclude that the equation has only one solution, and the correct option is B.

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can you find the slope -intercept equation of each line code ?​

Answers

Answer:

You can find and write the equations in Slope-Intercept form due to the slope and y-intercept.

Step-by-step explanation:

The Slope-Intercept Form Formula: y=mx+b

The m represents the slope while the b represents the y-intercept

You can also use y2 - y1 / x2 - x1 to find the slope which is the m in your formula.

Lastly, to find a y-intercept, you can plug in your coordinate for the x and y to do two-step linear equations.

karen has 3 1/3 hours to run errands spends 1 2/3 hour at grocery store and rest at library how muh time did she spend at library

Answers

Answer:

1 and 2/3 hours (One hour and 40 minutes.)

Step-by-step explanation:

Karen has 3 and 1/3 hours.

She spends 1 and 2/3 hours at the store.

3 and 1/3 - 1 and 2/3 = 1 and 2/3 or 5/3 is the time she had left after being at the grocery store.

Because the rest of the time was spent at the library, that is your answer.


Please help I need the answer PLEASE!!!

Answers

Answer:

245 Sq inches

Step-by-step explanation:

Surface area of the solid

= 7*7 + 4(1/2 * 7*14)

= 49 + 196

= 245 sq in

Compare using >,<,or=.
2/3 and 9/12

Answers

9/12= 3/4

2/3 and 3/4
Now 2*4=8 and 3*3=9
Since 9>8
So 2/3 <9/12

You are helping some friends assemble a kite. They want to add a ribbon around the outside of the kite using the lengths indicated in the diagram. The lengths given in the diagram are in inches.

How many inches of ribbon do you need to go the entire way around the kite?

Answer in a complete sentence. Provide supporting work in your solution.

Answers

5x=3x+122x=12x=6

And

11y-22=7y-64y=16y=4

So

7y-6=7(4)-6=28-6=225x=5(6)=30

Perimeter:-

2(30)+2(22)2(30+22)2(52)104in

Answer:

104 inches

Step-by-step explanation:

A kite has two pairs of consecutive, congruent sides.

Therefore, BC = AB  and  AD = DC

We can use this to determine the values of x and y, and then the perimeter of the kite.

If BC = AB

⇒ 5x = 3x + 12

Subtract 3x from both sides:

⇒ 2x = 12

Divide both sides by 2

x = 6

If AD = DC

⇒ 11y - 22 = 7y - 6

Subtract 7y from both sides:

⇒ 4y - 22 = -6

Add 22 to both sides:

⇒ 4y = 16

Divide both sides by 4:

y = 4

As BC = AB  and  AD = DC

⇒ perimeter = 2 (BC + AD)

                     = 2 (5x + 11y - 22)

Substituting found values of x and y:

⇒ perimeter = 2 (5(6) + 11(4) - 22)

                     = 2 (30 + 44 - 22)

                     = 2 (52)

                     = 104 inches

Which of the following are square roots of
256

A-16

B. 2561/2

C. 2561/2

D. 8

E. 16

F. 128​

Answers

Answer:

16

Step-by-step explanation:

16^2 = 256

E. the square root of 256 is 16

Takeru has 4 bird feeders. It takes 4/3 bags of bird seeds to fill each feeder. what is the minimum number of bags Takeru needs to fill all the feeders?

Answers

Answer: 6

Step-by-step explanation: You would divide 4 by 3 and divide your answer by 2.

is 24L greater than 240ml

Answers

Answer:

yes

Step-by-step explanation:

24L (litres) = 24000 ml

1L = 1000 ml

hope this helps!

Answer:

Yes

Step-by-step explanation:

We know that,

1 Litre = 1000 milliliters

Then,

24 L

= 24 * 1000

= 24000 mL

Also,

24000 mL > 240 mL

So,

Yes,  24L IS greater than 240ml.

[tex]\rule{150pt}{2pt}[/tex]

NEED HELP ASAP!!!!!!​

Answers

Answer:

Vertex: (-2,-8)

Axis of Symmetry: x = -2

x intercept(s): x = 2,-6

Min/Max Value: Min; y= -8

y-intercept: -6

Step-by-step explanation:

Which expression is equivalent to (-3m-2n³)²(4mn²p-4)?

Answers

Answer:

36

m

3

n

2

p

36

m

2

+

48

m

2

n

5

p

48

m

n

3

+

16

n

8

m

p

16

n

6

Step-by-step explanation:

Please help on math.​

Answers

Answer:

3

Step-by-step explanation:

First set up your data in order

0,0,0,0,1,1,1,2,2,2,2,3,3

Second subtract the lowest to the highest which is 3-0=3

Hope this helps!

O. Solve the equation using the Zero Product Property.
(2x-4)(2x-1) = 0
A. 2, - ;
B. 2, ;
C. -2, 2
D. -2, ;

Answers

Answer is D

Sorry if wrong

The solution to the equation is x = 2 , x = 1/2

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

( 2x - 4 ) ( 2x - 1 ) = 0

So , the two values of x are

when ( 2x - 4 ) = 0

Adding 4 on both sides , we get

2x = 4

Divide by 2 on both sides , we get

x = 2

And , when ( 2x - 1 ) = 0

Adding 1 on both sides , we get

2x = 1

Divide by 2 on both sides , we get

x = 1/2

Hence , the solution is x = 2 , 1/2

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-14 < 3 + 1 < 13 answer inequality

Answers

Answer: -14 < 1 < 3< 13

Step-by-step explanation:

This is the order from the lowest to greatest

Use data sets A, B, and C to answer the question that follows.
A {25, 24, 25, 22, 21, 23, 1}
B: {20, 23, 25, 21, 24, 22, 60}
C. 20, 21, 20, 22, 20, 24, 99}
Which answer shows the standard deviations of the data sets in order from greatest to least?
- C, B, A
-В, А, С
- A, B, C

Answers

The correct order which shows the standard deviations of the data sets A,B and C in order from greatest to least is C, B, A.

How to find the standard deviation of a data set?

Suppose that

[tex]x_i; \: \: i = 1,2, ... ,n[/tex] are n data values for the given data set.

Then we have: Variance as,

[tex]\sigma^2 = \dfrac{\sum_{\forall x_i} (x_i - \overline{x})^2}{n}[/tex]

As standard deviation is the positive root of variance, thus,

[tex]\sigma = \sqrt {\dfrac{\sum_{\forall x_i} (x_i - \overline{x})^2}{n}}[/tex]

If its sample, we divide by n-1 instead of n

Use data sets A, B, and C to answer the question that follows.

A {25, 24, 25, 22, 21, 23, 1}B: {20, 23, 25, 21, 24, 22, 60}C. {20, 21, 20, 22, 20, 24, 99}

The mean of the set A is,

[tex]\overline{x}_A=\dfrac{25+24+ 25+ 22+ 21+23+ 1}{7}=20.143[/tex]

Similarly, the mean of set B and C is,

[tex]\overline{x}_B=\dfrac{20+ 23+ 25+ 21+ 24+ 22+ 60}{7}=27.857\\\overline{x}_C=\dfrac{20+21+ 20+ 22+ 20+ 24+ 99}{7}=32.286[/tex]

The standard deviation of the set A is,

[tex]\sigma_A = \sqrt {\dfrac{(25-20.143)^2+(24-20.143)^2......+(1-20.143)^2}{7}}\\\sigma_A = 7.936[/tex]

Similarly, the standard deviation of set B and C is,

[tex]\sigma_B = \sqrt {\dfrac{(20-27.857)^2+(23-27.857)^2......+(60-27.857)^2}{7}}= 13.217\\\sigma_C = \sqrt {\dfrac{(20-32.286)^2+(21-32.286)^2......+(99-32.286)^2}{7}}= 27.27[/tex]

The value of standard deviation of set C is the highest while set A is lowest.

Thus, the correct order which shows the standard deviations of the data sets A,B and C in order from greatest to least is C, B, A.

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A deposit of $2,960 is placed into a scholarship fund at the beginning of every six months for 13 years. The fund earns 7% annual interest, compounded biannually, and paid at the end of the six months. How much is in the account right after the last deposit? Select the correct answer below:

Answers

Answer:

where are the awnsers??

The value of the initial deposit is $2,960, so a1=2960. A total of 26 six-month deposits are made in the 13 years, so n=26. To find r, divide the annual interest rate by 2 to find the biannual interest rate and add 1 to represent the new biannual deposit.

r=1+0.072=1.035

Substitute a1=2960, n=26, and r=1.035 into the formula for the sum of the first n terms of a geometric series and simplify to find the value of the annuity.

S26=2960(1−1.03526)1−1.035≈122286.78

Therefore, the account has $122,286.78 after the last deposit is made.

100 POINTS WILL MARK BRAINLIEST NEED BY 9:00
Solve the linear equation below. Show ALL your work AND explain the type of solution you found!

8 - 2(4v + 6) = - 4 - 8v

Answers

Answer:

See below ~

Step-by-step explanation:

8 - 2(4v + 6) = -4 - 8v8 - 8v - 12 = -4 - 8v-8v - 4 = -4 - 8vOn placing any value for v, they will be equalIt has infinitely many solutions

Answer:

Hello! The solution to this linear equation is 0 = 0. To find this solution:

Distribute -

8 - 2(4v+6) = -4 - 8v

8 - 8v - 12 = 14 - 8v

Subtract the numbers -

8 - 8v - 12 = -4 - 8v

-4 - 8v =  -4 - 8v

Rearrange terms -

-4 - 8v = -4 - 8v

-8v - 4 = -4 - 8v

Rearrange terms -

-8v - 4 = -4 - 8v

-8v - 4 = -8v - 4

Add 4 to both sides -

-84v - 4 = -8v - 4

-8v - 4 + 4 = -8v - 4 + 4

Simplify -

-8v - 4 + 4 = -8v - 4 + 4

-8v = -8v - 4 + 4

-8v = -8v

Add 8v to both sides -

-8v = -8v

-8v + 8v = -8v + 8v

Combine like terms and simplify -

-8v + 8v = -8v + 8v

0 = -8v + 8v

0 = 0

The solution is 0 = 0. This is an identity: it is true for all values.

Hope this helps! Have a great day.

50 points
Please show work !!!

Answers

sinx = 3/5 = opposite side/hypotenuse
cosx = 4/5 = adjacent side/hypotenuse
5^2 = 4^2 + 3^2
25 = 16 + 9

sin(x/2) = + or - sqr(1-cosx)/2 = + sqr(1-4/5)/2 = - sqr(1/5/2) = sqr(1/10), ignore the negative root as x is in the 1st quadrant, and so is x/2.

sin(x/2) = 1/sqr10 = sqr10/10 = about 3.16/10 = 0.316

The right triangle has legs a and b and hypotenuse c. If b=12 and c=13, then what does a equal?

Answers

Answer:

a = 5

Step-by-step explanation:

a^2 + b^2 = c^2

Substitute

b = 12

c = 13

a^2 + 12^2 = 13^2

a^2 + 144 = 169

a^2 = 25

a = [tex]\sqrt{25} \\[/tex]

a = 5

Mark brainliest please!

Answer:

use Pythagoras theorem

Step-by-step explanation:

[tex]a^{2} + b ^{2} = c ^{2} \\ a ^{2} + 12 ^{2} = 13 ^{2} \\ a = 5[/tex]

What are the zeros of the polynomial function F(x) = x2 -5x-6?
O A. x= -1 and x = 6
O B. x= -6 and x = 1
O C. x = 2 and x = 3
O D. x= -3 and x = -2

Answers

Answer:

C

Step-by-step explanation:

Remark

The zeros are found either by using the quadratic equation or by factoring and equating the factors to 0. I think factoring is the best and simplest way.

Solution

x^2 - 5x + 6 factors into

(x - 3)(x - 2)

-3 and - 2 must multiply to 6 (they do) -3 * -2 = 6

-3 and -2 must also add to - 5. They do. -3 - 2 = - 5

So the factors are correct.

x - 3  = 0

x - 3 + 3 = 0 + 3

x = 3

x-2 = 0

x -2 + 2 = 0 + 2

x = 2

Answer

x = 2 and x = 3

The answer is C

The following inequalities are equivalent
except ...
a) x<4
b) X-1<3
c) x + 1<4
d) x - 2<2

Answers

Answer:

c )

Step-by-step explanation:

To find equivalent inequalities, we are looking to isolate x on the left side.

a) x < 4 ✅

b) x -1 < 3 add 1 to both sides  x -1 +1 < 3 +1 result x < 4 ✅

c) x + 1 < 4 subtract 1 from both sides x + 1 -1 < 4 -1 result x < 3 ❌

d) x - 2 < 2 add 2 to both sides x - 2 +2 < 2+2 result x < 4 ✅

Please Solve |x+3| if x > 5

Answers

Answer:

x< -8 or x>2

Step-by-step explanation:

apply the absolute root

If lu| > a, a>0 then u< -a or u>a

it is equal to

x+3<-5 or x+3> 5

x<-8 or x>2

Scott wants to fence three sides of a rectangular exercise yard for his dog. The fourth side of the exercise yard will be a side of the house. He has 200 feet of fencing available. Find the dimensions that will enclose the
maximum area.
a
The fence parallel to the house is
the yard is
feet, the fence perpendicular to the house is
feet and the area of
square feet

Answers

Answer:

66 2/3     66  2/3      4 444.44 ft^2

Step-by-step explanation:

the largest area will be a square

200/3 = 66 2/3 feet  side length

How many lines of symmetry does the picture have?
A. 3
B. 2
C. 1
D. 0

Answers

the answers is D cuz there is no line in the picture

Allen finds the area of the woods to be approximately 9,680
square feet. Why is Allen incorrect?
A
Allen is incorrect because he applied the scale to the
sides and then found the total area of the woods.
B
Allen is incorrect because he found the total area of the
woods and then applied the scale.
Allen is incorrect because he did not apply the scale.
D
Allen is incorrect because he used the formula to find hm
perimeter instead of area.

Answers

is it c

(what is the scale)

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