Given the sequence 38, 32, 26, 20, 14, ..., find the explicit formula.

Answers

Answer 1

Answer:

The explicit formula for the sequence is

44 - 6n

Step-by-step explanation:

The above sequence is an arithmetic sequence

For an nth term in an arithmetic sequence

A(n) = a + ( n - 1)d

where a is the first term

n is the number of terms

d is the common difference

From the question

a = 38

d = 32 - 38 = - 6 or 20 - 26 = - 6 or

14 - 20 = - 6

So the formula for the sequence is

A(n) = 38 + ( n - 1)-6

= 38 - 6n + 6

We have the final answer as

A(n) = 44 - 6n

Hope this helps you

Answer 2

Answer:

[tex]\huge\boxed{a_n=-6n+44}[/tex]

Step-by-step explanation:

This is an arithmetic sequence:

32 - 38 = -6

26 - 32 = -6

20 - 26 = -6

14 - 20 = -6

The common difference d = -6.

The explicit formula of an arithmetic formula:

[tex]a_n=a_1+(n-1)(d)[/tex]

Substitute:

[tex]a_1=38;\ d=-6[/tex]

[tex]a_n=38+(n-1)(-6)[/tex]         use the distributive property

[tex]a_n=38+(n)(-6)+(-1)(-6)\\\\a_n=38-6n+6\\\\a_n=-6n+(38+6)\\\\a_n=-6n+44[/tex]


Related Questions

Antonio's toy boat is bobbing in the water next to a dock. Antonio starts his stopwatch, and measures the vertical distance from the dock to the height of the boat's mast, which varies in a periodic way that can be modeled approximately by a trigonometric function. The vertical distance from the dock to the boat's mast reaches its highest value of -27 \text{ cm}−27 cmminus, 27, space, c, m every 333 seconds. The first time it reaches its highest point is after 1.31.31, point, 3 seconds. Its lowest value is -44\text{ cm}−44 cmminus, 44, space, c, m. Find the formula of the trigonometric function that models the vertical height HHH between the dock and the boat's mast ttt seconds after Antonio starts his stopwatch. Define the function using radians.

Answers

Answer:

Step-by-step explanation:

Since we're given a time at which the height is maximum, we can use a cosine function for the model.

The amplitude is half the difference between the maximum and minimum: (-27 -(-44))/2 = 8.5 cm.

The mean value of the height is the average of the maximum and minimum: (-27 -44)/2 = -35.5 cm.

The period is given as 3 seconds, and the right shift is given as 1.31 seconds.

This gives us enough information to write the function as ...

  H(t) = (amplitude)×cos(2π(t -right shift)/period) + (mean height)

  H(t) = 8.5cos(2π(t -1.31)/3) -35.5 . . . . cm

factorise 8a^3+b^3+12a^2b+6ab^2​

Answers

Answer: See below

Explanation:

8a^3+b^3+12a^2b+6ab^2
= (8a^3+b^3) + (12a^2b+6ab^2)

= (2a+b)(4a^2+2ab+b^2)+6ab(2a+b)
= (2a+b)(4a^2+2ab+b^2)+6ab
= (2a+b)(4a^2 + 2ab+b^2+6ab)
= (2a+b)(4a^2+8ab+b^2)

Answer:

(2a+b)^3

Step-by-step explanation:

8a^3+b^3+12a^2b+6ab^2​

(2a)^3 + 3. (2a)^2 b + 3 (2a) b^2 + b^3

the above equation compare to (a+b)^3 = a^3 + 3a^2b+3ab^2 +b^3

when we compare both the equations

our a= 2a and b=b

so, our answer is (2a + b)^3

I'm marking brainliest bad answers grt a report an ban. ---- ----------- When solving this system of equations with substitution one of the following is a step. x+y=6, - 6x+8y = 6 * --------------------------------------------- -6(-x + 6) + 8y = 6 x+y = 6 -6x+8 (-x + 6) = 6 8y = 6x + 6

Answers

Answer:

-6x + 8(-x+6) = 6

Step-by-step explanation:

x+y = 6 => y = 6-x  ..............(1)

Substitute y (1) in

-6x+8y = 6 .......................(2)

to get

-6x + 8(6-x) = 6

or equivalently

-6x + 8(-x+6) = 6

Find the surface area of the regular pyramid shown in the accompanying diagram. If necessary, express your answer in simplest radical form.

Answers

Answer:

84 squared units.

Step-by-step explanation:

In order to find the surface area of the pyramid, you use the following formula:

[tex]S=b^2+\frac{1}{2}ps[/tex]           (1)

b: base of the pyramid = 6

p: perimeter of the base = 6*4 = 24

s: slant height

Then, you first calculate the slant height, by using the Pythagoras' theorem:

[tex]s=\sqrt{(5)^2-(\frac{6}{2})^2}=4[/tex]

Thus, you replace the values of b, p and s in the equation (1):

[tex]S=(6)^2+\frac{1}{2}(24)(4)=84[/tex]

The surface area of the pyramid is 84 squared units.

Answer:

Step-by-step explanation:

wrong

Thanks a lot... Plz answer with steps

Answers

24 and 16

Step-by-step explanation:

let's assume two part be x and (40 - x)

According to Question,

[tex] x\dfrac{1}{4} = (40 - x) \dfrac{3}{8} [/tex]

[tex] x= \dfrac{3(40 - x)}{2} [/tex]

[tex]2 \times x = 120 - 3x [/tex]

[tex]2x + 3x = 120[/tex]

[tex]5x = 120[/tex]

[tex] \cancel{5}x= \cancel{120}[/tex]

[tex]x = 24[/tex]

Hence one part is 24 and other is (40 - 24) = 16 .

Answer: 24 and 16

Step-by-step explanation:

explain briefly. in your own words.
Rational and irrational numbers.
give examples.
exponential equation. ​

Answers

rational numbers are numbers which can be expressed in fraction form whereas irrational is just opposite

Exponential equations are equations in which variables occur as exponents. For example, exponential equations are in the form ax=by .  

I'm going to mark whoever gets it right as brainliest Fred's coffee shop sells two blends of beans at the following prices. a) House Blend ($3.50/lb) b) Exotic Blend ($4.00/lb). House blend is 1/2 Costa Rican beans and 1/2 Ethiopian beans. Exotic blend is 1/4 Costa Rican beans and 3/4 Ethiopian beans. Every day Fred receives 200 lbs of Costa Rican Beans and 330 lbs of Ethiopian beans. Which inequality is a constraint? * 1/2x+1/4y or = to 530 x < or = 200

Answers

Answer:

(1/2)x + (1/4)y <= 200

Step-by-step explanation:

If

x = # of lbs of House blend he makes/sells a day

y = # of lbs of Exotic blend he makes/sells a day

then constraints are

(1/2)x + (1/4)y <= 200  ....................(1)

x+y <= 530  .....................................(2)

The exact answer choices are not very clear from the question, but either (or both) (1) or (2) must be one of them.  If not, please edit question or add a comment to show the answer choices.

What number on the number line represents ground level?
0
-1
-2
-3
-4
-5
-6​

Answers

Answer:

0 represents ground level.

Step-by-step explanation:

0 on the number line represents ground level. Based on the photo, the 0 is in between the underground and the space above. The answer cannot be one of the negative numbers because those are all shown to be underground in the photo.

Which of the following are identities? Check all that apply.

Answers

Answer:

The true answers:

A

B

C

Step-by-step explanation:

A P E X

David is making rice for his guests based on a recipe that requires rice, water, and a special blend of spice, where the rice-to-spice ratio is 15 : 1 15:1.He currently has 40 grams of the spice blend, and he can go buy more if necessary. He wants to make 10 servings, where each serving has 75 grams of rice. Overall, David spends 4.50 dollars on rice. What is the price of rice per gram?

Answers

Answer: Price of rice per gram =  $ 0.006  per gram or 0.6 cents per gram .

Step-by-step explanation:

Given: David wants to make 10 servings, where each serving has 75 grams of rice.

Total quantity of rice required = 10 x 75 = 750 grams

Overall, David spends 4.50 dollars on rice.

i.e. cost of 750 grams of rice = 4.50 dollars

Price of rice per gram =(cost of 750 grams of rice ) ÷ 750

= (4.50 dollars )  ÷ 750

=  $  0.006  per gram.

Price of rice per gram =  $ 0.006  per gram.

Answer:

0.006

Step-by-step explanation:

ehgfdcgmkmvnnrebsbhbnjrfjgnjkae

volume please 20* points

Answers

Answer:

1800cm^3

Step-by-step explanation:

l=10cm

w=10cm

h=18cm

V=l.w.h

V=10cmx10cmx18cm

V=100cm^2x18cm

V=1800cm^3

Hope this helps. ❤❤❤

Answer:

600 cm³

Step-by-step explanation:

Volume of a square-based pyramid = a² × h/3

a = 10

h = 18

10² × 18/3

100 × 6

= 600

9 divided by 2/3 equals

Answers

Answer:

[tex] \boxed{ \frac{27}{2} }[/tex]

Step-by-step explanation:

[tex] \mathrm{9 \div \frac{2}{3} }[/tex]

To divide by a fraction, multiply by the reciprocal of that fraction

[tex] \mathrm{ = 9 \times \frac{2}{3} }[/tex]

Calculate the product

[tex] \mathrm{ = \frac{27}{2} }[/tex]

Hope I helped!

Best regards!!

Answer:

[tex]\boxed{13\frac{1}{2} }[/tex]

Step-by-step explanation:

[tex]9 / \frac{2}{3}[/tex]

Changing "division" into "multiplication" and inverting the term after it:

[tex]9 * \frac{3}{2}[/tex]

[tex]\frac{9*3}{2}[/tex]

[tex]\frac{27}{2}[/tex]

=> [tex]13\frac{1}{2}[/tex]

Which statement is correct about the system of linear equations graphed below? A.The system of equations has one solution because the lines will eventually intersect. B.The system of equations has one solution because the lines will never intersect. C.The system of equations does not have one solution because the lines will eventually intersect. D.The system of equations does not have one solution because the lines will never intersect.

Answers

Answer: A

Step-by-step explanation:

They have one solution because as you look at the lines they have different slopes and different y intercepts which means it has one solution.It is not parallel to each other to have no solutions. They seems to be going to one direction and eventually they will intersect.

What did you multiply together to find the sales tax?

Answers

Answer:

Step-by-step explanation:

To find the sales tax on a purchased or sold item, first convert the sales tax percentage into the equivalent decimal fraction.  If the sales tax rate is 5.5%, then the desired decimal fraction is 0.055.  Next, multiply the selling price of the purchased or sold item by this decimal fraction.  If, for example, the selling  price is $100, the sales tax is 0.055($100) = $5.50

Hey loves!!! Plz help if you have the time.<3

Answers

Answer:

The first and last answer.

Step-by-step explanation:

If you look closely at the triangles you can tell which ones are the same and which differ.

Hope this helps!! <3

Help someone!! Thank you!

Answers

Answer:

D. 1.3

Step-by-step explanation:

Perimeter (square) = 4*side

4 = 4*side

side = 1

We have triangle QVR. QV is a hypotenuse.

If we look at the triangle QTR, QT is a hypotenuse.

QV should be less than QT.

Let's find QT using Pythagorean theorem.

c² = a² + b²

QT² = QR² + RT² = 1² + 1² = 2

QT = √2 ≈ 1.4

QV < QT

QV < 1.4

We have 1.3 and 1 that are less than 1.4, but 1 is a length of a leg of the triangle, so 1 is impossible.

Answer D. 1.3

The answer is D. Which is 1.3

Write a rule for the linear function in the table.
f(x) = 4x + 3
f(x) = -4x - 3
1
f(x) = x + 3

Answers

Answer:

I guess that you want to know the transformations:

We start with:

f(x) = y = 4*x + 3

a)the transformed function is:

f(x) = y = -4*x - 3

So the sign changed.

This means that we go from (x, y) to (x, - y)

This is a reflection over the x-axis which changes the sin of the y component.

b) Now we go to f(x) = 4*x + 3

So the coefficient in the leading term changed.

This is a horizontal contraction:

A horizontal contraction of factor K for the function g(x) is: g(K*x)

In our case, we have:

f(K*x) = 4*(k*x) + 3 = x + 3

4*k*x = x

4*k = 1

k = 1/4

Then the transformation is an horizontal contraction of scale factor 1/4.

Which movie had the audience with the younger median ?

A. Movie A

B. Movie B

C. Both

D. Cannot be determined

Answers

Answer: Movie A

How can we tell? Look at the vertical lines inside the box. This is where the median is located. For movie A, the inner vertical line is somewhere between 30 and 40 (perhaps 35 or so). So this is the median for movie A. Meanwhile, the median for movie B is somewhere between 40 and 50. I'd say maybe 46 or 47 as its a bit higher than the halfway point.

-----------

Extra info:

The left edge of the box is the first quartile (Q1).The right edge of the box is the third quartile (Q3).The tip of the left whisker is the min value, assuming there are no outliers to the left.The tip of the right whisker is the max value, assuming there are no outliers to the right.

Trigonometry.... plzzz helllppp​

Answers

Answer:

Hey there!

We can write this equation:

cosine xyz=6/15, or 0.4

arc cosine 0.4= 66.4

Thus, angle xyz is 66.4 degrees

Hope this helps :)

1+1+2+6+7+9x89x98x45x56/4

Answers

Answer:

49453757

Step-by-step explanation:

Answer:

49453757

Step-by-step explanation:

Dont forget to rate and thanks!

factorize (X + 2 y)square - (2 x minus y) square​

Answers

Answer:

- (x - 3y)(3x + y)

Step-by-step explanation:

Given

(x + 2y)² - (2x - y)² ← expand both parenthesis using FOIL

= x² + 4xy + 4y² - (4x² - 4xy + y²) ← distribute

= x² + 4xy + 4y² - 4x² + 4xy - y² ← collect like terms

= - 3x² + 8xy + 3y² ← factor out - 1 from each term

= - 1(3x² - 8xy - 3y²) ← factor the quadratic

Consider the factors of the product of the coefficient of the x² term and the coefficient of the y² term which sum to give the coefficient of the xy- term.

product = 3 × - 3 = - 9 and sum = - 8

The factors are - 9 and + 1

Use these factors to split the xy- term

3x² - 9xy + xy - 3y² ( factor the first/second and third/fourth terms )

= 3x(x - 3y) + y(x - 3y) ← factor out (x - 3y) from each term

= (x - 3y)(3x + y)

Thus

(x + 2y)² - (2x - y)² = - (x - 3y)(3x + y)

Mr. Sanchez's students were asked to add two positive integers. Juan subtracted by mistake and got 2. Maria mistakenly multiplied and got 120. What was the correct answer?

Answers

Answer:

22

Step-by-step explanation:

Given

From Juan's calculation,

Difference of two positive integers = 2

From Maria's calculation,

Product of same integers = 120

Required

Find the sum of the two numbers

Let the two integers be represented by a and b

a - b = 2 ------- (1)

a * b = 120 ------- (2)

Make a the subject of formula in (1)

a = 2 + b

Substitute 2 + b for a in (2)

(2 + b) * b = 120

Open bracket

2 * b + b * b = 120

2b + b² = 120

Rearrange

b² + 2b = 120

Subtract 120 from both sides

b² + 2b - 120 = 120 - 120

b² + 2b - 120 = 0

At this point, we have a quadratic equation.

We start by expanding the expression

b² + 12b - 10b - 120 = 0

Factorize

b(b + 12) - 10(b + 12) = 0

(b - 10)(b + 12) = 0

This implies that

b - 10 = 0 or b + 12 = 0

Make b the subject of formula in both cases

b = 10 or b = -12

From the question, we understand that both numbers are positive.

This means that

b = -12 will be discarded.

Hence, b = 10

Recall that a = 2 + b

Substitute 10 for b

a = 2 + 10

a = 12

This implies that the two numbers are 12 and 10.

Their sum = 12 + 10

Sum = 22

The correct answer is 22

How is the graph of y=(x+1)^2-9 transformed from the graph of y=x^2? a shifted 1 unit left and 9 units up b shifted 1 unit right and 9 units up c shifted 1 unit left and 9 units down d shifted 1 unit right and 9 units down

Answers

Answer:

Step-by-step explanation:

Due to the '+1', the graoph of x^2 is shifted 1 unit to the left.  The '+9' results in the entire graph being shifted downward 9 units.

an orphanage bought 119 1/4 m of cloth to stitch dresses for kids. The dress for one kid requires 2 1/4m of cloth. How many dresses of the size can be stitched

Answers

Answer:53 dresses

Step-by-step explanation:

First of all..if one kid required 2 1/4m of cloth,what about 119 1/4m of cloth?

So u take 119 1/4m of cloth and divide it by 2 1/4m of cloth.

Then change the mixed numbers into improper fractions.

So the question will be 477/4 m divided by 9/4 m.

The second improper fraction (9/4)m will be reciprocated to be (4/9)m.

Afterwards,take 477/4 m and multiply it by 4/9 m.

The result will be 53 dresses.

PLZZZ HELP WILL GIVE BRAINLIEST !!!!! NEED THIS FAST PLZZZ

Answers

Answer:

8

Step-by-step explanation:

Let's denote the number of members ordered chicken a, the number of members ordered beef b.

We have:

a + b = 12 (total number of members is 12)

10a + 14b = 136 (the chicken costs 10$, the beef costs 14$)

a + b = 12 => a = 12 - b

Substitute a into second equation, we have:

10(12 - b) + 14b = 136

=> 120 - 10b + 14b = 136

=> 4b = 16

=> b = 4

=> a = 12 - b = 12 - 4 = 8

=> Number of members ordered chicken: a = 8

Pls ASAP help me with number 14

Answers

Answer:

D. 19

Step-by-step explanation:

because they are parallel bases you can compare

63/57 = 21/x

x = 19

Answer: D. 19

Let x by the length of CG. Since the two bases are parallel, we can create the following equation using proportions:

[tex]\dfrac{63}{21}=\dfrac{57}{x}[/tex]

Simplify left side of equation

[tex]3=\dfrac{57}{x}[/tex]

Multiply both sides by x

[tex]3x=57[/tex]

Divide both sides by 3

[tex]x=19[/tex]

Let me know if you need any clarifications, thanks!

Can anyone else not see the answers?

Answers

Answer: no I cannot it hasn't been working since this late afternoon I believe

Step-by-step explanation:

Jose unlocks his cellphone by placing his right thumb on a square of 1 centimeter by 1 centimeter at the center of the screen. Upon recognizing his thumbprint, the square expands outward. The cellphone unlocks when the perimeter reaches 32 centimeters, taking a total of 2.5 seconds. What is the perimeter of the square after 1.5 seconds?

Answers

Answer:  20.8 cm

Step-by-step explanation:

Notice that the corners of the squares form a line.

Set the x-axis to time and the y-axis to length of a side (not perimeter) to create coordinates.

At 0 seconds the side length is 1 --> (0, 1)

At 2.5 seconds the perimeter is 32 (side length is 32/4 = 8) --> (2.5, 8)

First, find the slope between the coordinates using    [tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Let (x₁, y₁) = (0, 1) and (x₂, y₂) = (2.5, 8)

[tex]m=\dfrac{8-1}{2.5-0}\quad =\dfrac{7}{2.5}\quad =\dfrac{7}{\frac{5}{2}}\quad =\dfrac{14}{5}\quad =2.8[/tex]

Next, use the Point-Slope formula to find the equation of the line:

[tex]y-y_1=m(x-x_1)\\\\y-1=2.8(x-0)\\\\y=2.8x+1[/tex]

Lastly, find the side length (y) when x = 1.5

y = 2.8(1.5)x + 1

  = 4.2 + 1

  = 5.2

Perimeter of a square = 4 times the side length

P = 4(5.2)

  = 20.8

If $f(x)$ is a polynomial of degree 3, and $g(x)$ is a polynomial of degree 5, then what is the degree of polynomial $2f(x) + 4g(x)$?

Answers

Answer:

Degree 5

Step-by-step explanation:

Given

Degree of f(x) = 3

Degree of g(x) = 5

Required

Degree of 2f(x) + 4g(x)

Analyzing both polynomialsf(x)

2f(x) means 2 * f(x)

Since 2 is a constant

Multiplying f(x) by 2 will result in a polynomial with a degree of 3

Hence 2f(x) has a degree of 3

g(x)

4g(x) means 4 * g(x)

Since 4 is also a constant

Multiplying g(x) by 4 will result in a polynomial with a degree of 5

Hence 4g(x) has a degree of 5

Having said that;

When 2 polynomials of different degrees are added together, the degree of the result will be the higher degree of both polynomials;

This means that;

Adding a polynomial of degree 3 and another of degree 5 will result in a polynomial of degree 5

write the sum of twice a number and eleven as an algebraic expression

Answers

Answer:

2x-11

Step-by-step explanation:

2 x X = 2x + 11

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