What is the 52nd term of -11,-2,7,16,25,34

Answer:

65

Step-by-step explanation:

The sum of the first 16 terms of an arithmetic progression (A.P) is 240

The sum of the next 4 terms is 220

The sum of n terms in an A.P is given by;

[tex]s_{n}[/tex] = n/2(2a + (n - 1)d)

240 = 8(2a + 15d) ... (i)

460 = 10(2a + 19d) .... (ii)

Simplifying this gives;

2a + 15d = 30 ... (i)

2a + 19d = 46 ... (ii)

Subtracting (i) from (ii) we get;

4d = 16

d (common difference) = 4

and a (first term) = (30 - 60)/ 2 = -15

The sequence upto 21 terms is here:

-15, -11, -7, -3, 1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 51, 55, 59, 61, 65

So the next term (21^st term) is 65.

Answer:  a₂₁ = 65

Step-by-step explanation:

The Sum of an Arithmetic Progression is the sum of the first term plus the sum of the last term divided by 2 and multiplied by the number of terms.

[tex]a_1\ \text{is the first term}\\a_n=a_1+d(n-1)\quad \text{is the value of the nth term}\\\\[/tex]

Let's find the 16th term (n = 16)

[tex]a_{16}=a_1+d(16-1)\\\\.\quad =a_1+15d[/tex]

Now let's find the sum of the first 16 terms. This will be Equation 1:

[tex]S_{16}=\dfrac{(a_1)+(a_1+15d)}{2}\times 16=240\\\\\\.\qquad 8(2a_1+15d)=240\\\\\\.\qquad 2a_1+15d=30\qquad \leftarrow \text{Equation 1}[/tex]

************************************************************************************

Repeat what we did above for the next 4 terms (n = 17 to n = 20). This will be Equation 2:

[tex]a_{17}=a_1+d(17-1)\\\\.\quad =a_1+16d\\\\\\a_{20}=a_1+d(20-1)\\\\.\quad =a_1+19d[/tex]

[tex]S_{17-20}=\dfrac{(a_1+16d)+(a_1+19d)}{2}\times 4=220\\\\\\.\qquad 2(2a_1+35d)=220\\\\\\.\qquad 2a_1+35d=110\qquad \leftarrow \text{Equation 2}[/tex]

*********************************************************************************************

Now we have a system of equations. Solve using the Elimination Method:

2a₁ + 15d = 30   → -1(2a₁ + 15d = 30)     →    -2a₁ - 15d = -30    

2a₁ + 35d = 110  →  1(2a₁ + 35d = 110)    →     2a₁ + 35d = 110  

                                                                             20d = 80

                                                                                  d = 4

Input d = 4 into one the equations to solve for a₁:

Equation 1: 2a₁ + 15d = 30

                  2a₁ + 15(4) = 30

                    2a₁ + 60 = 30

                             2a₁ = -30

                               a₁ = -15

Given a₁ = -15 and d = 4, we can find the next term (n = 21)

[tex]a_n=a_1+d(n-1)\\\\a_{21}=-15+4(21-1)\\\\.\quad =-15+4(20)\\\\.\quad = -15+80\\\\.\quad = 65[/tex]

Answer:

3kg

Step-by-step explanation:

3kg because half of 2 is 1 which then means 2+1 will equal to 3

The total weight of the fish is = 3kg

Weight of an object or a body is the relative mass of that body in Kilogrammes.

The weight of the fish = 2kg + (1/2 × 2kg)

= 2 + 1 = 3kg

Therefore, the total weight of the fish is = 3kg

Learn more about weight here:

https://brainly.com/question/2337612

Answer:

4 centimeters

Step-by-step explanation:

The volume of a sphere can be found using the following formula:

v=4/3*π*r^3

We know the volume is 34 cm^3. Therefore, we can substitute 34 in for v.

34=4/3*π*r^3

We are trying to find r, or the radius. Therefore, we need to get r by itself on one side of the equation.

First, divide both sides by pi.

34/π=4/3*π*r^3 /π

34/π =4/3 * r^3

10.8225361= 4/3 * r^3

Next, divide both sides by 4/3, or multiply by the reciprocal of the fraction.

To find the reciprocal, flip the numerator and denominator of the fraction

4/3 ---flip top number and bottom number --> 3/4

3/4 * 10.8225361= 4/3*r^3 *3/4

3/4* 10.8225361= r^3

8.11690208= r^3

Finally, take the cube root of both sides of the equation.

∛8.11690208=∛r^3

∛8.11690208=r

2.00969477=r

Round to the nearest whole number.

r=2

Now, we must find the diameter. The diameter is twice the radius.

d=2r

The radius is 2 cm.

d= 2 * 2cm

d= 4 cm

The diameter is 4 cm

Answer:  7.8 days

Step-by-step explanation:

Painter can get the job done in 15 days so gets [tex]\dfrac{1}{15}[/tex] of the job done in 1 day.

Coworker can get the job done in 10 days so gets [tex]\dfrac{1}{10}[/tex] of the job done in 1 day.

Together, they get [tex]\dfrac{1}{15}+\dfrac{1}{10}[/tex] of the job done in 1 day.

Painter worked for 3 days so completed [tex]\dfrac{1}{15}(3)=\dfrac{1}{5}[/tex] of the job.

That leaves a remaining of [tex]1-\dfrac{1}{5}=\dfrac{4}{5}[/tex] of the job to be completed.

Let x represent the number of days it will take them to work together.

Painter + Coworker = Together

[tex]\dfrac{1}{15}(x)\quad +\quad \dfrac{1}{10}(x)\quad =\quad \dfrac{4}{5}[/tex]

Multiply by 30 to eliminate the denominator:

[tex]\dfrac{1}{15}(x)(30) +\ \dfrac{1}{10}(x)(30) = \dfrac{4}{5}(30)[/tex]

Simplify and solve for x:

    2x + 3x = 24

            5x = 24

              [tex]x=\dfrac{24}{5}[/tex]

              x = 4.8

Remember that Painter worked 3 days alone in addition to the 4.8 days they worked together.

So the total time to paint the building is 3 + 4.8 = 7.8

Answer:

No

Step-by-step explanation: he is 3 and 1/3 feet tall. 3 feet is 36inch and 1/3 feet is 4 inches, so 36+4 is 40 inches

Answer:

1.road 1

2. scooter

3. walk

Answer:

1. road 1

2. scooter

3. walk

Step-by-step explanation:

1. in the corresponding point on the tree, you have road 2. therefore, the most logical answer would be road 1.

2. you are given three options of travel. as "walk" and "bike" are already provided, they cannot be the answer to fill in for box 2. therefore, you are left with "scooter."

3. similarly, you are given three options of travel. as "bike" and "scooter" are already provided, they cannot be the answer to fill in for box 3. therefore, you are left with "walk."

Answer:

x = 80 degrees

Step-by-step explanation:

y degrees = 180 - 55 - 45 (Angles in a triangle add up to 180 degrees)

y degrees = 80 degrees

x = y (Vertically opposite angles are equal)

So,

x = 80 degrees

Answer:

14130 yd^3

Step-by-step explanation:

The volume of a sphere is

V = 4/3 pi r^3

The diameter is 30 so the radius is d/2 = 30/2 = 15

V = 4/3 pi (15)^3

V = 4500 pi

Letting pi = 3.14

V = 14130 yd^3

Answer:

Last one

Step-by-step explanation:

The volume of the sphere is given by the relation:

V= [tex]\frac{4}{3}[/tex] *π* 15³

V= 14137.166 yd³

wich is approximatively 14130yd³

Answer:

not perpendicular

Step-by-step explanation:

perpendicular line has opposite reciprocal slope

√3x-2√3 y=13

-2√3y=13-√3x

y=-13/(2√3)+√3 x/2√3

y=1/2 x-13/2√3  ( slope is 1/2)

6x-3y+11=0

-3y=-11-6x

y=-11/-3+6x/3

y=2x+11/3 slope =2

Answer:

1. 180 - 55 = 125

2. 180 - 125 = 55

3. 180 - 55 = 125

4. 180 - 70 = 110

5. 180 - 110 = 70

6. 180 - 70 = 110

7. 180 - 110 = 70

8. 180 - 141 = 39

These are all the right answers, can I please have brainliest I need 1 more.  

Answer:

1.  125º

2. 55º

3. 125º

4. 110º

5. 70º

6. 110º

7. 70º

8. 39º

Step-by-step explanation:

Hey there!

1.

XVR and WVX are supplementary angles meaning we can do,

180-55 = 125º

2.

Find RVS,

180 - 125 = 55º

3.

WVS,

180 - 55 = 125º

4.

RST,

We need RSV,

55 + 55 = 110

180 - 110 = 70

180 - 70 = 110º

5.

RSV = 70º

stated in A.4

6. VSU

110º

It is across from RST meaning it is 110.

7. UST

70º

Across from RSV

8. TUS

180 - 141

= 39º

Hope this helps :)

Answer:

140 toy cars

Step-by-step explanation:

The ratio of Ed's toy car to Pete's toy car is initially given as 5:2

Ed gave Pete a total number of 30 cars

Let x represent the greatest common factor that exists between both number

Number of Ed's car is represented as 5x

Number of Pete car is represented as 2x

Since they each have an equal number of cars which is 30 then we can solve for x as follows

5x-30=2x+30

Collect the like terms

5x-2x= 30+30

3x= 60

Divide both sides by the coefficient of x which is 3

3x/3=60/3

x=20

Ed's car is 5x, we substitute 20 for x

5(20)

= 100 cars

Pete car is 2x,we substitute 20 for x

2(20)

= 40 cars

Therefore, the total number of cars can be calculated as follows

= 100+40

= 140 toy cars

Hence they have 140 toy cars altogether

Answer:

140

Step-by-step explanation:

Answer:

a). x = 12

b). m∠H = 90°

    m∠I = 58°

    m∠J = 62°

Step-by-step explanation:

a). Use the property of a triangle,

  " Sum of all the angles in a triangle is 180°"

  (2x + 34)° + (4x + 14)° = 180°

  (2x + 4x) + (34 + 14) = 180

  6x + 48 = 180

  6x = 180 - 48

  6x = 132

   x = [tex]\frac{132}{6}[/tex]

   x = 12

b). m∠H = 90° [Given]

   m∠I = (2x + 34)° = [(2 × 12) + 34]°

   m∠I = 58°

   m∠J = (4x + 14)° = [(4 × 12) + 14]°

  m∠J = 62°

Answer:

( 1/25 x^-12 y^-14 )

Step-by-step explanation:

( 5 x^6 y^7 ) ^-2

We know that ( ab) ^c = a^ c * b^c

( 5^-2 x^6^-2 y^7^-2 )

We know that a^b^c = a^(b*c)

( 5^-2 x^-12 y^-14 )

We know that a^ -b = 1/ a^b

( 1/25 x^-12 y^-14 )

Answer:

Step-by-step explanation:

Given the system of equations;

a) x+3y=9

-4x+12y=12

This equation is a linear simultaneous equation with 2 equations and two unknown values. When the number of equations given is equal to the number of unknown variables, this means that the solution sets of the equations are unique and real and will provide us with just one solution.

b) For the system of linear equation

2x-y-4=0 .... *3

6x=3y+12  ... *1

First lets multiply equation 1 by 3, om multiplying by 3 we will have;

6x-3y-12 = 0

6x-3y = 0+12

6x-3y = 12

Rearranging equation 2 will give;

6x - 3y = 12

It is seen that both equation ate the same. This means that what we have is one equation with two unknowns. For a system of equation with one equation and two unknowns, there will be infinite number of solutions after solving the equation. Hence, the number of solutions for this system of equation is INFINITE

Answer:

No

Step-by-step explanation:

He's not correct because 5a² isn't a factor of a³ or 35b⁴; in order for something to be the GCF of a polynomial, all of the terms must be evenly divisible by it.

Answer:

a^3 – 25a^2b^5 – 35b^4

He is incorrect since the coefficient of the a^3 term is 1, the GCF cannot contain a coefficient of 5. Also, there is no a in all terms, so a^2 is also not a common factor.

Answer:

Step-by-step explanation:

Use F.O.I.L

F - First

O- Outside

I- Inside

L- Last

First multiply the ds from both to get [tex]d^{2}[/tex], next multiply the first d and the -4 and get -4d, then the 8 and the second d = 8d, and finally the 8 and -4 to get -32

you get [tex]d^{2}[/tex]-4d + 8d - 32

Answer:

The slower plane is flying at 175 miles per hour and complete the trip in 10 hours

The faster plane is flying at 250 Miles per hour and complete the trip in 7 hours

Step-by-step explanation:

Let s= speed of the slower plane s+75= speed of the faster plane

The time it takes the slower plane to make the flight = 1750/s

The time it takes the faster plane to make the flight is=1750/(s+75)

The difference in these two times is 3 hours

1750/s - 1750/(s+7)=3

{(s+75) / (s+75) * (1750/s)} - {(s/s) * (1750/s+75)} =3

(1750s+131250 / s^2+75s) - (1750s/s^2+75s) =3

1750s+131,250-1750s / s^2+75d =3

131,250 / s^2+75s = 3

Cross product

131,250=3(s^2+75s)

131,250=3s^2+225s

43,750=s^2+75s

s^2+75s-43,750=0

Solve the quadratic equation

x= -b +or- √b^2-4ac / 2a

a=1

b=75

c= -43750

x= -b +or- √b^2-4ac / 2a

= -75 +or- √(75)^2 - (4)(1)(-43750) / (2)(1)

= -75 +or- √(5625) - (-175,000) / 2

= -75 +or- √180625) / 2

= -75 +or- 425 / 2

x= -75 + 425/2 OR -75- 425/2

=350/2 OR -500/2

x=175 OR -250

We will ignore the negative sign because the planes are not flying Backward

The slower plane is flying at 175 miles per hour and complete the trip in 1750/175= 10 hours

The faster plane is flying at 250 Miles per hour and complete the trip in 1750/250= 7 hours

Answer:

The inequality that represents this situation is: [tex]140 + 45*n < p[/tex]

Step-by-step explanation:

Since the plane already had 140 pounds on board and "n" boxes will be loaded on it, then the weigh of each box multiplied by the number of box should be the extra cargo on the plane. This extra cargo added to the previous load must be less than the limit of cargo the plane can take as shown below:

[tex]140 + 45*n < p[/tex]

Answer:

A, B, E

Step-by-step explanation:

I attached everything that I thought it would help you.

Hope this helps ;) ❤❤❤

Answer:

(16a + 6b) (2x - 3y)      

Step-by-step explanation:

32ax + 12bx - 48ay - 18by

(32ax - 48ay) + (12bx - 18by)

16a(2x - 3y) + 6b(2x - 3y)         Factor out in both seperate expressions

(16a + 6b) (2x - 3y)                    Double factoring

Answer:

2(8a + 3b)(2x - 3y)

Step-by-step explanation:

32ax + 12bx - 48ay - 18by =

The first step in factoring is to factor out a common factor.

32, 12, -48, and -18 have the greatest common factor of 2.

= 2(16ax + 6bx - 24ay - 9by)

To factor a 4-term polynomial, factor it by parts. We factor out a common factor out of the first two terms, and we factor out a common factor out of the last two terms.

= 2[2x(8a + 3b) - 3y(8a + 3b)]

Now we have a common factor of 8a + 3b, so we factor that out.

= 2[(8a + 3b)(2x - 3y)]

Remove the unnecessary brackets.

= 2(8a + 3b)(2x - 3y)

Now we check every factor to confirm that no more factoring is possible.

There are no more common factors, and there are no methods of factoring binomials that are applicable, so the factoring is complete.

Answer: 2(8a + 3b)(2x - 3y)

Answer:

c

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

The perpendicular line bisect the base of isosceles triangle.

Then,

9^2=y^2-x^2

81=324-243

81=81

So the correct answer is D

I Hope this will be helpful for you

Answer:

Step-by-step explanation:

Use the following formulas:

surface area of rectangular prism: A = 2wl + 2lh + 2hw

volume of rectangular prism: lwh

surface area of cylinder: A=2πrh+2πr^2

volume of cylinder: V=πr^2h

using these formulas, the surface area of the box is 424.3

the volume of the box is about 511.3

the surface area of the cylinder is about 275.77

the volume is 342.12

knowing this, the cylinder uses less material but the box holds more soup.

Answer:

[tex]\boxed{\sf No}[/tex]

Step-by-step explanation:

[tex](q-r)^2[/tex]

Expand brackets.

[tex](q-r)(q-r)[/tex]

[tex]q^2 -rq -rq+r^2[/tex]

Combine like terms.

[tex]q^2 -2rq+r^2[/tex]

The expression is not equal to [tex]q^2 -r^2[/tex].

Answer:

Yes, they are.

Step-by-step explanation:

[tex](q - r) {}^{2} =( q) {}^{2} - (r) {}^{2} = q {}^{2} - r {}^{2} [/tex]

[tex](q - r) {}^{2} = q {}^{2} - r {}^{2} [/tex]

Hope this helps ;) ❤❤❤

Answer:

Step-by-step explanation:

-y = -3x - 12

y = 3x + 12

y - 5 = 3(x - 2)

y - 5 = 3x - 6

y = 3x - 1

Answer:

-100.204779...

or tenth to rounding, -100.2

Hope this helps!

//  Would you pick me Brainleist...?

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            Hi my lil bunny!

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All you have to do is simplify.

[tex]1 ( \frac{4}{6} - 2 \sqrt{7}) ( \frac{4}{6} + 21)\\\\= \frac{130}{9} + \frac{-130}{3} \sqrt{7}[/tex]  (Decimal: -100.204779)

So the answer is : [tex]\frac{130}{9} + \frac{-130}{3} \sqrt{7}[/tex]

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Hope this helped you.

Could you maybe give brainliest..?

❀*May*❀

Answer:

x = - 1, x = 1

Step-by-step explanation:

Given

f(x) = [tex]\frac{2x^2+3x+6}{x^2-1}[/tex]

The denominator cannot be zero as this would make f(x) undefined.

Equating the denominator to zero and solving gives the values that x cannot be and if the numerator is non zero for these values then they are vertical asymptotes.

x² - 1 = 0 ← difference of squares

(x - 1)(x + 1) = 0

x - 1 = 0 ⇒ x = 1

x + 1 = 0 ⇒ x = - 1

x = - 1 and x = 1 are vertical asymptotes

Answer:

f. 85

Step-by-step explanation:

All triangles add up to 180 degrees

BCE=25

then you need to find DBC, you can do that since ABD is isocilies that means all sides are equal in length and angle so 180 divided by 3 (number of side) is 60

isoceles triangle have 2 sides that are equiangular, cince we know BCA is 25 we also know BAC is 25, leaving angle ABC to be 130 (180-50=130)

we subtract angle ABD from angle ABC to get angle DBC, leaving angle DBC to equal 70 degrees

since 70 (angle DBC) + 25 (Angel BCA)= 95

we just subtrract 95 from 180 to get the answer 85 (:

Answer:

85 degrees

Step-by-step explanation:

if Δ ABD is equilateral  then the 3 sides and three angles are equal

sum of angles of Δ=180

180/3=60 degrees (∠A,∠B,∠D)

ΔBCA is isosceles then the two angles A and C are equal = 25

∠B=180-50=130

∠B in Δ BEC=130-60=70

∠E+∠B+∠C in Δ BEC=180

∠E= 180-70-25=85 degrees

Answer:

Step-by-step explanation:

28800 = 2 * 2 * 2 * 2 * 2 * 3 * 3 * 10 * 10

You need one 2

You need one 3

You need one 10

28800 * 2 * 3 * 10 = 2 * 2 * 2 * 2 * 2 * 2 * 3 * 3 * 3 * 10 * 10 * 10

(2*6 * 3* 3^3 * 10^3) ^(1/3)

2*2 * 3 * 10 is the cube root

120

Answer:

11.9 cm.

Step-by-step explanation:

A cube has a SURFACE AREA of 850 cm^2.

A cube has six congruent sides. That means that each side measures 850 / 6 = 141.666666667 cm^2.

Since a side measures 141.66667 cm^2, a side length will be the square root of that (the area of a square is a side length times the side length, and they are the same).

[tex]\sqrt{141.666666666667}[/tex]

= 11.90238071

So, the side length of the cube is 11.9 cm.

Hope this helps!

Answer:

95

Step-by-step explanation:

a=3,b=2

3^2+3(2)-2^2

a=11,b=13

11^2+11(13)-13^2

= 95

Answer:

95

Step-by-step explanation:

If a ∆ b = a² + ab - b²,

Then (3 ∆ 2) ∆ 13:

a = 3

b = 2

3 ∆ 2 = 3² + 3 × 2 - 2² = 11

a = 11

b = 13

11 ∆ 13 = 11² + 11 × 13 - 13² = 95

The answer is 95.