Use mathematical induction to prove the statement is true for all positive integers n. 8 + 16 + 24 + ... + 8n = 4n(n + 1)? Please show work

Answers

Answer 1

Answer:

The sum of the series is Sₙ = n/2 [2·a + (n - 1)·d] where a = 8 and d = 8, therefore 8 + 16 + 24 + ... + 8·n = 4·n·(n + 1)

Step-by-step explanation:

The parameters given are;

8 + 16 + 24 + ... + 8·n = 4·n·(n + 1)

The given series of numbers can be checked to find;

16 - 8 = 24 - 16 = 8

Therefore, the series of numbers is an arithmetic progression with first term = 8, and common difference = 8, we have;

The sum of n terms of an arithmetic progression, Sₙ, is given as follows;

Sₙ = n/2 [2·a + (n - 1)·d]

Where;

a = The first term of the series of numbers = 8

d = The common difference = 8

∴ Sₙ = n/2 × [2×8 + (n - 1)×8] = n [2×8/2 + (n - 1)×8/2]  =  n × [8 + (n - 1)×4]

Sₙ =  n × [8 + (n - 1)×4] =  n × [8 + 4·n - 4] = n × [8  - 4 + 4·n] = n × [4 + 4·n]

Sₙ =n × [4 + 4·n] = 4 × n×(n + 1) = 4·n·(n + 1).


Related Questions

The sides of two cubes are in ratio of 1:3. What is the ratio of the areas of these cubes ? What is the ratio of their volume ? ​

Answers

Answer:

The ratio of their surface areas would 1:9 and the ratio of their volumes would be 1:27

Step-by-step explanation:

Given Info: The sides of two cubes are in ratio of 1:3. We can assign one square x and the other square 3x.

We know that the area of a square is its side squared, and that a cube has 6 sides. So thus if we assign one side of the cube x we can assume that surface area is 6x^2:

Surface Area of Cube #1= 6x^2

Surface Area of Cube #2= 6((3x)^2) = 6(9x^2) = 54x^2

Ratio of Surface Area: 6x^2 : 54x^2 = 6:54 = 1:9

Now for the volume we know that it is equivalent to one side cubed. So after assigning x to one cube, we can assume that volume would be x^3.

Volume of Cube #1= x^3

Volume of Cube #2= (3x)^3 = 27x^3

Ratio of Volume: x^3: 27x^3 = 1:27

Hope this helps!

Find a101 of the sequence 5,8,11,

Answers

Answer:

305

Step-by-step explanation:

This sequence es the sum of 3

5+3 =8

8+3 = 11

then

101 = 100 + 1

the fisrt date is 5

the another 100:

100*3 = 300

300 + 5 = 305

What is the multiplicity of each of the roots of the graph of
f(x) = 2x4 + 12x} + 16x2 – 12x – 18?
A.-3, multiplicity 2; -1, multiplicity 1; 1, multiplicity 1
B.-3, multiplicity 2; 1, multiplicity 2
C.-3, multiplicity 1; -1, multiplicity 1; 1, multiplicity 1
D.-3, multiplicity 2; -1, multiplicity 3; 1, multiplicity 1

Answers

Answer:

The correct option is;

C. -3, multiplicity 2; -1, multiplicity 1; 1, multiplicity 1

Please find attached the required function graph

Step-by-step explanation:

To solve the equation f(x) = 2·x⁴ + 12·x³ + 16·x² -12·x - 18, by graphing the function, we have;

x [tex]{}[/tex]       F(x)

-4[tex]{}[/tex]       30

-3[tex]{}[/tex]       0

-2[tex]{}[/tex]       6

-1[tex]{}[/tex]        0

0 [tex]{}[/tex]      -18

1[tex]{}[/tex]         0

2[tex]{}[/tex]       150

The shape of a graph with multiplicity of 2

Given that the graph bounces of the horizontal axis at the y-intercept at point x = -3, the factor (x - 3) must be a quadratic of the form (x - 3)², thereby having a multiplicity of 2 in the solution which are;

x = 1, -1, and, giving

(x - 1)·(x + 1)·(x - 3)² = 0

Therefore, the correct option is -3, multiplicity 2; -1, multiplicity 1; 1 multiplicity 1.

Answer:

C

Step-by-step explanation:

What is the final concentration if a saline solution consisting of 20% NaCl is diluted using a 1/4 solution?

Answers

Answer: C.V=C1.V1 +C2.V2

Step-by-step explanation: C=(C1V1 + C2V2)/V -> C=(20%.V+25%V)/2V-> C=22,5%

WILL MARK BRAINLIEST!!!!20 POINTS!!!!URGENT!!!

Answers

Answer:

the firsts third and last one

Step-by-step explanation:

hope this helped

The mean number of people per day visiting an art show in July was 110. If
20 more people each day visited the museum in August, what was the mean
number of people per day visiting in August?
A. 130
B. 620
C. 640
D. 110

Answers

Answer:

I believe the answer is A. 130

Answer:

A 130

Step-by-step explanation:

The angles of a triangle are in the ratio 11 : 5 : 2. The side opposite the largest angle is 5.5 centimeters. The length of the side opposite the smallest angle of the triangle is centimeters.

Answers

Answer:

  2.0 cm

Step-by-step explanation:

The sum of ratio units is 11 +5 +2 = 18, so each one stands for 10° of angle. Then the largest angle is 110°, and the smallest is 20°. The law of sines can help us find the smallest side (x):

  x/sin(20°) = 5.5/sin(110°)

  x = 5.5·sin(20°)/sin(110°) ≈ 2.00

The side opposite the smallest angle is 2.0 cm.

Answer:

the anser is 2

Step-by-step explanation:

Given that v = u + 10t, find y when
u= 6 and t = 9.

Answers

Answer:

hey here is the answer

Step-by-step explanation:

Subject of the formula:

It is a variable which is expressed in terms of other variables involved in the formula.

Formulas are written so that a single variable, the subject of the formula is on the L.H.S. of the equation. Everything else goes on the right side of the equation. We evaluate the formula by substituting for the literal numbers on the right hand side.

For example:

In the formula v = u + at, v is the subject.

To find v in the example, we substitute the values u, a and t in the R.H.S. of the equation.

Changing the subject of the formula:

To change the subject of a formula, begin with the variable to become the new subject, and apply inverse operation as for solving equations in the opposite order to the order conventions.  

1. To make ‘u’ the subject of the formula in v = u + at,  

  [subtract at from both sides]

v - at = u

or, u = v - at

2. To make ‘t’ the subject of the formula, v = u + at,

 [subtract u from both sides]

v - u = at

or, (v - u )/a = t

or, t = (v - u)/a

Change the Subject of a Formula

The value of the equation is v = 96 when u = 6 and t = 9

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

v = u + 10t   be equation (1)

when u = 6 and t = 9

Substitute the value of u and t in the equation , we get

v = 6 + 10 ( 9 )

On simplifying the equation , we get

v = 6 + 90

v = 96

Therefore , the value of v is 96

Hence , the equation is v = 96

To learn more about equations click :

https://brainly.com/question/19297665

#SPJ2

find the Perimeter Of a circle whose radius is 14cm​

Answers

Answer:

Step-by-step explanation:

Firstly, we will use the formula π × d

Which will be 22\7 × 28 (this is the radius multiplied by 2)

After multiplying you will get 88 cm as your perimeter

=88 cm

Which is a complete list of factors of each term in the expression 15 + 20 x? 15: 1, 3, 5, 15 20x: 1, 2, 4, 5, 10, 20, x 15: 1, 3, 5, 15 20x: 1, 2, 4, 5, 10, 20 15: 3, 5 20x: 4, 5, x 15: 1, 3, 5 20x: 1, 2, 4, 5, 10, x

Answers

Answer:

15: 1 3 5 15

20: 1 2 4 5 10 20

Step-by-step explanation:

This assumes you are only factoring the coefficients of the expression.  Using this assumption, we simply create a list of factors of the coefficients.

15 -> 1 * 15, 3 * 5 --> 1 3 5 15

20 -> 1 * 20, 2 * 10, 4 * 5 --> 1 2 4 5 10 20

If you don't assume factoring of just the coefficients, then 20x factors

20x:  1 2 4 5 10 20 x

Cheers.

Answer:

b

Step-by-step explanation:

what is the value of F? (ap physics summer hw) show work

Answers

See the attached picture.

Ruben goes to a shop to buy 24.5m of cloth and 13.5m ribbon. The cloth costs Rs.85.40 per metre and the ribbon costs Rs.8.5 per metre. If he pays Rs. 2300 to the shopkeeper, how much money will he get back?

Answers

Answer:

Rs.92.95

Step-by-step explanation:

Given the following :

Metres of cloth purchased = 24.5m

Metres of ribbon = 13.5m

Cost of cloth per metre = Rs.85.40

Cost of Ribbon per metre = Rs.8.50

Total amount given to shopkeeper = Rs. 2300

how much money will he get back?

Total cost of cloth:

Cost per metre * number of metres

85.40 * 24.5 = Rs. 2092.30

Total cost of Ribbon :

Cost per metre * number of metres

8.50 * 13.5 = Rs. 114.75

Total cost of goods purchased :

Rs. (2092.30 + 114.75) = Rs. 2,207.05

Amount of change :

Rs. (2300 - 2207.05) = Rs.92.95

Interior angles are located on the a. Inside b. Outside of a polygon. Exterior angles are located on the a. Inside b. Outside of a polygon.

Answers

Answer:

Interior angles are inside. Exterior angles are outside.

Step-by-step explanation:

"Interior" means inside. "Exterior" means outside.

Answer:

inside, outside

Step-by-step explanation:

What is 12x-10y=-19 in slope intercept form?

Answers

Answer:

-10y=-12x-19

-y=  -12x-19

           10

y=  12x + 19

            10

Step-by-step explanation:

form slope intercept its y=mx+b

so you find y what equal .

Malia measures the longer side of a dollar bill using a ruler at school. Which of the following is most likely the quantity she measured?

Answers

Answer:

Step-by-step explanation:

The most likely quantity is centimetres.

The second option can be inches.

Hope this helps

plz mark it as brainliest!!!!!!!!!

solve for x 3x - 4 = 3x - 10

Answers

Answer:

no solution

Step-by-step explanation:

3x - 4 = 3x - 10

Subtract 3x from each side

3x-3x - 4 = 3x-3x - 10

-4 = -10

This is never true so there is no solution

Answer:

Step-by-step explanation:

I think you might have copied down the problem incorrectly.

If you try and solve this problem by moving the variables onto one side and the constants onto the other, you get:

3x-4=3x-10

   +10    +10

3x+6=3x

-3x     -3x

6=0 (which is FALSE)

Hope this helps!

P.S. Please give me brainliest. Thanks :)

23458+98432 find the sum

Answers

Answer:

121,890

Step-by-step explanation:

23458+98432

=121,890

Tan x is ........ Cos x is ........ Sin x is ..........

Answers

Answer:

Tan x= 3/4 Cos x= 4/5 Sin x=3/5

Step-by-step explanation:

"soh-cah-toa"

Just an easy way to remember how Sine, Cosine and Tangent work:

Soh...

Sine = Opposite / Hypotenuse

...cah...

Cosine = Adjacent / Hypotenuse

...toa

Tangent = Opposite / Adjacent

Answer:

tan(x)=0.75 sin(x)=0.6 Cos(x)=0.8

Step-by-step explanation:

[tex]tan(x)=\frac{opposite}{adjacent}=\frac{3}{4}=0.75[/tex]

[tex]cos(x)=\frac{adjacent}{hypotenuse}= \frac{4}{5} =0.8[/tex]

[tex]sin(x)=\frac{opposite}{hypotenuse}=\frac{3}{5}=0.6[/tex]

opposite=3

adjacent=4

hypotenuse=5

try remembering it as SOH CAH TOA


[tex] \frac{15x - 8 }{3} + \frac{9x - 3}{2} [/tex]

Answers

Greetings from Brasil...

Here is the problem:

[(15X - 8)/3] + [(9X - 3)/2]

Let's multiply everything by 6

[6.(15X - 8)/3] + [6.(9X - 3)/2]

[2.(15X - 8)] + [3.(9X - 3)]

30X - 16 + 27X - 9

57X - 25

For which system of inequalities is (3,-7) a solution? A. x + y < -4 3x + 2y < -5 B. x + y ≤ -4 3x + 2y < -5 C. x + y < -4 3x + 2y ≤ -5 D. x + y ≤ -4 3x + 2y ≤ -5

Answers

Answer:

The correct option is;

D x + y ≤ -4, 3·x + 2·y  ≤-5

Step-by-step explanation:

A. For the system of inequality, x + y < -4, 3·x + 2·y  <-5

We have;

y < -4 - x, When x = 3, y < -7

y < -2.5 - 1.5·x, When x = 3, y = -7

B. For the system of inequality, x + y ≤ -4, 3·x + 2·y  <-5

We have;

y ≤ -4 - x, When x = 3, y ≤ -7

y < -2.5 - 1.5·x, When x = 3, y < -7

C. For the system of inequality, x + y < -4, 3·x + 2·y  ≤-5

We have;

y < -4 - x, When x = 3, y < -7

y ≤ -2.5 - 1.5·x, When x = 3, y ≤ -7

D. For the system of inequality, x + y ≤ -4, 3·x + 2·y  ≤-5

We have;

y ≤ -4 - x, When x = 3, y ≤ -7

y ≤ -2.5 - 1.5·x, When x = 3, y ≤ -7

Therefore, the system of inequality for which (3, -7) is a solution is D, x + y ≤ -4, 3·x + 2·y  ≤-5.

Aisha saves 2 Dhs on first week of the month of June, 4Dhs on second week of the month, 8 Dhs on third week of the month and so on. What will be her saving at the end of second week of July? What value is being shown by Aisha? Is saving is a good habit? How often do you save money? What are the different ways of saving money?

Answers

Answer:

she is saving in an exponential way, that is an amazing habit that will multiply her savings over time. At the end of the second week of July she will have 126 if she kept multiplying the amount every week from June into July but she will  have 38 if she starts over with saving 2 on the 1st week of the second month. I save money often, my way of saving is only spending the money i have on things I need rather than want. I also save in a linear way buy saving five dollars every month which is slower than aishas way in the long run but it is easy for me. There are so many different ways of saving money but some are slower than others and some are faster.

Step-by-step explanation:

Hope this helps, please give brainliest, i never got it before

Bob and Carol want to hire Able Refinishing to sand and refinish the dining room floor to match the floor in the living room. Able charges $2.41 per square foot to sand and refinish a hardwood floor. The dining room is rectangular and measures 17 feet 10 inches by 11 feet 9 inches. Find the area of the dining room floor and the cost of the work.

Answers

Answer:

Area = 209.5 ft² (nearest tenth)

Cost = $505 (approximated)

Step-by-step explanation:

Step 1: convert the inches to be in feet by dividing length in inches by 12.

17 feet 10 inches => [tex] 17 + \frac{10}{12} = 17.83 ft [/tex]

11 feet 9 inches => [tex]11 + \frac{9}{12} = 11.75 ft[/tex]

Step 2: Find the area of the floor of the dinning room

Area = 17.83*11.75 = 209.5 ft² (nearest tenth)

Step 3: Find the cost of the work.

Cost = 209.5 ft² × $2.41 = $505 (approximated)

s the value of the expression 6x − y when x = 3 and y = 1? (5 points) 3 8 12 17

Answers

Answer:

(6)(3)−1

=17

Step-by-step explanation:

Answer:

17

Step-by-step explanation:

6x − y

Let x =3 and y=1

6*3 -1

18-1

17

please help will give you a 5 star rating

Answers

Answer:

3

Step-by-step explanation:

To find the average rate of change

f(0) - f(-2)

-----------------

0 - -2

Taking the values for f(0) = 6 and f(-2) =0  

6 - 0

---------

0+2

6/2

3

Answer:

Slope I think its says, so: 3

Step-by-step explanation:

Take

6 = y2 , 0 = y1 , 0 = x2 , -2 = x1

y2 - y1 over x2 - x1

6-0

0+2 (because 2 is negative)

=

6/2

which reduced makes 3!

Hope this helps, and have a good day.

And for the 0 + 2:

its

0 - ( - 2 )

- ( - makes a big plus so add :)

Find four rational number between 1/4 and 2/3.

Answers

Answer:

4/12, 5/12, 6/12, 7/12

Step-by-step explanation:

1/4 x 3/3 = 3/12

2/3 x 4/4 = 8/12

between 3/12 and 8/12

4/12, 5/12, 6/12, 7/12

you can simplify these if you wish

Hope that helped!!! k

The point (6, 6) is on the graph y = f(x) . Find the corresponding coordinates of this point on the graph y = 4f[1/3x +9] -7

a. (-9,17)
b. (17,-9)
c. (11,11)
d. (9,17)

Answers

Answer:

Correct answer is:

a. (-9,17)

Step-by-step explanation:

We are given that a point (6, 6) lies on the graph of [tex]y =f(x)[/tex].

Putting the values from the given point:

[tex]6 =f(6)[/tex]

That means we are given that [tex]f(6) =6[/tex] ..... (1)

And we have to find the corresponding coordinates of this point on the graph of [tex]y = 4f[\frac{1}3x +9] -7[/tex]

From equation (1), we know the value of [tex]f(6)[/tex].

so, let us convert [tex]f[\frac{1}3x +9][/tex] to a form such that it becomes equal to [tex]f(6)[/tex]

[tex]\Rightarrow \dfrac{1}{3}x +9 =6\\\Rightarrow \dfrac{1}{3}x=-3\\\Rightarrow x = -9[/tex]

So, let us put [tex]x = -9[/tex] in the given function:

[tex]4f[\frac{1}3\times (-9) +9] -7\\\Rightarrow 4f[-3 +9] -7\\\Rightarrow 4f(6) -7[/tex]

Now, using equation (1), putting [tex]f(6)=6[/tex]

[tex]\Rightarrow 4\times 6 -7\\\Rightarrow 24-7 \\\Rightarrow y = 17[/tex]

Therefore, the point the corresponding point is:

a. (-9,17)

How do I solve for x.

Answers

Answer:

x = 17

Step-by-step explanation:

(whole secant) x (external part) =  (whole secant) x (external part)

(x+7) * 7 = ( 13+8) *8

(x+7) * 7 = ( 21) *8

Divide each side by 7

x+7 = 21/7 *8

x+7 = 3*8

x+7 = 24

Subtract 7

x = 17

Answer:

The answer is x = 17

Though I think the other guy explained it better

What are the possible steps involved in solving the equation shown? Select three options. 3.5 + 1.2(6.3 – 7x) = 9.38 Add 3.5 and 1.2. Distribute 1.2 to 6.3 and –7x . Combine 6.3 and –7x . Combine 3.5 and 7.56. Subtract 11.06 from both sides. Mark this and return Save and Exit Next Submit

Answers

Answer:

1) Distribute 1.2 to 6.3 and -7x

2)Combine 3.5 and 7.56

3)Subtract 11.06 from both sides

Step-by-step explanation:

3.5 + 1.2(6.3 - 7x) = 9.38

Distribute 1.2 to 6.3 and -7x

3.5 + 1.2* 6.3 - 1.2 * 7x = 9.38

        3.5 + 7.56 - 8.4x = 9.38

Combine 3.5 and 7.56

11.06 - 8.4x = 9.38

Subtract 11.06 from both sides

11.06 - 8.4x -11.06 = 9.38 - 11.06

                    -8.4x = -1.68

To find solution:

Divide both sides by (-8.4)

-8.4x/-8.4 = -1.68/-8.4

 x = 0.02

Answer:

B, D, and E

its right cus i took the test soo..

Please answer this question now

Answers

Answer:

320 sq in

Step-by-step explanation:

4(1/2*8*16) + (8*8)

= 4(64) + (64)

= 5(64)

= 320

HELP ME ASAP I DONT UNDERSTAND

Answers

Answer

False

Step-by-step explanation:

3 is an element of A but {3} is not so it is false.

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