Mathematics High School

Consider the arithmetic series:

1 + 9 + 17 + 25 + ...

Write a formula for the sum of the first n terms in this series.
A) 4n2 - 3n
B) 6n2 - 7n
C) 8n2 - 5n

Answers

Answer 1
The sum of an Arithmetic Series is given as:

[tex] S_{n}= \frac{n}{2}(2a_{1}(n-1)*d) [/tex]

where,
d = Common Difference = Difference of any two consecutive terms.
So,
d = 8

a1 = First term = 1

Using the values, we get:

[tex] S_{n}= \frac{n}{2}(2*1+(n-1)*8) \\ \\ S_{n}= \frac{n}{2} (2+8n-8) \\ \\ S_{n}= \frac{n}{2}(8n-6) \\ \\ S_{n}=n(4n-3) \\ \\ S_{n}==4n^{2}-3n [/tex]

The above equation gives the formula for n terms of an Arithmetic Series.

So, option A is the correct answer

Related Questions

Please help due tomorrow! Math

Answers

The seats in the theater follows the sequence given by:
7,9,11,..
This is an arithmetic sequence which follows an explicit formula given by:
an=a+(n-1)d
where:
a=first term
d=common difference
but
a=7 and d=9-7=2 
thus
an=7+(n-1)2
an=7+2n-2
an=2n-5
Thus the number of seats in nth row is:
an=2n-5

For a circle with a diameter of 6 meters, what is the measurement of a central angle (in degrees) subtended by an arc with a length of 7 3 π meters? A) 35° B) 50° C) 70° D) 140°

Answers

By definition, the arc length is given by:
 S = R * Theta
 Where,
 R: radio 
 Theta: central angle
 Substituting values we have:
 (7/3) π = (6/2) * Theta
 Clearing the angle we have:
 Theta = (7/9) π
 Rewriting the angle in degrees:
 Theta = (7/9) π * (180 / π)
 Theta = 140 degrees
 Answer:
 The measurement of a central angle (in degrees) is:
 Theta = 140 degrees
 D) 140 °

Answer:

the answer is (D)

Step-by-step explanation:

Someone please help me?

Answers

EB * AE = DE *EF

x+3 *3 = 6*x-2 

simplify:

3x+9 = 6x-12
subtract 3x from each side

9 = 3x -12

add 12 to each side

21 = 3x
divide both sides by 3

x = 21/3
x = 7

replace x with 7 to find EB

EB = 7+3 = 10 cm

What is the y-intercept of the line whose equation is y = x - 3?

Answers

Answer:

-3

Hope this helps! Please mark as brainliest.

Let logba=3 logbc=2 logbd=5 what is the value of logba^3d^4/c^2

Answers

[tex]Use:\\\log_ax+\log_ay=\log_a(xy)\\\\\log_ax-\log_ay=\log_a\dfrac{x}{y}\\\\\log_ax^n=n\cdot\log_ax[/tex]

[tex]\log_ba=3;\ \log_bc=2;\ \log_bd=5[/tex]

[tex]\log_b\dfrac{a^3d^4}{c^2}=\log_b(a^3d^4)-\log_bc^2=\log_ba^3+\log_bd^4-\log_bc^2\\\\=3\log_ba+4\log_bd-2\log_bc=3\cdot3+4\cdot5-2\cdot2=9+20-4=25[/tex]

Answer:

25

Step-by-step explanation:


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Which does NOT represent the interior angle measures of a triangle? A.5°, 75°, 100°B.10°, 80°, 90°C.20°, 60°, 100°D.45°, 45°, 45°E.50°, 50°, 80°

Answers

The angles should measure 180º.

5° + 75°+ 100° = 180°

10°+ 80°+ 90° = 180°

20° + 60° + 100° = 180°

45° + 45° + 45° = 135°

50° + 50° +  80° = 180°

So D does not represent interior angle measures of a triangle.

Hope this Helps!!

Which answer best describes the shape of this distribution?

Answers

skewed to the left
i believe im am not 100% sure tho

A helicopter hovers 950 over......

Answers

Okay, so here's the equation:
tan 44 = d/950
0.01770469927 (I used a calculator to solve tan 44, so let's just use to the nearest hundredth)
0.02 = d/950
100d = 1900
isolate d:
d = 19
19 feet
Comment
You have to assume that P is on the coast.
You also have to assume that d and the horizontal dotted line defining the 46 degrees are parallel. 

Givens
The angle of depression = 46 degrees
The height of the helicopter = 950 feet.

Formula
height helicopter / d = Tan(46)

The thing is that the angle of elevation from P forms an angle with the angle of depression that  made 2 alternate interior angles which are equal when two parallel lines and a traversal  are given.

The line connecting P and the helicopter is the traversal. 

Solution
height of helicopter = 950
d = ??
angle = 46o

Tan(46) = 950/d
d = 950 / tan(46)
d = 950 / 1.03553
d = 917 feet from the island to P <<<<<< answer

10. simplify the rational expression by rationalizing the denominator.( 1 point ) 4√150/√189x

Answers

rationalizing the denominator, simply means "getting rid of that pesky root at the bottom", and we do so by simply multiplying it by something to take it out, of course, we multiply the bottom, we have to also multiply the top,

[tex]\bf \cfrac{4\sqrt{150}}{\sqrt{189x}}\cdot \cfrac{\sqrt{189x}}{\sqrt{189x}}\implies \cfrac{4\sqrt{150}\sqrt{189x}}{(\sqrt{189x})^2}\implies \cfrac{4\sqrt{(150)({189x})}}{189x}[/tex]

[tex]\bf \cfrac{4\sqrt{28350x}}{189x}\qquad \begin{cases} 28350=2\cdot 3\cdot 3\cdot 3\cdot 3\cdot 5\cdot 5\cdot 7\\ \qquad 2\cdot 3^2\cdot 3^2\cdot 5^2\cdot 7\\ \qquad 2\cdot (3^2)^2\cdot 5^2\cdot 7\\ \qquad 2\cdot (3^2\cdot 5)^2\cdot 7\\ \qquad 2\cdot (45)^2\cdot 7\\ \qquad 14\cdot 45^2 \end{cases}\implies \cfrac{4\sqrt{14\cdot 45^2}}{189x} \\\\\\ \cfrac{4\cdot 45\sqrt{14}}{189}\implies \cfrac{180\sqrt{14}}{189x}\implies \cfrac{20\sqrt{14}}{21x}[/tex]

For bananas are to be selected from a group of seven in how many ways can this be done

Answers

Seven ways since there are 7 bananas but you said for

Which equation is NOT true?

A. 15x + 55 = 6x + 4x

B. 15x + 55 = 26x

C. 25x + 55 = 180

D. m ∠S = 6x + 4x

Answers

Answer:

C

Step-by-step explanation:

Answer:

A. 15x + 55 = 6x + 4x

Step-by-step explanation:

Process of elimination the rest are true so this one is not. The angles of one side are supplementary with these angles which means they are not congruent.

Find the slope of the line on the graph

Answers

find 2 points on the line:

(-4,0) and (0,3)

slope = change in y /  change in x

slope = 3-0 / 0 - -4

slope = 3/4

Sin (2x -9)= Cos (x +30) to solve for x

Answers

A graphing calculator shows four (4) zeros of
  f(x) = sin(2x -9°) -cos(x +30°)
in the range 0° ≤ x ≤ 360°

Solutions are x ∈ {23°, 129°, 143°, 263°).

_____
You can make use of a couple of trig identities to rearrange this equation.
  cos(x) = sin(x+90°)
  sin(a) -sin(b) = 2*cos((a+b)/2)*sin((a-b)/2)
So
  sin(2x -9°) -sin(x +120°) = 2*cos((3x +111°)/2)*sin((x -129°)/2) = 0
The cosine factor will be zero for
  (3x +111°)/2 = n*180° +90°
  3x -69° = n*360°
  x = 23° +n*120° . . . . . . for any integer n
The sine factor will be zero for
  (x -129°)/2 = n*180°
  x = 129° +n*360° . . . . . for any integer n

Combined, these solutions give the ones listed above in the range 0..360°.

I really need this answer to be correct

Answers

it is unchanged because the same number would still be in the middle and there would still be the same amount of numbers

if
11,15,21,22,23,27,30 before 22 is the median

if
11,15,21,22,23,27,30 after 22 is still the median

The median is unchanged

Which image of figure WXYZ is under the composition T 2,7 . D 0,2?

A.figure A

B. figure B

C.figure C

D.figure D

Answers

I Know the answer is Figure A i've done the test.

Answer:

A. Figure A

Step-by-step explanation:

We are given the figure WXYZ.

It is required to find the final figure after [tex]T_{2,7}D_{0,2}[/tex].

Now, [tex]D_{0,2}[/tex] means to dilate the figure by 2 units and [tex]T_{2,7}[/tex] means to translate it by 2 units to the left/right and seven units up/down.

As we have to apply [tex]T_{2,7}D_{0,2}[/tex] to the figure.

This means that first dilation is applied and then translation.

Since, the all the figures are dilated. We focus on the translations.

We can see that, only figure A is translated 2 units to the right and 7 units upwards.

So, option A is correct.

Challenger Elementary School has 8 0 0 800800 students. Every Wednesday, 1 2 % 12%12, percent of the students stay after school for Chess Club. How many students attend Chess Club on Wednesdays?

Answers

You need to calculate 12% of 800.

To find a percent of a number, multiply the percent by the number.
Change the percent into a decimal by dividing the percent by 100 (move the decimal point of the percent two places to the left.)

12% of 800 =

= 12% * 800

= 0.12 * 800

= 96

Answer: 96 students

Which ordered pair is a solution of y = x + 12?
(24, 12)

(9, 21)

(–12, –24)

(0, –12)

Answers

the answer is (9,21) because is you plug in 9 for x, and add 12, you get 21.
The (24,12) because 12 + 12 = 24

ABCD is a square. Given only the choices below, which properties would you use to prove AEB ≅ DEC by SAS? The diagonals are ⊥ to each other. Opposite sides are | |. The diagonals bisect each other. All sides are congruent.

Answers

All sides of a square re equal and opposite sides are parallel to each other. 
Assuming that E is the point where the diagonals intersect (since we are not told in the question), then AEB ≅ DEC.
 By SAS, 
  2 sides are equal. That is AE = EC and DE = EB.
  The triangles share a common angle. That is <DEC=<AEB

The property used the diagonals bisect each other.

Solve this application using logarithms.

How long will money in savings take to double at 5% interest compounded annually? Round the answer to the nearest hundredth of a year.

Answers

Ao is your initial value but since you want your initial to double doesn't matter what that exact value is. R is the rate at 5% (as a decimal) and n is the compounding annually, which is equal to 1.

Answer:

14.21

Step-by-step explanation:

A shipping container is in the shape of a right rectangular prism with a length of 13.5 feet, a width of 10.5 feet, and a height of 2.5 feet. The container is completely filled with contents that weigh, on average, 0.33 pound per cubic foot. What is the weight of the contents in the container, to the nearest pound?

Answers

The total weight of the container is given by:
Total weight=(volume of the container)*(weight per cubic volume)
volume of the container
=length*width*height
=13.5×10.5×2.5
=354.375 ft³

weight per cubic volume=0.33 pound per cubic ft

Total weight=354.375×0.33=116.94375 pounds~117 pounds 

The weight of the contents in the container, to the nearest pound, is 117 pounds.

To calculate the weight of the contents, we first find the volume of the container, then multiply it by the weight per cubic foot.

Step 1: Calculate the volume of the container.

Volume = length × width × height

Volume = 13.5 ft × 10.5 ft × 2.5 ft

Volume = 354.375 cubic feet

Step 2: Calculate the weight of the contents.

Weight = Volume × Weight per cubic foot

Weight = 354.375 cubic feet × 0.33 pounds per cubic foot

Weight ≈ 116.8725 pounds

Rounded to the nearest pound, the weight of the contents is 117 pounds.

First, we find the volume of the container by multiplying its length, width, and height together. The formula for the volume of a rectangular prism is length × width × height. In this case, the dimensions are given as 13.5 feet for the length, 10.5 feet for the width, and 2.5 feet for the height.

Next, we multiply the volume of the container by the weight per cubic foot of the contents to find the total weight. The average weight per cubic foot is given as 0.33 pounds.

Finally, we round the calculated weight to the nearest pound to match the desired precision. In this case, the weight of the contents is rounded to 117 pounds.

Complete question:

A shipping container is in the shape of a right rectangular prism with a length of 13.5 feet, a width of 10.5 feet, and a height of 2.5 feet. The container is completely filled with contents that weigh, on average, 0.33 pound per cubic foot. What is the weight of the contents in the container, to the nearest pound?

which of the following equations can be used to solve for the radius

Answers

Choice 4 is correct ... r = the square root of area over pi
Transpose the equation so that r is a function of A.

r = sqrt(A/pi)

Given the following functions f(x) and g(x), solve f over g(−4) and select the correct answer below:

f(x) = 4x − 4

g(x) = x − 1

Answers

x = -4
As g(x) is replaced by g(-4)
plug in -4 for x inside the equation.
g(-4) = (-4) - 1g(-4) = -5
Plug in -4 for x in f(x)f(-4) = 4(-4) - 4f(-4) = -16 - 4f(-4) = -20
Now solve for f(x) over g(x)
remember, f(x) = -20, and g(x) = -5
-20/-5  = 4
4 should be your answer
hope this helpsClick to let others know, how helpful is it

What is the value of x

Answers

For this case, we observe that the triangles are similar.
 We observe that the triagnules have three equal angles.
 Therefore, to find the value of x we can use the following relationship:
 [tex]x / 15 = 5/12 [/tex]
 Clearing x we have:
 [tex]x = (5/12) * (15) x = 6.25[/tex]
 Answer:
 The value of x is given by:
 x = 6.25

If the sum of two numbers is 20 and one of those numbers is three times the other, what is the smaller number?

Answers

x = smaller number
y = bigger number

y = 3x

x+y = 20
x+3x = 20
4x = 20
x = 5

The smaller number is 5.

Explain the process of solving the following equation: 4^x - 2 = 20

Answers

this is an exponential equation:  4^x - 2 = 20.  First thing:  combine the -2 and the 20:  4^x = 22.

Next, take the logarithm (natural or common log) of both sides.  We get:

                                            log 22
x log 4 = log 22.  Then x = -----------  (answer).  You could, of course, evaluate
                                            log 4       this on a suitable calculator.

Hi,

[tex]4^x-2=20\\ \Rightarrow\ 4^x=22\\ \Rightarrow\ x*ln(4)=ln(22)\\ \Rightarrow\ x= \dfrac{ln(22)}{ln(4)}\\\\ \Rightarrow\ \boxed{ x=2,2297158...\approx{2.23}} [/tex]
ln means natural log (neper's log)

Given a possible triangle ABC with a=5, b=11, and A=23 degrees, find a possible value for angle b. Round to the nearest tenth. A. 10.2° B. 11.2° C. 59.3° D. no solution Please select the best answer from the choices provided

Answers

Using the law of the sine, we have the following relationship:
 Sine (A) / a = Sine (B) / b
 Substituting values we have:
 Sine (23) / 5 = Sine (B) / 11
 Clearing we have:
 (Sine (23) / 5) * (11) = Sine (B)
 B = Asine ((Sine (23) / 5) * (11))
 B = 59.27 degrees
 Rounding off we have:
 B = 59.3 degrees
 Answer:
 C. 59.3 °

Huixian needs to pack 171 pens 63 pencils and 27 erasers into identical gift bags so that each item is equally distributed among gift bags.find the largest number of gift bags can be packed

Answers

To find The largest number of gift bags that can be packed, you will need to find the biggest way all three of these numbers can be divided evenly. You can find this answer by finding the greatest common factor.

I will show this by listing the prime factorization's for each number, and then we will look for all the common factors.

171 = 3 x 3 x 19
63 = 3 x 3 x 7
27 = 3 x 3 x 3

All three lists share two 3s. The means that the biggest way they could be divided is into nine bags (3 x 3).

Answer:

The largest number of gift bags that can be packed is:

9

Step-by-step explanation:

To find The largest number of gift bags that can be packed, we need to find the greatest common divisor of these numbers.

Listing the prime factorization's for each number:

171 = 3 x 3 x 19

63 = 3 x 3 x 7

27 = 3 x 3 x 3

As we can clearly see from the prime factorization the greatest common factor of these numbers is 9(3×3)

The largest number of gift bags that can be packed is:

9

Solve the system of equations -4x + 3y = -2 y = x - 1

Answers

You can use the substitution method.
Plug in x-1 to the first equation and solve.
-4x+3(x-1)=-2
-4x+3x-3=-2
-x=1
X=-1
You then plug x into one of the original equations and solve
Y=-1-1
Y=-2
Answer:(-1,-2)

The solution to the system of equations -4x + 3y = -2 and y = x - 1 is x = -1 and y = -2.

What is the solution to the system of equations?

Given the system of equations in the question:

-4x + 3y = -2

y = x - 1

Solve the system of equations by substituting the expression for y from the second equation into the first equation:

-4x + 3y = -2

Plug in y = x - 1:

-4x + 3( x - 1 ) = -2

Simplifying, we get:

-4x + 3x - 3 = -2

Solve for x:

-x = -2 + 3

-x = 1

x = -1

Now, plug x = -1 into equation 2 and solve for y:

y = x - 1

y = -1 - 1

y = -2

Therefore, the solution is x = -1 and y = -2.


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The monthly rent of Marilyn's house went from $500 to $400, if p is the percent decrease in the rent, which proportion can be used to calculate p?

Answers

Answer:

D

Step-by-step explanation:

doing the test right now

the bottle of water contains 32 fluid ounces of water. How many cups of water are in a bottle.

Answers

There are 8 fluid ounces in a cup.

Divide 32 by 8 = 4.

There are 4 cups of water in a bottle.

There are 4 cups of water in a bottle containing 32 fluid ounces.

We have,

The number of cups in a bottle of water depends on the conversion rate from fluid ounces to cups.

1 cup is equivalent to 8 fluid ounces.

To find the number of cups in a bottle containing 32 fluid ounces of water, we can divide the total number of fluid ounces by the conversion rate:

So,

= 32 fluid ounces / 8 fluid ounces per cup

= 4 cups

Therefore,

There are 4 cups of water in a bottle containing 32 fluid ounces.

Learn more about unit conversion here:

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