Hello, would be very nice if someone could help me ! :)

A finite geometric series is the sum of a sequence of numbers. Take the sequence
1, 2, 4, 8, ..., for example. Notice that each number is twice the value of the
previous number. So, a number in the sequence can be represented by the
function f(n) = 2^n-1. One way to write the sum of the sequence through the 5th
number in the sequence is ∑^5 n-1 2^n-1.
This equation can also be written as S5 = 2^0+2^1+ 2^2+ 2^3+ 2^4. If we multiply this equation by 2. the equation becomes 2(S5) = 2^1+ 2^2+ 2^3+ 2^4+ 2^5

What happens if you subtract the two equations and solve for S5? Can you use this information to come up with a way to find any geometric series Sn in the
form ∑^a n-1 b^n-1 ?

Answer:

Step-by-step explanation:

y = -1(x + 2)(x - 3)(x - 3)(x + 0)(x + 0)(x + 1)(x + 1)(x + 1)

The 8 degree polynomial for the given roots can be written as  p(x) =  x⁸ - x⁷- 12x⁶ - 4x⁵ + 30x⁴ + 51x³ + 18x².

The factor theorem states that for a polynomial p(x) if there exists a real number a such that p(a) = 0, then (x - a) is one of the factors of p(x).

The roots of the polynomial are given as follows,

Number of roots at -2 = 1

Number of roots at 3 = 2

Number of roots at 0 = 2

And, number of roots at -1 = 3.

Now, the polynomial can be written using factor theorem as,

p(x) = x²(x + 2)(x - 3)²(x + 1)³

      = x²(x + 2)(x²- 6x + 9)(x³ + 3x² + 3x + 1)

      = x⁸ - x⁷- 12x⁶ - 4x⁵ + 30x⁴ + 51x³ + 18x²

Hence, the polynomial for given roots can be written as p(x) =  x⁸ - x⁷- 12x⁶ - 4x⁵ + 30x⁴ + 51x³ + 18x².

To know more about factor theorem click on,

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[tex]\\\\\\x^2 -8x +16 = 0\\\\\implies x^2 - 2(4) + 4^2 =0\\\\\implies (x-4)^2 =0\\\\\implies x -4 =0\\\\\implies x =4\\\\\text{This equation has only one solution.}[/tex]

Answer:

Image below!

Step-by-step explanation:

Plotting [tex]\underline{y=2x+3}[/tex]

Step 1: determine the y-intercept

[tex](0,3)[/tex]

Step 2: Move 2 units up, and 1 unit left (keep repeating this process until you have reached the limit of the graph)

Step 3: Go to the other side of the graph of the first point (y-intercept)

When you've completed this process, it should look like this:

Answer:

20 inches

Step-by-step explanation:

Use the Pythagorean Theorem.

[tex]a^2 + b^2 = c^2\\15^2 + b^2 = 25^2\\225 + b^2 = 625\\b^2 = 400\\b = \sqrt{400} \\b = 20[/tex]

Answer:

a. 6

b. 21

c. 78

d. 13.5

e. 14

f. 24

Hope that helps!

Answer:

0.4 or 2

Step-by-step explanati

that easy

Answer:

y=7

Step-by-step explanation:

Standard form = ax+by+c=0

= Writing the given eq. in standard form =

= y+7=-3x-3

= 3x+y+7+3=0

= 3x+y+10=0

Answer:

Explained below :)

(I tried my best, sorry if it doesn't make sense.)

Step-by-step explanation:

Example: 1/4 - 1/8= ?

1: Find the common denominator (bottom number)

2: If the common denominator is 8 then you multiply 1/4 by 2/2 to get the denominator of 8. If you needed then you can multiply the other fraction to get the same denominator.

3: Once you get multiply that then you get 2/8 -1/8.

4: Subtract the numerator (top number) 1

5: Keep the numerator (8)

6: Your answer would be 1/8

Answer:

b = 14

Step-by-step explanation:

Since both angles are diagonal each other, they are equal to each other.

5b = b + 56

-b      -b           (subtract b from both sides)

4b = 56

4       4            (divide both sides by 4 to solve for b)

 b = 14

Answer:

  82/63

Step-by-step explanation:

The sum can be found using the formula ...

  [tex]\dfrac{a}{b}+\dfrac{c}{d} =\dfrac{ad+bc}{bd}[/tex]

For the given fractions, the sum is ...

  [tex]\dfrac{6}{7}+\dfrac{4}{9} =\dfrac{6\cdot9+7\cdot4}{7\cdot9}=\dfrac{54+28}{63}=\boxed{\dfrac{82}{63}}[/tex]

_____

Additional comment

When the denominators have no common factor, the least common denominator is their product, as here.

Answer:

For this question, you can make the denominators the same to get the answer.

LCM of 7 and 9 = 63

[tex]\frac{6}{7} + \frac{4}{9} = \frac{54}{63} + \frac{28}{63} \\[/tex]

         = [tex]\frac{82}{63}[/tex]

         = 1[tex]\frac{19}{63}[/tex]

Answer:

[tex]2\sqrt[3]{5}[/tex]

Step-by-step explanation:

40 = 8 x 5 and 8 is the cube of 2, so 2 goes on the outside but 5 can't be simplified

Answer:

148302

Step-by-step explanation:

Answer:

148302

Step-by-step explanation:

Because that's the answer

Answer:

y=5/4x-5

Step-by-step explanation:

y-y1=m(x-x1)

y-0=5/4(x-4)

y=5/4(x-4)

y=5/4x-20/4

y=5/4x-5

Step-by-step explanation:

Volume=length*width*height

V = (3/2)*(4)*(1/2)

= 12/4 = 3cm^3

Answer:

Percent change in the price of gas is [tex]9.85\%[/tex]

Step-by-step explanation:

Percentage change equals the change in value divided by the absolute value of the original value, multiplied by  .

[tex]\text { Percentage Change }=\frac{\Delta V}{\left|V_{1}\right|} \times 100[/tex]

Here

[tex]\Delta V=2.26-2.03\\\\=0.23\$/gallon[/tex]

[tex]V_{1}=2.03\$/gallon[/tex]

The percent change in the price of gas

[tex]=\frac{0.23}{2.03} \times100\\\\=9.85\%[/tex]

Percent change in the price of gas is [tex]9.85\%[/tex]

Answer:

LQ = 54

Median = 69

UQ = 94

Step-by-step explanation:

This list is already sorted for you, so you don't need to worry about that, otherwise you would need to sort the numbers in ascending order. To find the median, we do [tex]\frac{n+1}{2}[/tex], where n is the amount of numbers. This gives us 4, so the median is at position 4, so the median is 69. The lower quartile is simply [tex]\frac{n+1}{4}[/tex], so 2, so the lower quartile is 54. The upper quartile is [tex]\frac{n+1}{2} X 3[/tex], so 6, so the upper quartile is 94.

Answer:

B. (0,-1)

Step-by-step explanation:

see.. i'm not rude.... :/

Answer: the answer is b=9

Step-by-step explanation:

Step 1: Subtract 32 from both sides.

104-32= 72

Step 2: Divide both sides by 8.

72 divided by 8 is 9

therefor the answer is 9

Answer:

using the pithagerum therom

a² + b² = c²

this formula is to find the side of your triangle with 2 sides already known

the answer is A) 17.7

Answer:

center = (5 ,-3) and radius = 5

Step-by-step explanation:

Answer:

Answer B- 1034

7% annual rate is 70. divide by 52 (total amount of weeks in a year) =1.35. 1.35 × 25=33.75 rounded up 34. 1000+34=1034

Answer:

The slope is 1/2

Step-by-step explanation:

To find slope, use the formula y2-y1/x2-x1

Plug the points in and solve.

9-6/(-3)-(-9)

3/-3+9

3/6

1/2

Answer:

[tex]m=\frac{1}{2}[/tex]

Step-by-step explanation:

Formula:

[tex]\boxed{\frac{y_2-y_1}{x_2-x_1}}[/tex]

Assign the points as [tex]x_1[/tex], [tex]x_2[/tex], and, [tex]y_1[/tex], [tex]y_2[/tex]

[tex](-9 = x_1, 6=y_1) \:\:\:\:(-3=x_2, 9=y_2)[/tex]

Plug these points into the formula; solve

[tex]\frac{y_2-y_1}{x_2-x_1}\\\\=\frac{9-6}{-3-(-9)}\\=\frac{1}{2}[/tex]

[tex]\bold{m=\frac{1}{2}}[/tex]

Therefore, [tex]\frac{1}{2}[/tex] is the slope of the line through [tex](-9, 6)[/tex] and [tex](-3, 9)[/tex].

Answer:

9x = 72; x = 8 times as many stamps

Step-by-step explanation:

Answer:

9×=72;×=8 times as many stamps

The potential gain that could have come with golfing

Step-by-step explanation:

Opportunity cost is the loss of something you could have gotten from the choice you didn't go with. so I'm this case, the opportunity cost of chosing the movies is what you missed out on by not going golfing.

Answer:

y = 35 degrees

Step-by-step explanation:

y + 55 = 90

(subtract 55 from both sides)

y = 35