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:

  10, 12, 14  or  -10, -8, -6

Step-by-step explanation:

We can let x represent the middle integer. Then the smaller one is x-2 and the larger one is x+2. The given relation is ...

  (x-2)(x) = 92 +2(x+2)

  x^2 -2x = 92 +2x +4 . . . eliminate parentheses

  x^2 -4x = 96 . . . . . . . . . subtract 2x

  x^2 -4x +4 = 100 . . . . . . add 4 to complete the square

  (x -2) = ±√100 = ±10 . . . take the square root

  x = 2 ± 10 = -8 or +12 . . . . add 2

The three integers might be ...

  -10, -8, -6  or  10, 12, 14

Answer:

Step-by-step explanation:

x²+y²-2x-10y+1=0

compare with x²+y²+2gx+2fy+c=0

center is (-g,-f)

radius=√(g²+f²-c)

2g=-2

g=-1

2f=-10

f=-5

radius=(1,5)

c=1

let eq. of circle be x²+y²-2x-10y+c=0

∵ it passes through (2,-3)

2²+(-3)²-2(2)-10(-3)+c=0

4+9-4+30+c=0

c=-39

eq. of circle is is x²+y²-2x-10y-39=0

Answer:

the answer is

[tex] {3}^{5} [/tex]

Answer:

Step-by-step explanation:

I am not sure what the first question is asking but yes y does very direction with x.

Lemme know if i can help with anything else

:)

Step-by-step explanation:

40×65=2600

2600/ 52=50

50×80=4000

4000/50=80

Answer:

x < -y + 1

Step-by-step explanation:

Answer: 9 11 19

Step-by-step explanation

9 11 19

Answer:

18 and 8

Step-by-step explanation:

Range= 18-8

Mean=(18+8)/2=13

Answer:

Step-by-step explanation:

Given,

Length of the rectangle = 5m 20cm = 5.2m

Breadth of the rectangle = 3.5m

Therefore,

Perimeter of the rectangle

= 2(Length + Breadth)

= 2(5.2m + 3.5m)

= 2 × 8.7m

= 17.4m

Hence,

Area of the given rectangle is 17.4 sq.m (Ans)

Answer:

C. 9

Step-by-step explanation:

K(3)=3*3=9........................

Answer:

25.13ft

Step-by-step explanation:

The length of the fence will be the circumference.

[tex]C=2*pi*r=2*pi*8/2=8pi=25.13ft[/tex]

Explanation:

There are two hearts out of four cards in this particular hand. The probability of picking a heart card is 2/4 = 1/2

In other words, we have a 50% chance of getting a heart. The prior stuff dealing with the 52 card deck is just extra unneeded info.

Answer:

x=18

Step-by-step explanation:

x - 3 = 15

+3

x=18

Answer:

round to cent 20.59

Step-by-step explanation:

Answers:

Starting inequality: [tex]10(x+0.75) \le 50[/tex]

Ending inequality:  [tex]x \le 4.25[/tex]

==================================================

Work Shown:

x = amount spent per bag, ignoring the bag fee

x+0.75 = amount per bag including bag fee

10(x+0.75) = total amount spent on the ten bags

This amount cannot be more than $50. This means 50 dollars is the highest we can go, aka the ceiling value.

That means we'd write [tex]10(x+0.75) \le 50[/tex] as one possible starting inequality.

Let's solve for x

[tex]10(x+0.75) \le 50\\\\10x+7.5 \le 50\\\\10x \le 50-7.5\\\\10x \le 42.5\\\\x \le 42.5/10\\\\x \le 4.25[/tex]

The most he can spend on the items for any single bag is $4.25, which is ignoring the $0.75 fee

If we tack that fee on, then he spends 4.25+0.75 = 5 dollars per bag and ten of such bags leads to 5*10 = 50 dollars total. The answer is confirmed.

Answer:

2 and 7.3

Step-by-step explanation:

[tex]P=2x+2y=18.6[/tex]

[tex]2x=18.6-2y\\x=9.3-y[/tex]

We'll replace x with (9.3-y)

[tex]A=x\cdot y=14.6\\(9.3-y)\cdot y=14.6\\-y^2+9.3y=14.6\\ \\y^2-9.3+14.6=0[/tex]

Now we solve this equation by sum and product:

[tex]S=9.3\\P=14.6\\y=2\ or \ y=7.3[/tex]

Replacing back in the Perimeter equation:

[tex]2x+2y=18.6[/tex]

if y=7.3

[tex]2x+2\cdot7.3=18.6\\2x+14.6=18.6\\2x=4\\x=2[/tex]

if y=2

[tex]2x+2\cdot2=18.6\\2x+4=18.6\\2x=14.6\\x=7.3[/tex]

So, the dimensions are 2 and 7.3 km

Answer:

The product of two irrational numbers will not be irrational.

Step-by-step explanation:

Answer:

The product of two irrational numbers will not be irrational.

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

-3 xy = -18

-3(2)(3) = -18

Answer:

Diego's result is the same as Noah's result.

Step-by-step explanation:

Noah: 5+5+5+5=20

Diego: (1x5) + (1x5)+(1x5)+(1x5)= 20

Answer:

5,5

Step-by-step explanation:

Answer:

I believe 1000

Step-by-step explanation:

Therefore, the answer is 3/10.

Hoped this helped.

[tex]BrainiacUser1357[/tex]

Answer:

9x + 1 = 7x - 8x + 4

9x + 1 = -x + 4

9x + 1 - 1 = -x + 4 - 1

9x = -x + 3

9x + x = -x + 3 + x

10x = 3

x = 3/10

Answer:

3.025

Step-by-step explanation:

the answer is 3.025 because 1/40 simplified is 0.025 and add the 3 to get 3.025

Answer: 3.0250

Step-by-step explanation: To convert this mixed number (fraction) to a decimal just follow these two steps:

Step 1: divide numerator (1) by the denominator (40): 1 ÷ 40 = 0.025

Step 2: add this value to the the integer part: 3 + 0.025 = 3.025. So,

3 1/40 = 3.025

Answer:

1. 50

2. 130

Step-by-step explanation:

If we number the angle opposite 2 as 3 we know that angle 3 is equal to the 130 already provided.

Therefore, resulting in number 2 being equal to angle 3.

If we know that angle 2 and 3 is 130, we should add the numbers together to get 260.

A circle has a degree of 360, so we minus 260 from the 360.

We would get 100, so we divide it by 2.

Thus, angle 1 would be equivalent to 50.

Hope this makes sense :)

Answer:

Is it The numbers on the ruler?

Step-by-step explanation:

Answer:

10000

Step-by-step explanation:

you have four digits and each one of them can be 0-9, so 10 possibilities for each digit

10×10×10×10= 10,000

Answer:

160

Step-by-step explanation:

I believe the answer is 160 because it is a four-digit passcode, and 10 different numbers can be used ( 10 * 4 = 40, and 40 * 4 = 160).

The accurate line represented by line b because during such experiment ( osmosis or mass transfer) there would be a time where the system be in equilibrium meaning that that the net movement will be zero. In line B at time starting 15 min equilibrium is reached no further movement is attained beyond it.