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Andrej [43]
3 years ago
14

The sum of the first 6 terms of a geometric series is 15,624 and the common ratio is 5.

Mathematics
1 answer:
nikitadnepr [17]3 years ago
5 0

Answer:

  4

Step-by-step explanation:

The sum of n terms of a geometric series with first term a1 and common ratio r is given by ...

  Sn = a1·(r^n -1)/(r -1)

for r=5 and n=6, this becomes ...

  15624 = a1·(5^6 -1)/(5 -1) = a1·(15624/4)

Then we have ...

  1 = a1/4 . . . . . divide by 15624

  4 = a1 . . . . . . multiply by 4

The first term of the series is 4.

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What is the sum of all values of m that satisfy 2m (squared) -16m+8=0?
vodomira [7]
<h2>Steps:</h2>

So for this, we will be completing the square to solve for m. Firstly, subtract 8 on both sides:

2m^2-16m=-8

Next, divide both sides by 2:

m^2-8m=-4

Next, we want to make the left side of the equation a perfect square. To find the constant of this perfect square, divide the m coefficient by 2, then square the quotient. In this case:

-8 ÷ 2 = -4, (-4)² = 16

Add 16 to both sides of the equation:

m^2-8m+16=12

Next, factor the left side:

(m-4)^2=12

Next, square root both sides of the equation:

m-4=\pm \sqrt{12}

Next, add 4 to both sides of the equation:

m=4\pm \sqrt{12}

Now, while this is your answer, you can further simplify the radical using the product rule of radicals:

  • Product rule of radicals: √ab = √a × √b

√12 = √4 × √3 = 2√3.

m=4\pm 2\sqrt{3}

<h2>Answer:</h2>

In exact form, your answer is m=4\pm \sqrt{12}\ \textsf{OR}\ m=4\pm 2\sqrt{3}

In approximate form, your answers are (rounded to the hundreths) m=7.46, 0.54

6 0
3 years ago
Can someone help<br><br> Write an equivalent expression for<br> 63.62.65.6.
Otrada [13]

When multiplying the same number raised to different powers add the powers together.

3 + 2 + 5 = 10

Because you are also multiplying a value without a power you need to add 1 to the sum of the powers:

10 + 1 = 11

Answer: 6^11

5 0
3 years ago
What is the slope of the line passing through (-5,2) and (1,8)
nikdorinn [45]

Answer:

go to slope calclculator

Step-by-step explanation:

6 0
3 years ago
At the season finale, you present the winner of Canadian Superstar with a recording-and-tour contract. The contract states that
Zina [86]

Answer:

Kindly check explanation

Step-by-step explanation:

Given that:

Winner is paid :

Monthly pay while on tour = $5000

Pay per CD sold =. $2

A) Equation which relates total earning in terms of number of months 'm' while on tour and the number 'n' of CD's sold.

(Monthly pay * number of months) + (pay per CD * number of CD's)

Earning = 5000m + 2n

B) How much will the winner earn after the first month if 500 CDs are sold?

m = 1, n = 500

5000(1) + 2(500) = $6000

C) Suppose after the third month on tour the new recording artist has earned a total of $74 000. How many GDs were sold?

m = 3

74000 = 5000(3) + 2n

74000 = 15000 + 2n

74000 - 15000 = 2n

59000 = 2n

n = 59000 / 2

n = 29500 CD's

D) In Canada, a record album or CD achieves gold status once it seLls 50 000 units. How much will the artist make if the CD goes gold after 6 months of touring?

n = Gold = 50000 ; m = 6

5000(6) + 2(50000)

30000 + 100000 = 130,000

3 0
3 years ago
Polygon ABCD is translated to create polygon A'B'C'D'. Point A is located at (1,5), and point A' is located at (-2,1). What is t
Keith_Richards [23]

Answer:

5

Step-by-step explanation:

Distance from B to B' is equal to the distance from A to A', AA'=5 so BB'=5

6 0
4 years ago
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