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velikii [3]
3 years ago
6

2. Evaluate the geometric series given a = -120, r = 0.5 and n = 6

Mathematics
1 answer:
Tju [1.3M]3 years ago
8 0

Here we're discussing the "nth partial sum of a geom series."

                                                       1 - r^n

The formula for that is s(n) = a(1) --------------- 

                                                         1-r

We can subst. the given values and see where that takes us:

                  1 - (-2)^6        1 - 64

105 = a(1)*---------------- = ----------*a(1)  =  -21*a(1)

                    1-(-2)                3

                                              105

Solving this for a(1):  a(1) = --------- = -5    (answer)

                                              -21

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The altitude of the isosceles triangle (upper left vertex to side 4) can be found from the Pythagorean theorem as
.. altitude = √(5^2 -2^2) = √21
So, the area of the isosceles triangle is
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3 years ago
43. Write a system of equations that is equivalent to each of the systems of equations below
olchik [2.2K]

1.

The <u>new system</u> of equivalent equations are 4x + 6y = 8 and 12x + 3y = 1

To get an equivalent equation, we multiply the original equation by a constant and replace it with the new equation.

So, 2x + 3y = 4 (1)

12x + 3y = 1 (2)

We multiply equation (1) by 2

So, 2x + 3y = 4 (1) × 2

⇒4x + 6y = 8 (3)

Replacing (1) by (3), we have

4x + 6y = 8 (3)

12x + 3y = 1 (2)

So, the <u>new system</u> of equivalent equations are 4x + 6y = 8 and 12x + 3y = 1.

2.

The <u>new system</u> of equivalent equations are 3x - 21y = 24 and 5x + 4y = 20

To get an equivalent equation, we multiply the original equation by a constant and replace it with the new equation.

So,

x - 7y = 8  (1)

5x + 4y = 20 (2)

We multiply equation (1) by 3, we have

So, x - 7y = 8 (1) × 3

⇒3x - 21y = 24 (3)

Replacing (1) by (3), we have

3x - 21y = 24 (3)

5x + 4y = 20 (2)

So, the <u>new system</u> of equivalent equations are 3x - 21y = 24 and 5x + 4y = 20.

Learn more about equivalent equations here:

brainly.com/question/2972832

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2 years ago
Which of the following is a composite number? A.87 B.31 C.59 D.41
kicyunya [14]
87 is a composite number because it is divisible by 3, all of the rest of the numbers are prime
8 0
3 years ago
△ABC ≅ △BAD. Points C and D are placed on different sides of line AB. Make a guess about how lines AC and BD relate. Explain.
Hunter-Best [27]

Answer:

See below  

Step-by-step explanation:

It looks like

  • AB⟂CD
  • AB and CD bisect each other.

3 0
3 years ago
Which inequality correctly compares Two-fifths, Six-sevenths, Five-eighths, and 1?
Ronch [10]

Answer:

<u>2/5 < 5/8 < 6/7 < 1 </u>

   <u>OR</u>    

<u>1 > 6/7 > 5/8 > 2/5</u>

Step-by-step explanation:

It is required to compare Two-fifths, Six-sevenths, Five-eighths, and 1

Two-fifths = 2/5

Six-sevenths = 6/7

Five-eighths = 5/8

So, the given numbers are: 2/5, 6/7, 5/8, and 1

We need to make the numbers in order from the least to the greatest or from the greatest to the least

The easy method is convert the rational numbers to decimal numbers

So,

2/5 = 0.4

6/7 ≈ 0.857

5/8 = 0.625

1 = 1

So, the numbers form the least to the greatest are:

0.4 , 0.625 , 0.857 , 1

So,

2/5 , 5/8 , 6/7 , 1

The inequality correctly compares the numbers are:

<u>2/5 < 5/8 < 6/7 < 1</u>

Or can be written from the greatest to the least as:

<u>1 > 6/7 > 5/8 > 2/5 </u>

6 0
3 years ago
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