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LUCKY_DIMON [66]
3 years ago
14

Find the sum is of the geometric series 12+6+3+...

Mathematics
1 answer:
olga55 [171]3 years ago
3 0
S=12+6+3+...\\\\a_1=12;\ a_2=6;\ a_3=3\\\\r=a_2:a_1\\\\r=6:12=\dfrac{1}{2} \ \textless \  1\\\\therefore\ S=\dfrac{a_1}{1-r}\\\\S=12+6+3+...=\dfrac{12}{1-\frac{1}{2}}=\dfrac{12}{\frac{1}{2}}=12\cdot\dfrac{2}{1}=24\\\\Answer:\boxed{12+6+3+...=24}
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4. Castles and Coasters charges $12 to get
Vlad1618 [11]

20+x = 12+2x is the answer and x=8

5 0
3 years ago
Find the x-intercept and the y-intercept without graphing. Write the coordinates of each intercept.
ANEK [815]

Answer:

Point of x-intercept: (2,0).

Point of y-intercept: (0,6).

Step-by-step explanation:

1. Finding the x-intercept.

This point is where the graph of the function touches the x axis. It can be found by substituting the "y" for 0. This is how you do it:

y=-3x+6\\ \\-3x+6=0\\ \\-3x=-6\\\\x=\frac{-6}{-3} \\ \\x=2

Hence, the point of x-intercept: (2,0).

2. Finding the y-intercept.

This point is where the graph of the function touches the y axis. It can be found by substituting the "x" for 0. This is how you do it:

y=-3(0)+6\\ \\y=6

Hence, the point of y-intercept: (0,6).

7 0
1 year ago
Read 2 more answers
Find the missing side length, and enter your answer in the box below. If
Savatey [412]

The missing side length is c = 25 units.

Step-by-step explanation:

Step 1:

The given triangle has a 24 unit long adjacent side and a 7 unit long opposite side.

As we have two sides of the triangle, we can solve for the length of the other side by using Pythagoras' theorem.

The length of the hypotenuse is given as c units.

Step 2:

According to Pythagoras theorem,

c^{2} = 24^{2} + 7^{2} = 576 + 49.

c^{2} = 625, c = 25.

So the missing length, c of the given triangle is 25 units.

8 0
3 years ago
N is a positive integer.Explain why n(n-1) must be an even number.
V125BC [204]

Answer:

n and (n - 1) are consecutive integers.

Step-by-step explanation:

We are given 'n', a positive integer.

This 'n' can either be odd or even.

Case I:

When 'n' is odd

The n - 1 is even.

Note that the product of odd and even is always even. That is the product of n and (n - 1) is even.

Case II:

when 'n' is even

Then n - 1 is odd.

Again, using the similar logic we can say that the product of n and n - 1 should be even because here, 'n - 1' is even and 'n' is odd.

4 0
3 years ago
La media de una población es 683.5g y su desviación estándar 52.1g. Determina la puntuación estándar para el valor 652.1​
Ket [755]

Respuesta:

- 0,60

Explicación paso a paso:

Dado que:

Media poblacional, μ = 683,5

Desviación estándar, σ = 52,1

Puntuación, x = 652,1

La puntuación estandarizada, Z = (x - μ) / σ

Puntuación Z = (652,1 - 683,5) / 52,1

Puntuación Z = - 31,4 / 52,1

Zscore = −0.602687

Puntaje estandarizado = - 0.60

7 0
3 years ago
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