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gogolik [260]
3 years ago
15

Write a recursive and explicit rule for each geometric sequence, and then find the next 3 terms.

Mathematics
1 answer:
Murljashka [212]3 years ago
6 0
Hello,

1)
a_{0}=2
a_{1}=a_{0}*4=8
a_{2}=a_{1}*4=a_{0}*4^2=32
a_{3}=a_{2}*4=a_{0}*4^3=128
a_{4}=a_{3}*4=a_{0}*4^4=512
a_{5}=a_{4}*4=a_{0}*4^5=2048
...
a_{n+1}=a_{n}*4=a_{0}*4^{n+1}


2)
a_{0}=1024
a_{1}=a_{0}*0.5=512
a_{2}=a_{1}*0.5=a_{0}*0.5^{2}=256
a_{3}=a_{2}*0.5=a_{0}*0.5^{3}=128
a_{4}=a_{3}*0.5=a_{0}*0.5^{4}=64
a_{5}=a_{4}*0.5=a_{0}*0.5^{5}=32
....
a_{n+1}=a_{n}*0.5=a_{0}*0.5^{n+1}

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Write the equation in point-slope form of the line that passes through the given points.
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Answer:

y-6=-1/3(x+6)

Step-by-step explanation:

y-y1=m(x-x1)

m=(y2-y1)/(x2-x1)

m=(3-6)/(3-(-6))

m=-3/(3+6)

m=-3/9

simplify

m=-1/3

y-6=-1/3(x-(-6))

y-6=-1/3(x+6)

4 0
3 years ago
2. what value of b makes the following equation true
Svetradugi [14.3K]

Answer:

  2. 10

  3. D.  1 for all n

Step-by-step explanation:

2. The applicable rules of exponents are ...

  (a^b)(a^c) = a^(b+c)

  a^b = 1/a^-b

__

  \dfrac{4^8}{(4^2)^{-3}}\div 4^4=\dfrac{4^8}{4^{-6}\cdot4^4}=\dfrac{4^8}{4^{-2}}\\\\=4^8\cdot4^2=4^{10}

The value of n is 10.

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3. Using the above rules of exponents, the expression simplifies to ...

  6^(-n+n) = 6^0 = 1

The value is 1 for any n.

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2 years ago
prove that the fast squaring trick for two-digit numbers ending in 5 works. the trick: if you have a 2-digit number that ends in
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The procedure to squaring a two digit number is by multiplying the first number by a integer greater than the number and putting 25 beside it.

Finding the Square of a Value is a simple method. Multiply the specified integer by itself to determine the square number. The square term is always represented as an integer multiplied by two. For example, the square of 5 is 25 multiplied by 5, giving 5×5 = 5² = 25.

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Simply multiply a single-digit number by itself to find its square. Furthermore, by memorizing the tables from 1 to 10.

We taught about two triangles and how to find the point of any base of a triangle given the other two sides using Pythagoras' theorem.

A right triangle has three sides: the hypotenuse, perpendicular, and base. Pythagoras' theorem states that

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5 0
1 year ago
24. Find the slope and y-intercept of the line.<br> Y=7/5x-3
Ad libitum [116K]

Answer:

slope = m = 7/5

y-intercept = b = -3

Step-by-step explanation:

y = mx + b

m = slope

b = y-intercept

y = 7/5 x - 3

slope = m = 7/5

y-intercept = b = -3

4 0
1 year ago
Read 2 more answers
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