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Anit [1.1K]
3 years ago
11

In a geometric sequence, a2=2, a3=16, and a4=128.

Mathematics
1 answer:
Oduvanchick [21]3 years ago
4 0

Answer:

an = 1/4(8)^n-1

Step-by-step explanation:

Given the following in a geometric sequence, a2=2, a3=16, and a4=128.

nth term of a sequence = ar^n-1

a is the first term

r is the common ratio

r = a3/a2 = a4/a3

r = 16/2 = 128/16

r = 8

a2 = ar

2 = 8a

a = 2/8

a = 1/4

The nth term by substituting the parameters will be;

an = 1/4(8)^n-1

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1/4 times the sum of a number and −3.2 is 1.8. What is the number?
joja [24]

Answer:

10.4

Step-by-step explanation:

Let the number be x

Sum of  x  and -3.2 : x + (-3.2) = x - 3.2

1/4 times the sum of a number and −3.2 = (1/4) * (x - 3.2)

\dfrac{1}{4}* \left( x - 3.2 \right) = 1.8\\\\\Multiply \ the \ whole \ equation \ by \ 4 \\\\4*\dfrac{1}{4} *(x - 3.2) = 1.8*4\\\\\\x - 3.2 = 7.2\\\\Add \  3.2 \ to \ both \ sides\\\\\\x = 7.2 + 3.2\\

x = 10.4

5 0
3 years ago
URGENT HELPP!!!
Aleonysh [2.5K]
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The dilated triangle will be similar to the original triangle, which means all angles will be the same. 

</span><span>The sides of the two triangles will also be parallel. You can test this by observing the slopes:
Line XY has a slope of 2/3, moving from -4,2 and passing through -1,4.
Line X'Y' has the same slope, moving from (-6,3) to (-3,5)

You can see that this is the case for all corresponding sides' slopes. </span>
3 0
3 years ago
Read 2 more answers
What is the area of the composite figure
lara [203]

Answer:

Area of composite figure = 216 cm²

Hence, option A is correct.

Step-by-step explanation:

The composite figure consists of two figures.

1) Rectangle

2) Right-angled Triangle

We need to determine the area of the composite figure, so we need to find the area of an individual figure.

Determining the area of the rectangle:

Given

Length l = 14 cm

Width w = 12 cm

Using the formula to determine the area of the rectangle:

A = wl

substituting  l = 14 and w = 12

A = (12)(14)

A = 168 cm²

Determining the area of the right-triangle:

Given

Base b = 8 cm

Height h = 12 cm

Using the formula to determine the area of the right-triangle:

A = 1/2 × b × h

A = 1/2 × 8 × 12

A = 4 × 12

A = 48 cm²

Thus, the area of the figure is:

Area of composite figure = Rectangle Area +  Right-triangle Area

                                            = 168 cm² +  48 cm²

                                            = 216 cm²

Therefore,

Area of composite figure = 216 cm²

Hence, option A is correct.

4 0
3 years ago
A bag contains pieces of paper numbered from 5 to 9. A piece of paper is drawn at random. What is the theoretical probability of
NeTakaya

Answer: 3/5 probability of choosing a number LESS THAN 8

8 0
3 years ago
How do you do series with an n
SOVA2 [1]
The problem can be solved step by step, if we know certain basic rules of summation.  Following rules assume summation limits are identical.
\sum{a+b}=\sum{a}+\sum{b}
\sum{kx}=k\sum{x}
\sum_{r=1}^n{1}=n
\sum_{r=1}^n{r}=n(n+1)/2

Armed with the above rules, we can split up the summation into simple terms:
\sum_{r=1}^n{40r-21n+8}=n
=40\sum_{r=1}^n{r}-21n\sum_{r=1}^n{1}+8\sum_{r=1}^n{1}
=40\frac{n(n+1)}{2}-21n^2+8n
=20n(n+1)-21n^2+8n
=28n-n^2

=> (a) f(x)=28n-n^2
=> f'(x)=28-2n 
=> at f'(x)=0 => x=14
Since f''(x)=-2 <0  therefore f(14) is a maximum
(b) f(x) is a maximum when n=14

(c) the maximum value of f(x) is f(14)=196
4 0
3 years ago
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