mathematics of inequality

The first five terms of a geometric sequence are 5, 10, 20, 40, 80.

A geometric sequence is also known as Geometric Progression (GP) is a non-zero numerical series whereby each term succeeding the very first is determined by multiplying the preceding one by a fixed, non-zero value designated as the common ratio.  

It can be expressed by using the formula:

[tex]\mathbf{a_n = ar^{n-1}}[/tex]

where;

Given that;

∴

The second term of the sequence is:

[tex]\mathbf{a_2 = 5 \times 2^{2-1}}[/tex]

[tex]\mathbf{a_2 = 5 \times 2^{1}}[/tex]

[tex]\mathbf{a_2 = 10}[/tex]

The third term of the sequence is:

[tex]\mathbf{a_3 = 5 \times 2^{3-1}}[/tex]

[tex]\mathbf{a_3 = 5 \times 2^{2}}[/tex]

[tex]\mathbf{a_2 = 20}[/tex]

The fourth term of the sequence is:

[tex]\mathbf{a_4 = 5 \times 2^{4-1}}[/tex]

[tex]\mathbf{a_3 = 5 \times 2^{3}}[/tex]

[tex]\mathbf{a_4 = 40}[/tex]

The fifth term of the sequence is:

[tex]\mathbf{a_5 = 5 \times 2^{5-1}}[/tex]

[tex]\mathbf{a_3 = 5 \times 2^{4}}[/tex]

[tex]\mathbf{a_4 = 80}[/tex]

Learn more about the Geometric sequence here:

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Answer:

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Step-by-step explanation:

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9514 1404 393

Answer:

  -13 < x ≤ 4

Step-by-step explanation:

The round bracket means the lower limit is not included in the interval. The square bracket means the upper limit is included.

  -13 < x ≤ 4

Answer:

13

Step-by-step explanation:

❤️❤️❤️❤️❤️

Answer:

i think its A i may be wrong

The answers are :

a) The derivative of this function at the point (3,256) is -96.

b) The speed at which the supply bundle is falling is negative.

What is derivative ?

Derivative is the slope of the graph of function or the slope of the tangent line at a point.

A function is given which is h(t) = 400 - 16t².

Here , h(t) gives the height of the supply bundle in feet , t seconds after it is dropped from a height of 400 feet.

a)

We have to find out the derivative of the given function at a point (3,256).

h'(t) = [tex]\frac{d}{dt}[/tex] (400 - 16t²)

h'(t) = 0 - 2 × 16 × t

h'(t) = -32 t

This function at (3,256) so , value of t is 3.

h'(t) = -32 × 3

h'(t) = -96

b)

Speed = -32 t

So , the speed at which the supply bundle is falling is negative. With increase in value of t it will keep decreasing.

Therefore , the answers are :

a) The derivative of this function at the point (3,256) is -96.

b) The speed at which the supply bundle is falling is negative.

Learn more about derivative here :

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#SPJ2

Answer:

that's false

Step-by-step explanation:

3.2 is like 3x2 which equals 6

Hope this helps sorry if i'm wrong loll

Answer: 30

Step-by-step explanation: You should be correct because 1.5*20=30

Answer:

31/35x^7

Step-by-step explanation:

3/5x^4 +2/7x^3

you find the lcm of the denominators

21/35x^7 + ,10/35x^7 =31/35x^7

Answer:

The area is 1,015,968

Step-by-step explanation:

Answer:

1,015,968 (otherwise known as a ridiculously large bedroom lol)

Step-by-step explanation:

912 x 1114 = 1,015,968

Do it on any calculator and it will give you the same thing

I don't know if this was a typo because again that is a ridiculously large bedroom so if it is lemme know and I'll edit my answer

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The Correct choice is A :

Answer:

A, because ∆ QRS isn't a right angled triangle unlike the other choices and its height is in the middle,the rest of the choices are right angled and the line segments in the choice are all their hypotenuse,and the hypotenuse of a triangle isn't it's height

Answer:

2

Step-by-step explanation:

I believe it is 2 sorry if you get it wrong.

Answer:

2 are linear

Step-by-step explanation:

They create a straight line when a line is drawn through the points

Answer:

45degres

Step-by-step explanation:

Answer:

55+45+X=180

X=180-100

X=80

Step-by-step explanation:

Add

Inverse the sum of 55 and 45

Then subtract

Answer:

41

Step-by-step explanation:

Since it is only being reflected, the letters would match up with their primes and still equal the same amount for the sides. Since B'C' is 41, it would mean that BC is 41 too

i used polynomial division.. i hope this helps :)

Answer:

Step-by-step explanation:

Answer:45

Step-by-step explanation:

3 3/4 x 12 bc a dozen=12 u would get 45

Answer:

64

Step-by-step explanation:

40x1.6

Answer:

SA = 29.75 cm^2

inequality form: x>3

interval form: (3,infinity)

Step-by-step explanation:

Answer:

x>3

Step-by-step explanation:

Answer:

First Game: 65 points

Second Game : 65 points

Third Game : 59 points

Step-by-step explanation:

Average = sum of values/number of values

The number of values = 3, an d average = 63

63 = x/3

63 * 3 = x

189 = x

Now 189 is the sum of points over two games.

Their first two games are worth the same, so lets call that s +s = 2s

Their 3rd game is worth 6 less points than s, so s-6

let's add up all the terms:

2s + (s - 6) = 3s - 6

Solve:

3s - 6 = 189

3s = 195

s = 65

The first two games are worth 65, and the third game is worth 65 - 6 = 59.

-Chetan K

Answer:65, 65 and 59

Step-by-step explanation:

If represented by x and y, (2x+y)/3=63

So 2x+y=189

So if x=y+6

Put the value of x into the equation

2x + y = 189

2(y + 6) + y = 189

2y + 12 + y = 189

3y = 189 - 12

3y = 177

y = 177/3

y = 59

Therefore, x = y + 6 = 59 + 6 = 65

Answer:

w= -4

Step-by-step explanation:

Distribute to get 4w+12-7w=24

then combine like terms

-3w+12=24

isolate the variable (minus 12)

-3w=12

w= -4

Step-by-step explanation:

0 and 1. is better according to me

Answer:

[tex]x = 56.02 \degree[/tex]

Step-by-step explanation:

To find the angle you have to use sin rule

[tex] \sin( \theta) = \frac{opposite}{hypotenuse} [/tex]

Let the unknown angle be x

[tex] \sin(x) = \frac{o}{h} \\ \sin(x) = \frac{34}{41} \\ \sin(x) = 0.8292 \\ x = \sin ^{ - 1} 0.8292 \\ x = 56.02 \degree[/tex]

Hope this helps you

Let me know if you have any other questions :-):-)

Answer:

no, you're just simplifying the fraction.

Step-by-step explanation:

4/6=2/3

Q: (2a-b) * (a-2b)

[tex](2−)(−2)[/tex]

[tex]2(−2)+(−2)(−)[/tex]

[tex]22−4+(−2)(−)[/tex]

[tex]22−4−(−2)⋅[/tex]

[tex]22−4+22−⋅[/tex]

Q: (4x - 2) * (x -4)

[tex](4−2)(−4)[/tex]

[tex]4(−4)−2(−4)[/tex]

[tex]42−16−2(−4)[/tex]

[tex]42−16−2+8[/tex]

[tex]42−16−2+8[/tex]

[tex]42−18+8[/tex]

[tex]42−18+8[/tex]

Hope its help you !!

Answer:

4xy+10y²=2y(2x+5y)

Hope it helps!!!

Answer:

Answer is 10% of 30 = 3

five hundred twenty-one billion