the sum of the first n terms of a sequence is 20 - 10 / 2 ^ n - 1 find the sum of the first five terms​

Answer:

Step-by-step explanation:

1,

-10,20,-40,80,...

common ratio=20/-10=-2

it is a geometric sequence.

2.

15,-5,-25,-45

common difference=-5-15=-20

it is an arithmetic sequence.

Answer:

107,100

Step-by-step explanation:

[tex]h(t) = 9 {t}^{2} + 900t \\ \\ plug \: t = 70 \\ \\ h(70) = 9 {(70)}^{2} + 900(70) \\ = 9 \times 4900 + 63000 \\ = 44100 + 63000 \\ = 107,100 \: cm[/tex]

Answer:

Since, the given solution is (2, 14). Therefore, 7x−y=0. Similarly, another equation can be−x+y=−2+14=12. Similarly, another equation can be−2x−y=−2(2)−14=18.

Answer:

-- increase in entropy

-- second law of thermodynamics

Step-by-step explanation:

The 1st law of thermodynamic states that there is conservation of energy, i.e. we cannot create energy and we cannot destroy energy also in an isolated system.

The given example is not a representative of the 1st law.

The [tex]\text{2nd law of thermodynamics}[/tex] states that there is a natural tendency of an isolated system to [tex]\text{degenerate}[/tex] into a more [tex]\text{disordered state.}[/tex] Before dropping the notes and papers were in an isolated ordered system.

After dropping the papers scattered and did not remain in a stack position. It moves into a more disordered state.

Begore dropping down the notes and papers, they were in a stable position, i.e. no kinetic energy is there. No randomness when the notes and the papers were dropped. There is an increase in kinetic energy. There is randomness among the molecules by bombardment. So there is an increase in entropy.

Thus, above illustrations represents :

Answer:

Is it the answer is C?

2+4+3+5+1=15

12 1/2 years

Step-by-step explanation:

Let the unknown be n. Then 40+n = 3(5+n).

Performing the multiplication:

40+n = 15+3n

Isolate n and combine the constant terms:

25=2n, so n= 25/2 years

Answer:

angles Q and Q' are congruent, angles R and R' are congruent

Step-by-step explanation:

For two triangles to be congruent, we need to show is two of the  

1. corresponding angles are congruent,

or,

2. all three pairs of corresponding sides are proportional,  

or,

3. two pairs of corresponding sides are proportional AND the included angles are congruent.  

And, angles are always congruent when a figure is dilated

(satisfies the first criterion that at least two corresponding angles are congruent)

Answer:

-4sin(4x-3)

Step-by-step explanation:

Given y = cos u, u = 4x - 3

dy/dx = dy/du * du/dx

dy/du = -sinu

du/dx = 4

dy/dx = -4sinu

since u = 4x - 3

dy/dx = -4sin(4x-3)

Answer:

D. 160

Step-by-step explanation:

Answer:

you would divide an equation from the multiple and then you would simplify the equation for an answer

Answer:

A. 35 square centimeters

Step-by-step explanation:

The area of a triangle is (b*h)/2.

7 * 10 = 70

70/2 = 35

Step-by-step explanation:

answer what ?

all we can see is a grid of coordinates with a functional graph drawn into it.

and we know this function is called y=h(x).

that is it.

what answer is needed ? there is no question visible.

Answer:

Step-by-step explanation:

I'm assuming you're looking for the age of the mammal hide, since there's no question here, but there's also nothing else to solve for. Remember a few things before we move on. First, if we are not told the initial amount with which we start, we have to assume that it's 100%. Second, remember that natural log and e are inverses of each other so they eliminate each other in application. Now to set up the problem. It looks like this:

[tex]71=100e^{-.0001t}[/tex] and begin by dividing both sides by 100 to get

[tex].71=e^{-.0001t}[/tex] and take the natural log of both sides. The other important thing to remember about the rules for logs and natural logs is that when you take the natural log of something, you are "allowed" to move the exponent down out front, which is why we do this. We cannot currently solve for t when it's stuck up there where it is right now. Taking the natural log allows us to bring that exponent down AND eliminate both the natural log and the e at the same time:

ln(.71) = -.0001t and we divide to solve for t:

[tex]\frac{ln(.71)}{-.0001}=t[/tex] and

[tex]\frac{-.3424903089}{-.0001}=t[/tex] so

t = 3424.9 years, or rounded, 3425 years.

Answer:

D(-3, -1)

Step-by-step explanation:

The given coordinates are;

A(-1, -5), B(5, -2) and (1, 1)

The coordinates and the coordinates of the point D form a trapezium

The parallel sides of the trapezium ABCD = AB and DC

The angle ∠BAD = 90°

The coordinates of the point D = Required

Let (x, y) represent the x and y-coordinates of the point D, by the given information, we get;

The slope of the line DC = The slope of the line AB

The slope of AB = (-2 - (-5))/(5 - (-1)) = 3/6 = 1/2

∴ The slope of CD, m = 1/2

From the point C(1, 1),the equation of the line CD is therefore;

y - 1 = (1/2)·(x - 1)

∴ y = x/2 - (1/2) + 1 = x/2 + 1/2

y = x/2 + 1/2

Given that ∠BAD is 90°, therefore, AD is perpendicular to DC and we have;

The slope of AD = -1/m

∴ The slope of AD = -1/(1/2) = -2

From the point A(-1, -5), the equation of the line AD is therefore;

y - (-5) = -2·(x - (-1))

y = -2·x - 2 - 5 = -2·x - 7

y = -2·x - 7

Equating both (simultaneous) values of y to find the value of x gives;

y = y, therefore;

x/2 + 1/2 = -2·x - 7

x/2 + 2·x = 5·x/2 = -7 - (1/2) = -15/2

∴ 5·x/2 = -15/2

x = (-15/2) × (2/5) = -3

x = -3

From y = -2·x - 7, and x = -3, we get;

y = -2 × (-3) - 7 = 6 - 7 = -1

The coordinates of the point D(x, y) = (-3, -1).

Answer:

A. 5

Step-by-step explanation:

PQ + QR + RS = PS

2x - 6 + 1 + x - 4 = 18

3x - 9 = 18

3x = 27

x = 9

RS = x - 4

RS = 9 - 4

RS = 5

1) 520

2)60

3)2600

4)3760

Answer:

1. 520

2. 60

3. 2600

4. 3760

Step-by-step explanation:

[tex]{hope it helps}}[/tex]

Answer:

The first one: 3x+4=-2x-1

Step-by-step explanation:

3(-1)+4=1

-2(-1)-1=1

Answer:

$40000

Step-by-step explanation:

The nearest thousand dollar is rounding the thousand value from its hundred value, which in this case is 4. Since 4 is less than half of 10, the thousand value must round down to $40000.

Answer:

$40000.00

Step-by-step explanation:

Report this answer if its incorrect ^_^

Answer:

2.39

Step-by-step explanation:

Convert everything to a decimal.  

To do that with a fraction divide the numerator by the denominator.  

185 divided by 100 = 1.85

185/100 = 1.85

To convert a percent to a decimal divide the number by 100.

50 divided by 100 = 0.5

50/100 = 0.5

4 divided by 100 = 0.04

4/100 = 0.04

Now add:

1.85 + 0.5 + 0.04 = 2.39

Answer:

[tex]2(a + 8) \\ if \: a = 7 \\ 2 \times (7 + 8) \\ 2 \times 15 \\ = 30 \\ [/tex]

please mark as brainliest

Answer:

[tex] \frac{1}{4}x[/tex]

Step-by-step explanation:

take the reciprocal of 4 which is 1/4

Step-by-step explanation:

Hey there!

According to the question;

Perimeter of rectangle (p) = 154 m

Let the breadth of rectangle be "X" then length will be 2x+2.

Then;

Perimeter (p) = 2(l+b)

154 = 2((2x+2) + x)

154 = 2(3x+2)

154 = 6x + 4

or, 6x = 154-4

or, X = 150/6

Therefore, X= 25.

Hence;

Length = 2*25+2 = 52 m

Breadth = 25 m

Hope it helps!

We can assume,

Perimeter of rectangle = 154 m

Breadth = x

Length = 2x + 2

Now, perimeter = 2(l+b)

[tex] \sf \to 154= 2((2x+2) + x)[/tex]

[tex] \sf \to 154 = 2(3x+2)[/tex]

[tex] \sf \to 6x = 154-4[/tex]

[tex] \sf \to x = \frac{150}{6} = 25[/tex]

Then,

Breadth = 25 m

Length [tex] \sf = 2x + 2[/tex]

[tex] \sf \to (2 \times 25) + 2[/tex]

[tex] \sf \to 52 \: m[/tex]

Hello,

Answer D

ax-b < -c or ax-b >c

If ax-b >0 then |ax-b| = ax-b ==> ax-b > c

if ax-b <0 then |ax-b|=-(ax-b) > c ==> ax-b <-c

The equivalent compoud inequality is (d) ax - b > c or ax - b < -c

The absolute value expression is given as:

| ax -b | > c

Given that c > 0, then it means that:

| ax -b | > 0

So, we have the following inequalities from | ax -b | > c

Hence, the equivalent compoud inequality is (d) ax - b > c or ax - b < -c

Read more about compoud inequality at:

https://brainly.com/question/24544713

Answer:

p = -1          q = -2

Step-by-step explanation:

3p - 7q = 11      -7q = -3p + 11           q = 3/7p - 11/7

2p - 5(3/7p - 11/7) = 8

2p - 15/7p + 55/7 = 8

-1/7p + 55/7 = 8

-1/7p = 1/7

p = -1

2(-1) - 5q = 8

-2 - 5q = 8

-5q = 10

q = -2

Answer:

C= 15

Step-by-step explanation:

[tex] \frac{9}{5} C + 32 = 59 [/tex]

subtracting 32 from both sides

[tex] \frac{9}{5}C = 59 -32 [/tex]

[tex] \frac{9}{5} C = 27[/tex]

Dividing both sides by 9/ 5

[tex]C = 27 \times \frac{5}{9} [/tex]

[tex]C = 3 \times 5[/tex]

[tex]C = 15[/tex]

Answer:

number line is shown from negative 5 to 0 to positive 5. There are increments of 1 on either side of the number line. All the numbers are labeled on either side of the number line. An arrow pointing from 0 to negative 4 is shown. Above this, another arrow pointing from negative 4 to negative 3 is shown. A vertical bar is shown at the tip of the arrowhead of the top arrow

Answer:

5x^3+15x^2-35x

Step-by-step explanation:

Firstly, you want to combine the "x"s in the (5x*x^2) and the (5x*3x). Once you have that (you will get 5x^3 and 15x^2), you can move onto the last set of parenthesis. We can get 35x from here. Finally, the last step is to add the correct signs. Our final answer will then be 5x^3+15x^2-35x. I hope this helped and please don't hesitate to reach out with more questions!