what is the change in each term of the sequence? 1,4,13,40,121,....​

Answer:

121

Step-by-step explanation:

2^3x - 4 = (2^x )^3 - 4 = 125 - 4 = 121

[tex]\implies\tt 2^x = 5 [/tex]

[tex]\implies\tt \Big( 2^x \Big)^3 - 4 [/tex]

[tex]\implies\tt 125 - 4 [/tex]

[tex]\huge\implies\tt 121 [/tex]

Answer:

x(5)/(6)y(1)/(2)

Step-by-step explanation:

Hoped I helped

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Answer:

The reciprocal of n must be less than 10.

Step-by-step explanation:

It can be inferred from the question given that n is not a negative number.

But,

[tex](n)^{2}[/tex] < [tex]\frac{1}{100}[/tex]

Find the square root of both sides,

n < [tex]\sqrt{\frac{1}{100} }[/tex]

⇒ n < [tex]\frac{1}{10}[/tex]

n < 0.1

The reciprocal of n can be estimated as;

[tex](n)^{-1}[/tex] < [tex](\frac{1}{10}) ^{-1}[/tex]

[tex]\frac{1}{n}[/tex] < 10

The reciprocal of n is less than 10.

Answer:

$91.00

Step-by-step explanation:

From the above question, we obtained the following information.

James charges:

1 compact car = $7.00

1 mid sized car = $10.00

1 SUV = $15.00

On Saturday, he washed:

a) 3 compact cars

1 compact car = $7.00

3 compact cars = ?

= $7.00 × 3

= $21.00

b) 4 mid-sized cars

1 mid- sized car = $10.00

4 mid-sized cars = ?

= $10.00 × 4

= $40.00

c) 2 SUVs.

1 SUV = $15.00

2 SUVs = ?

= $15.00 × 2

= $30.00

How much money did he earn?

$21.00 + $40.00 + $30.00

= $91.00

Therefore, James earned $91.00

Answer:

18

Step-by-step explanation:

1/3 of 27 is 9 so 2/3 is 18

Answer:

6

Step-by-step explanation:

12/2=6/1=6

Answer:

6

Step-by-step explanation:

Answer:

im not sure how the data should be interpreted but here is the distribution. It goes up by .416

Step-by-step explanation:

the average of the first 8 games is 24

the average of the 12 games is 24.416

The mean of the data of the given basketball player will increase if she scored 24, 22, 27, and 28 points in her next four games.

A mean is an arithmetic average of a set of observations. it is given by the formula,

Mean = (Sum of observations)/Number of observations

Given that the number of points scored by a basketball player in the first eight games is 15, 35, 18, 30, 25, 21, 32, and 16. Therefore, the mean of the first 8 games is,

Mean = (15 + 35 + 18 +30 + 25 + 21 + 32 + 16)/8

          = 176/8

          = 22

Now, the player scored 24, 22, 27, and 28 points in her next four games. Therefore, the mean will be,

New Mean = (15 + 35 + 18 +30 + 25 + 21 + 32 + 16 + 24 + 22 + 27 + 28)/12

                  = 277 / 12

                  = 23.0833

Hence, the mean of the data of the given basketball player will increase if she scored 24, 22, 27, and 28 points in her next four games.

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Answer:

D

Step-by-step explanation:

So we have the equation:

[tex]ax+by+c=0[/tex]

First, let's convert this to slope-intercept form.

Subtract ax from both sides:

[tex]by+c=-ax[/tex]

Subtract c from both sides:

[tex]by=-ax-c[/tex]

Divide everything by b:

[tex]y=-\frac{a}{b}x-\frac{c}{b}[/tex]

We are told that a>0, b<0, and c>0.

In other words, a is positive, b is negative, and c is positive.

The slope of the equation is -a/b.

Since a is positive and b is negative, we will have:

-(+)/(-).

The negatives will cancel out. Therefore, our slope will be positive.

Since our slope is positive, our line must be upwards sloping. Eliminate answers A and C.

Also, our y-intercept is:

-c/b.

c is positive and b is negative. Thus, similarly:

-(+)/(-).

Again, the negatives cancel. This means that the y-intercept must be positive.

Out of B and D, the graph that has a positive y-intercept is D.

D is our answer :)

Answer:

See below.

Step-by-step explanation:

1)

For Ben's social media post, we are told that it was initially shared to only 2 people. However, each of those shares it with 3 people. In other words, Ben's post triples every day. This means that the rate of growth is 3. Thus, Ben's post as an exponential function is:

[tex]f(x)=2(3)^x[/tex]

The 2 represents the initial amount at day 0, and the 3 represents the rate at which the post grows each day.

2)

Similarly, Carter's post was originally sent to 10 people. However, each of the 10 shares it with two others. Therefore, it doubles each day. Thus, the rate is 2. So, Carter's exponential function is:

[tex]f(x)=10(2)^x[/tex]

The 10 represents the initial amount while the 2 represents the rate.

3)

I've use Desmos to graph the functions. Refer to the picture attached. Red is Amber, blue is Ben, and green is Carter.

4)

To find out the number of shares each student's post will receive on day 3 and day 10, simply plug the numbers into the functions. Therefore:

For Amber:

Day 3:

[tex]f(3)=3(4)^3=192[/tex]

Day 10:

[tex]f(10)=3(4)^{10}=3,145,728[/tex]

For Ben:

Day 3:

[tex]f(3)=2(3)^3=54[/tex]

Day 10:

[tex]f(10)=2(3)^{10}=118,098[/tex]

And for Carter:

Day 3:

[tex]f(3)=10(2)^3=80[/tex]

Day 10:

[tex]f(10)=10(2)^{10}=10,240[/tex]

5)

Amber's new graph of:

[tex]f(x)=3(4)^x+45[/tex]

will be a shifted version of her original graph. The new graph will be shifted upwards by 45 units. However, since the 45 is not affected by the x in any way, the change will be minuscule. For instance, her number of shares on day 10 of the old graph is 3,145,728. Even with the additional 45, it will just be: 3,145,773. With enough days, the additional number becomes trivial.

6)

On the 10th day, Amber's post was shared almost 3 million times, while Ben's was shared "only" 118,098 times and Carter's with 10,240. Undoubtedly, Amber's post was the fastest.

7)

If you want to most shares as possible, choose Amber with fewer friends initially but more shares. This is because the exponential potential of a number even just a bit higher is insane. For instance, 3^10 (Ben's rate at 10th day) is only 59,049 while Amber's rate will be 4^10 which is 1,048,576. Amber's number is almost 18 times higher than Ben's. Even if Ben's initial number was say 1,000 or even 1,000,000, Amber would catch up rather quickly. Therefore, the rate is the quintessential part of an exponential growth function.

Answer:

Here is the slope:

[tex]y = zy + dsince m = 0c = 9[/tex]

Hope this helps

Answer:

14 adults and 5 children

Step-by-step explanation:

Set up a system of equations, where a is the number of adults and c is the number of children:

2.5a + c = 40

a + c = 19

Multiply the bottom equation by -1 to solve by elimination:

2.5a + c = 40

-a - c = -19

1.5a = 21

a = 14

Now, plug in 14 as a  to find the number of children:

a + c = 19

14 + c = 19

c = 5

So, 14 adults and 5 children attended

Answer:

15

Step-by-step explanation:

5bc = 5(-3)(-1) = -15(-1) = 15

Answer:

a) The standard form of the equation

[tex]y=\frac{16}{x^{2} }[/tex]

Step-by-step explanation:

Explanation:-

    A parabola is the set of all points in a plane that are equidistant from a fixed line and a fixed point (not in a line) in the plane

• The Fixed line is called the directrix of the parabola.

• The Fixed point is called the focus of the parabola.

• A line through the focus and perpendicular to the directrix is called the axis of the parabola.

• The point of intersection of parabola with the axis is called the vertex of the parabola.

Given Focus of the parabola S(0,a)= (0,4)

Given Focus is lies on y-axis and the directrix is parallel to x-axis

Given directrix of the parabola y = -4

Directrix     y = -a

Standard form of the parabola

                                x² = 4ay

                               x² = 4(4)y

                              x² = 16y

                              [tex]y=\frac{16}{x^{2} }[/tex]

Answer:  see proof below

Step-by-step explanation:

Use the Sum & Difference Identity: tan (A - B) = (tanA - tanB)/(1 + tanA tanB)

Use the Half-Angle Identity: tan (A/2) = (1 - cosA)/(sinA)

Use the Unit Circle to evaluate tan (π/4) = 1

Use Pythagorean Identity:     cos²A + sin²A = 1

Proof LHS → RHS

[tex]\text{Given:}\qquad \qquad \qquad\dfrac{2\tan\bigg(\dfrac{\pi}{4}-\dfrac{A}{2}\bigg)}{1+\tan^2\bigg(\dfrac{\pi}{4}-\dfrac{A}{2}\bigg)}[/tex]

[tex]\text{Difference Identity:}\qquad \dfrac{2 \bigg( \frac{\tan\frac{\pi}{4}-\tan\frac{A}{2}}{1+\tan\frac{\pi}{4}\cdot \tan\frac{A}{2}}\bigg)}{1+ \bigg( \frac{\tan\frac{\pi}{4}-\tan\frac{A}{2}}{1+\tan\frac{\pi}{4}\cdot \tan\frac{A}{2}}\bigg)^2}[/tex]

[tex]\text{Substitute:}\qquad \qquad \dfrac{2 \bigg( \frac{1-\tan\frac{A}{2}}{1+\tan\frac{A}{2}}\bigg)}{1+ \bigg( \frac{1-\tan\frac{A}{2}}{1+\tan\frac{A}{2}}\bigg)^2}[/tex]

[tex]\text{Simplify:}\qquad \qquad \qquad \dfrac{1-\tan^2\frac{A}{2}}{1+\tan^2\frac{A}{2}}[/tex]

[tex]\text{Half-Angle Identity:}\qquad \quad \dfrac{1-(\frac{1-\cos A}{\sin A})^2}{1+(\frac{1-\cos A}{\sin A})^2}[/tex]

[tex]\text{Simplify:}\qquad \qquad \dfrac{\sin^2 A-1+2\cos A-\cos^2 A}{\sin^2 A+1-2\cos A+\cos^2 A}[/tex]

[tex]\text{Pythagorean Identity:}\qquad \qquad \dfrac{1-\cos^2 A-1+2\cos A}{2-2\cos A}[/tex]

[tex]\text{Simplify:}\qquad \qquad \qquad \dfrac{2\cos A-2\cos^2 A}{2(1-\cos A)}\\\\.\qquad \qquad \qquad \qquad =\dfrac{2\cos A(1-\cos A)}{2(1-\cos A)}[/tex]

                               =  cos A

LHS = RHS:  cos A = cos A   [tex]\checkmark[/tex]

Answer:

x = - 2

Step-by-step explanation:

[tex]5x + 4 = 8x + 10 \\ 5x - 8x = 10 - 4 \\ - 3x = 6 \\ x = \frac{6}{ - 3} \\ x = - 2[/tex]

The solution of the equation 8x + 10 = 5x + 4 will be negative 2.

The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.

A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.

The linear equation is given below.

8x + 10 = 5x + 4

Simplify the equation, then we have

8x - 5x = 4 - 10

3x = - 6

x = - 6 / 3

x = - 2

The solution of the equation 8x + 10 = 5x + 4 will be negative 2.

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Answer:

the answer is /36

Step-by-step explanation:

3 goes into 36

4 goes into 36

9 goes into 36

Answer:

Below

Step-by-step explanation:

● x-20 = y+20 (1)

● 2(y-22) = x+22 (2)

This is a system of simulataneous equations

Let's simplify the expressions first

● x -20 = y + 20 (1)

Add 20 to both sides

● x -20 + 20 = y+20 +20

● x = y + 40 (1)

● 2(y-22) = x+22 (2)

● 2y - 44 = x +22

Substrat 22 from both sides

● 2y-44-22 = x+22-22

● 2y -66 = x (2)

This is the new system:

● x = y+40 (1)

● x = 2y-66 (2)

Substract (2) from (1)

● x-x = y+40-(2y-66)

● y+40-2y+66 = 0

● -y +106 = 0

● y = 106

Replace y with 106 in (1)

● x = y +40

● x = 106+40

● x = 146

So the solutions are (146,106)

Answer:

18 square units.

Step-by-step explanation:

Area of the triangle = ½*AB*CD

First of all, find the length of AB and CD using the distance formula, [tex] d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]

[tex] AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]

A(-6, 2) => (x1, y1)

B(3, 2) => (x2, y2)

[tex] AB = \sqrt{(3 -(-6))^2 + (2 - 2)^2} [/tex]

[tex] AB = \sqrt{(9)^2 + (0)^2} = \sqrt{81} = 9 [/tex]

[tex] CD = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]

C(-2, 6) => (x1, y1)

D(-2, 2) => (x2, y2)

[tex] CD = \sqrt{(-2 -(-2))^2 + (2 - 6)^2} [/tex]

[tex] CD = \sqrt{(0)^2 + (-4)^2} = \sqrt{16} = 4 [/tex]

AB = 9

CD = 4

Area of rectangle = ½*AB*CD = ½*9*4 = 9*2 = 18 square units.

Answer:

18

Step-by-step explanation:

Answer:

Hello!!!!

The answer is y-6=3/2(x+6)

Step-by-step explanation:

point slope form is y-y1=m(x-x1)

-6 is x1 and 6 is y1

m=3/2

then plug in these values

hope this helps!!!!

Answer:

y-6=3/2(x--6)

Step-by-step explanation:

I am the best at the maths thing

Answer:

17.3825

Step-by-step explanation:

First I figured out the area of the square which is 18×18=324

Then I found out the are of the circle which is 254.47, so 324 - 254.47 = 69.53

Then there are 4 times the shaded are so divided by 4, so 69.53  ÷ 4 = 17.3825

PLEASE GIVE BRAINLIEST!

Answer:

shaded area = 17.38 cm²

Step-by-step explanation:

given:

diameter of circle = 18 cm and = side of square

π = 3.142

shaded area = ( Area of square - Area of circle ) x 1 / 4

Area of square = s² = 18² = 324 ²cm

Area of circle = π d² / 4

                       = 3.142 (18²) / 4

                       = 254.5 cm²

therefore, shaded area = ( 324 cm² - 254.5 cm² ) * 1/4

                                       = 17.38 cm²

Answer: rs 4800, rs 3456

Step-by-step explanation:j

given data:

length of a sid = 48m

cost of ploughing the field = rs 25/m

cost of fencing the field = rs 18/m

solution:

we know a square has four equal sides. so total length of the field is

= m ( 48 + 48 +48 + 48 )

= 192m

cost of ploughing the field

= 192m * rs 25

= rs 4800

cos of fencing the field

= 192m * rs 18

= rs 3456

Answer:

y = 3x

Step-by-step explanation:

Use rise over run (y2 - y1) / (x2 - x1) to find the slope

(12 - 6) / (4 - 2)

6/2

= 3

The plant will be 0 cm at 0 weeks, since 3(0) = 0

So, the equation will be y = 3x

Answer: 1

Step-by-step explanation:

You just simplify each number by the square and then you multiply all of them!!

Answer: To simplify this problem you combine the like terms in the equation (numbers with the same variables.)

Demo: 12r + -4r = 8r

Answer:

8r + 14s - 7T

Step-by-step explanation:

Hello!

We have to make sure the terms are like terms before we add them.

Like terms are terms with the same variable so we can add r's with r's, t's with t's, etc.

There are two r's and two s's so we can simplify those

12r - 4r = 8r

5s + 9s = 14s

Now put these all together with the T in the original equation to get the answer

8r + 14s - 7T

Hope this helps!

Answer:

f=2.93cm

Step-by-step explanation:

SOH CAH TOA [the length you are finding is adjacent to the angle and opposite to right angle is the hypotenuse, therefore use cosine]

cos(43°)=f/4

[times 4x on both sides it cancels on the left]

4cos(43°)=f

2.93=f

Answer:

The answer is 1,000

Answer:

Option R

Step-by-step explanation:

The point S is the end point of ray.

What is line?

A line has length but no width, making it a one-dimensional figure. A line is made up of a collection of points that can be stretched indefinitely in opposing directions. Two points in a two-dimensional plane determine it.

According to the given information,

A ray's endpoint is a single point that denotes the conclusion of a line segment. In this instance, only one of the three lines that extend from point S contains a ray's terminus.

We must comprehend a ray's qualities in order to establish which location is the endpoint of a ray.

A ray originates at a single place and travels in one direction indefinitely. The beginning of the line segment is the endpoint of a ray.

We can see from the provided lines that the vertical line runs from point S via point R. Since it doesn't go on forever in one direction, this is not a ray example.

Similar to the vertical line,

The horizontal line also extends from point S through point T,

But it does not go on forever.

The third line is a ray because it is infinitely long in one direction and extends right and up from point S via point U.

Therefore, point S, the beginning of the line, is the endpoint of this ray.

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Answer:

x=10

Step-by-step explanation:

13x-7+7x-13=180

Combine like terms

20x-20 = 180

Add 20 to each side

20x -20+20 = 180+20

20x=200

Divide by 20

20x/20 = 200/20

x = 10

Answer:x=10

Step-by-step explanation:

1.add the number

2.add the same term to bothe sides of the equation

3.simplify

4.divide bothe side of the equation by the same term

5.simplify

Answer:

[tex]P = 3.5\ million[/tex]

Step-by-step explanation:

Given

Represent 1950 Population with P and 2003 Population with Q

[tex]Q = 19.5\ million[/tex]

Required

Determine the value of P

From the question; we have that

[tex]Q = 2\ million + 5 * P[/tex]

Substitute 19.5 million for Q

[tex]19.5\ million = 2\ million + 5 * P[/tex]

Subtract 2 million from both sides

[tex]19.5\ million - 2\ million= 2\ million - 2\ million + 5 * P[/tex]

[tex]19.5\ million - 2\ million= 5 * P[/tex]

[tex]17.5\ million = 5 * P[/tex]

Divide both sides by 5

[tex]\frac{17.5\ million}{5} = \frac{5 * P}{5}[/tex]

[tex]\frac{17.5\ million}{5} = P[/tex]

[tex]3.5\ million = P[/tex]

[tex]P = 3.5\ million[/tex]

Hence, the 1950 population is 3.5 million

Answer:

[tex]\dfrac{1}{12}[/tex]

Step-by-step explanation:

Given:

Two fair number cubes i.e. two dice consisting the numbers 1, 2, 3, 4, 5, 6 on their faces and have equal probability of each number.

The dice are rolled.

To find:

Probability of getting the sum of two numbers as 4.

Solution:

First of all, let us have a look at the total possibilities when two dice are rolled:

([1][1], [1][2], [1][3], [1][4], [1][5], [1][6],

[2][1], [2][2], [2][3], [2][4], [2][5], [2][6],

[3][1], [3][2], [3][3], [3][4], [3][5], [3][6],

[4][1], [4][2], [4][3], [4][4], [4][5], [4][6],

[5][1], [5][2], [5][3], [5][4], [5][5], [5][6],

[6][1], [6][2], [6][3], [6][4], [6][5], [6][6])

These are total 36 possible outcomes.

For getting a sum as 4:

Possible number of favorable cases are 3 (as highlighted in BOLD in above)

Formula for probability of an event E can be observed as:

[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]

Required probability is:

[tex]\dfrac{3}{36} = \bold{\dfrac{1}{12}}[/tex]