Which is a term in both the sequence f(n)=f(n-1)+4 and the sequence f(n)=3(5)^n-1 if f(1)=3?
a. 7
b. 15
c. 27
d. 135​

The translation from words to an algebraic expression, denoting the unknown by n is 0.15(n + 10,000)

let

unknown number = n

= n + 1000

= 15%(n + 10000)

= 15/100(n + 10,000)

= 0.15(n + 10,000)

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Option 1 is correct. The correct solution about these functions is that The original population of State A was double of the original population of State B.

The function in the question is given as

For A:

[tex]F(x) = 4*(1.08)^x[/tex]

For B

[tex]g(x) = 2*(1.08)^x[/tex]

The exponential growth equation that is used to solve this is

[tex]h(x) = A(r)^x[/tex]

such that A is the initial and r is the rate of growth.

f(x) and g(x) are at the same rate but the exponential function is known to grow faster.

Hence the correct option is The original population of State A was double of the original population of State B.

Which conclusion is correct about the population of State A and State B? 1. The original population of State A was double of the original population of State B.

2. The original population of State A was half of the original population of State B.

3. The original population of State B was one-fourth of the original population of State A.

4. The original population of State A was one-fourth of the original population of State B.

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Answer:

Step-by-step explanation:

honestly thats what it is

Hello !

56)

[tex]5 {x}^{2} + 8x = - 1 \\ 5 {x}^{2} + 8x + 1 = 0[/tex]

[tex]\Delta = {b}^{2} - 4ac \\ = {8}^{2} - 4 \times 5 \times 1 \\ = 64 - 20 \\ = 44[/tex]

The value of the discriminant is 44.

57) ∆>0 : there are two solutions.

58)

[tex]x_1 = \frac{ - b + \sqrt{\Delta} }{2a} \\ = \frac{ - 8 + \sqrt{44} }{2 \times 5} \\ = \frac{ \sqrt{11} - 4 }{5} [/tex]

[tex] x_2 = \frac{ - b - \sqrt{\Delta} }{2a} \\ = \frac{ - 8 - \sqrt{44} }{2 \times 5} \\ = \frac{ - \sqrt{11} - 4 }{5} [/tex]

Have a nice day

56. 44

57. 2

58. Image attached.

First, let's simplify some things. Let's make this a quadratic equation.

Moving the -1 (by adding 1 to both sides) gives us 5x^2 + 8x + 1 = 0. Note that this is the standard form of a quadratic, which is ax^2 + bx + c = 0.

Now, the discriminant. The discriminant is helpful because it tells us if we have 2 real solutions, 1 real solution, or if this equation is imaginary and thus impossible to solve using elementary techniques. If the discriminant is greater (>) than 0, then it has 2 solutions. If the discriminant equals (=) 0, it has 1 solution. If the discriminant is less than (<) 0, then it is imaginary.

The discriminant of a quadratic equation is defined as b^2 - 4ac (from the quadratic formula.) We just plug in b, a and c. b will be 8, a will be 5, and c will be 1. Now we just solve. (8)^2 - 4 * 5 * 1 = 64 - 20 = 44. Since 44 is greater than 0, we have 2 solutions for this. 44 is the discriminant. (Answer to 56.) We also have 2 solutions (answer to 57.)

Now, I'll solve the quadratic equation using the quadratic formula. I'll attach my work in an image (answer to 58.)

Hope this helped!

The measure of the angle x is 53.13 degrees after applying the sin ratio.

The trigonometric ratio is defined as the ratio of the pair of a right-angled triangle.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

Applying sin ratio:

sinx = 12/15

sinx = 0.8

x = 53.13 degrees

Thus, the measure of the angle x is 53.13 degrees after applying the sin ratio.

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X = 1 4 5 6

Y = 20 8 4 0

From the function: Y = 24 - 4X

If X = 1, then Y = 24 - 4(1) = 20

If X = 4, then Y = 24 - 4(4) = 8

If X = 5, then Y = 24 - 4(5) = 4

If X = 6, then Y = 24 - 4(6) = 0

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Answer:

The second graph.

Step-by-step explanation:

If you plug the equation into the desmos graphing calculator, you'll get the second graph.

Hope this helped! :)

The equation of the function g(x) will be g(x) = - ln (x + 2).

Exponents can also be written as logarithms. A number base logarithm is similar to some other number. It is the exact inverse of the exponent expression.

Let the equation of the function f will be

f(x) = ln x

If the function is multiplied with negative sign, then the function gets flipped about the x-axis.

And if we add 2 in the variable of the function, then the function gets shifted towards left.

Then the equation of the function g(x) will be

g(x) = - ln (x + 2)

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Answer:

B. 8

Function's:

Given following:

To solve for f(g(-2)), substitute x = -2 in function g(x)

⇒ f(g(-2))

⇒ f((-2)² + 1)

⇒ f(5)

Now, substitute x = 5 in function f(x)

⇒ 2(5) - 2

⇒ 8

Answer:

Answer:

with mark '√'

Step-by-step explanation:

all the details are in the attachment. Note, the black mark means 'much solutions', the blue one means 'one solution'.

Answer:

[tex]x=i\sqrt6[/tex]

[tex]x=-i\sqrt6[/tex]

Step-by-step explanation:

x^2=-6

x=[tex]\sqrt-6[/tex]

Answer:

Sir, as for as I can tell that is the correct answer. Maybe you put it in wrong or added a space but that’s correct 100%.

Unless it’s not supposed to be in y = mx + b format?

Step-by-step explanation:

Answer:

y = -x - 1

Step-by-step explanation:

The equation of the line is written in the slope-intercept form,

y = mx + b

where m represents the slope

number that describes both the direction and the steepness of the line

slope = rise/run

            b represents the y-intercept  

point where crosses the y-axis

y = mx + b → y = -1x + (-1)

this can be simplified by -x - 1

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Step-by-step explanation:

From the conversation of angular momentum

Initial momentum=final momentum

Here,

Since body is initially resting, it's momentum must be zero.

Let v be velocity of third piece. Then

0= 10(-3i+2j) + 18(5i-4j) + 22v

Solving this we get,

v= 4/22(15i+13j).

The velocity of third piece is 2/11(13 j - 15i)

Velocity defines the direction of the movement of the body or the object.

Given:

As the body is at rest so the initial momentum is zero.

Let v be velocity of third piece.

so,

0= 10(-3i+2j) + 18(5i-4j) + 22v

0= -30i + 20j + 90i -72j + 22 v

0= 60i - 52j + 22 v

-60i +52j = 22v

v= 2/11( 13j - 15 i)

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Answer:

half question

Step-by-step explanation:

I'm sorry sir but I would like you to make sure if you have posted the whole question

thank you

Answer:

2

Step-by-step explanation:

mum

The graph that shows the solution to the given system of linear inequalities is shown below

From the question, we are to draw the graph that shows the solution to the given system of linear inequalities

The given system of linear inequalities is

y>2x+3

y<-2x-4

The graph that shows the solution to the given system of linear inequalities is shown below

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The 90% , 99% confidence interval for the population mean is 32.145 < [tex]\rm \mu[/tex] < 35.855 and 31.093 <  [tex]\rm \mu[/tex] < 36.907

Probability is the study of likeliness of an event to happen.

It is given that

Total Population = 50

Mean = 35

The confidence interval is given by

[tex]\rm CI = \mu + z \dfrac{s}{\sqrt n}[/tex]

[tex]\rm \mu[/tex] is the mean

z is the confidence level value

s is the standard deviation

n is the population width

(a) The 90% confidence interval for the population mean

90% [tex]\rm \alpha / 2[/tex]  = 0.05

Z = 1.64

34 [tex]\rm \pm[/tex] 1.64 * 8 / √50

34 [tex]\rm \pm[/tex]  1.855

32.145 < [tex]\rm \mu[/tex] < 35.855

(b)  The 99% confidence interval for the population mean

99% [tex]\rm \alpha / 2[/tex]  = 0.005

Z=2.57

34  [tex]\rm \pm[/tex] 2.57 * 8 / √50

34 [tex]\rm \pm[/tex]  2.907

31.093 <  [tex]\rm \mu[/tex] < 36.907

Therefore the confidence interval for population mean has been determined.

The complete question is

A simple random sample of 50 items from a population width =7  resulted in a sample mean of 35. If required, round your answers to two decimal places.

a. Provide a 90% confidence interval for the population mean

b. Provide a 99% confidence interval for the population mean

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The solution of the linear equations will be ( -2, 4).

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

Given equations are:-

Solving the equations by elimination method:-

2x +3y = 8

3x+y= -2

Multiply the second equation by 3 and subtract from the first equation.

2x +3y = 8

-9x -3y = 6

----------------

      -7x = 14

         x = -2

Out of the value of x in any one equation, we will get the value of y.

3x+y= -2

3 ( -2) + y = -2

-6 + y = -2

y = 4

The graph of the equations is also attached with the answer below.

Therefore the solution of the linear equations will be ( -2, 4).

The complete question is given below:-

Exploring Systems of Linear Equations 2x +3y =8 and 3x+y= -2. Find the value of x and y and draw a graph for the system of linear equations.

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Answer:1 and 3

Explanation:by definition a rhombus is parallelogram a with opposite equal acute angles, opposite equal obtuse angles, and four equal sides.

Answer:

3519.248

Step-by-step explanation:

Searched it up ngl

Answer:

Area = 49.15

Step-by-step explanation:

area = 0.5 * side a * side b * sin(Angle)

area = 0.5 * 10 * 12 * sin(55)

area = 60 * 0.8192

49.15

By applying the definition of functions and composition between two functions, we find that (g ° f) (x) = 4 when x is equal to 6. (Correct choice: B)

Let be f and g functions, there is a composition of f in terms of g when the input of the former is output of the latter. Hence, we have the following relationships:

g(x):

- 2 → 4

f(x):

6 → - 2

By applying the definition of functions and composition between two functions, we find that (g ° f) (x) = 4 when x is equal to 6. (Correct choice: B)

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Answer:

1.275

Step-by-step explanation:

Answer:

51/40

= 1.275 in decimal

hoping help

The number of different collections of writing utensils could Faruq bring to class if he doesn't want to show up empty-handed is ab + a + b

Since Faruq has a identical markers, b identical pencils, and no other writing utensils in his locker and we require the number of collections or ways he could bring them to school without coming to school empty-handed, we use combination mathematics since order does not matter.

Now, Faruq can either come to school with one marker and one pencil or one pencil or one marker.

So, the combination for one marker and one pencil is n = a × b = ab

The combination for one marker is n' = a

The combination for one pencil is n" = b

So, the total combination is N = n + n' + n"

= ab + a + b

So, the number of different collections of writing utensils could Faruq bring to class if he doesn't want to show up empty-handed is ab + a + b

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The construction is to draw a parallel line to a given line AB passing through point P. To fix the error, the 3rd arc must be reconstructed. Thus the correct option is D. The third arc should be drawn centered at F.

The given construction involves drawing a parallel line through a given point P to a given line AB.

From the construction shown, drawing a straight line through P and G would not be parallel to the given line AB. Thus there is an error in the construction of the 3rd arc. To draw the required corresponding angle, the 3rd arc has to be reconstructed.

Therefore to fix the error the correct step to follow is: Option D. The third arc should be drawn centered at F.

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Kindly contact a 1-on-1 tutor if more explanations are needed.

Answer:

C. 76.81

Step-by-step explanation:

We must use one of the trigonometric ratios to find the length, L,  of the ramp.  If we use 16 as the reference angle, the 22 in would be our opposite side and the ramp length is the adjacent.

Therefore, we must use tan, which is [tex]\frac{opposite}{adjacent}[/tex]:

[tex]tan (16)=\frac{22}{L} \\\\L*(tan(16)=22)\\\\L*tan(16)=22\\[/tex]

[tex]\frac{L*tan(16)}{tan(16)}=\frac{22}{tan(16} \\\\L=79.815=79.82 in.[/tex]

Answer:

C

Step-by-step explanation:

the area (A) of a triangle is calculated as

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )

here b = z and h = w , then

A = [tex]\frac{1}{2}[/tex] zw

Answer:

C is the correct answer 100 percent sure

Answer:

5

Step-by-step explanation:

Anything below 5 is a fail:

3, 2, 0, 1, 3

That's 5 students.