What is the inverse of function f?
f(x)=10/9x+11

(d) f(1) = 4 f(n) = 4 + d(n-1) , n>0 is the arithmetic formula to find the number of layers in the project

In the above question it is given that

A project is being created by a group of students by arranging layers.

The first layer is having 4 layers and as we move to the next layers, it is getting 2 times of the number of layers in the first layer.

i,.e f(1) = 4

Number of layers in the second layer = 8 layers

f(2) = 4.2 = 8

Now, we need to find the general arithmetic formula to determine the subsequent n number of layers in the project

As the subsequent layers are getting n times of the first layer, so we'll also find the similar arithmetic formula where addition to the first layer with n times of it is happening

So, after checking all the given options we find, (d) as the appropriate option

f(1) = 4

f(n) = 4 + d(n-1) , n>0

We'll find the number of layers in the 3 layers

Here, n = 3

Putting in the formula, we'll find.

f(3) = 4 + d(3-1)

f(3) = 4 + d(2)

where d(2) = 8 (given)

so, f(3) = 4 + 8 = 12

Hence, f(1) = 4 f(n) = 4 + d(n-1) , n>0 is the arithmetic formula to find the number of layers in the project

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Answer:

32 units

Step-by-step explanation:

calculate the distance using the absolute value of the difference.

| - 9 - 23 | = | - 32 | = 32

or

| 23 - (- 9) | = | 23 + 9 | = | 32 | = 32

The system of inequalities has no solution because the lines do not meet at any point

The system of inequalities is given as

y ≥ x² + 3

y < x + 1

From the above system of inequalities, we can see that the function types are

Next, we plot the graph of both inequalities in the system (see attachment for the graph)

From the graph, we can see that the lines and the curves of the functions do not intersect

This means that the system has no solution

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Answer: I think it's 9 days.

Step-by-step explanation:

Answer:

£4.50

Step-by-step explanation:

ratio of Pat : Alex = 5 : 2 = 5x : 2x ( where x is a multiplier )

then

5x + 2x = 63

7x = 63 ( divide both sides by 7 )

x = £ 9

Pat has 5 × £9 = £45

Alex has 2 × £9 = £18

let the amount they spend on sweets be x , then ratio of money is 3 : 1

so 45 - x : 18 - x = 3 : 1

express the ratio in fractional form and equate proportionally

[tex]\frac{45-x}{18-x}[/tex] = [tex]\frac{3}{1}[/tex] ( cross- multiply )

45 - x = 3(18 - x)

45 - x = 54 - 3x ( add 3x to both sides )

45 + 2x = 54 ( subtract 45 from both sides )

2x = 9 ( divide both sides by 2 )

x = 4.5

Pat spent £4.50 on sweets

The inequality that describes this scenario would be; A. 200 + 256C ≥ 870.

Inequality is defined as the relation which makes a non-equal comparison between two given functions. If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality.

Given that lisa checks and finds that she has 200 gigabytes available on her phone. It is going to use memory cards that each hold 256 gigabytes.

Let consider that C represent the number of memory cards that Lisa buys.

Then the inequality ;

200 + 256C ≥ 870

Hence, The inequality that describes this scenario would be; A. 200 + 256C ≥ 870.

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Answer:

neither of them are right

Answer:

a = 84

Step-by-step explanation:

[tex]\frac{a}{6} - 5 = 9\\\frac{a}{6}} - \frac{5*6}{6} = \frac{9*6}{6}\\ a - 30 = 54\\ a = 54 + 30\\ a = 84[/tex]

[tex]\cfrac{1}{3}x^2~~ = ~~\cfrac{4}{27}\implies \cfrac{x^2}{3}~~ = ~~\cfrac{4}{27}\implies x^2=\cfrac{(3)4}{27}\implies x^2=\cfrac{12}{27} \implies x=\pm\sqrt{\cfrac{12}{27}} \\\\\\ x=\pm\cfrac{\sqrt{12}}{\sqrt{27}} \implies x=\pm\cfrac{\sqrt{2^2\cdot 3}}{\sqrt{3^2\cdot 3}}\implies x=\pm\cfrac{2\sqrt{3}}{3\sqrt{3}}\implies x=\pm\cfrac{2}{3}[/tex]

Answer:

390

Step-by-step explanation:

Paul receive about 13 advertisement via email each day. about how many advertisement emails will he receive in 30 days?

13 × 30 = 390

The diameter is decreasing at a rate of  - 0.101 cm/min

Given that,

Surface area is decreasing at a rate of [tex]7cm^{2}[/tex]/min,

We know that,

Surface Area of a sphere:

S = 4 π r2

dS/dt = - 7cm2/min

our aim is to find rate of decrease of Diameter:

dD/dt =?

Substitute r in the equation with radius = 1/2*Diameter:

r = 1/2D

Take the derivative of the surface area function with respect to time:

d/dt [S = 4 π (1/2D)2]

d/dt [S = 4 π 1/4*D2]

d/dt [S = π *D2]

dS/dt = 2πD*dD/dt

Solve for dD/dt:

dD/dt = dS/dt / 2πD

Substitute, dS/dt = - 7cm2/min and D = 11 cm

dD/dt = dS/dt / 2πD

dD/dt = - 7cm2/min / 2π*11cm

dD/dt = - 7cm2/min / 22π cm

dD/dt = - 7cm / 22π min

dD/dt = - 0.101 cm/min

Therefore, the diameter is decreasing at a rate of - 0.101 cm/min

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0.101331789 cm/min is the rate at which the diameter decreases when the diameter is 11 cm

if a snowball melts so that its surface area decreases at a rate of 7 cm2/min,

find the rate at which the diameter decreases when the diameter is 11 cm.

Surface area: S

radius: r

diameter: e

time: t

[dS/dt] = [dS/de]*[de/dt] => de/dt = [dS/dt] / [dS/de]

S = 4pi*r^2 = 4p*i(e/2)^2 = pi*e^2 => dS/de =2pi*e

dS/dt = 7cm^2 / min

de / dt = [2pi*e] / [7cm^2/min] =[7cm^2/min] /  [2pi*11cm]

= 0.101331789 cm/min

Hence , 0.101331789 cm/min is the rate at which the diameter decreases when the diameter is 11 cm

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Step-by-step explanation:

Answer:

= 5.51 × 10⁻⁴

scientific notation

= 5.51e-4

scientific e notation

= 551 × 10⁻⁶

engineering notation

millionth; prefix micro- (u)

= 5.51 × 10⁻⁴

standard form

-4

Order of Magnitude

for scientific and standard forms

= 0.000551

(real number)

= five hundred fifty-one millionths

word form

The change in the elevation is 0.275 miles.

An elevation simply means the her that above the sea level. It's used to describe a geographical location.

Thethe change in elevation from the top of the grade to the bottom of the grade in feet will be:

= Percentage of change × Length given

= 5% × 5.5 miles

= 0.05 × 5.5 miles

= 0.275 miles.

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The required point on the cartesian plane is (0,1).

Definition of a Cartesian Plane. The intersection of two perpendicular lines results in the formation of the cartesian plane, a two-dimensional coordinate plane. The X-axis is the horizontal line, and the Y-axis is the vertical line.

In a graph (1,7) lies in the first quadrant

And if we go 1 unit left then that means that we will be on the y axis

Then if we go down 6 units we will reach at point 1 unit away from the origin on the y axis . This particular point can be represented as (0,1).

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Answer:

21

Step-by-step explanation:

63 divided by 3 is 21

210 divided by 10 is 21

Answer:

i think the answer is 2<x<5

Step-by-step explanation:

As per transformation of graph, h(x) = 1/4x² - 11 represents that the graph of f(x) is horizontally compressed by a factor of 4 and shifted down by 11 units.

To know the effect on the graph

Given, the graph is f(x) = x².

We know that, at the time of horizontally compressing a graph we need to multiply it by a factor of (1/a).

Again, at the time of shifting a graph up we need to add a positive number of (b).

Therefore, a = 4 and b = - 11.

Now, if we horizontally compress f(x) it by a factor of (1/4) then it be (1/4)x².

Again,  if we shifted down f(x) by 11 units, then it be (1/4)x² - 11.

Therefore, h(x) = (1/4)x² - 11 represents that the graph of f(x) is horizontally compressed by a factor of 4 and shifted 11 units down.

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The x- and y-intercepts of the graph of x+y=18 are; (18, 0) and (0, 18) respectively.

The x-intercept of a function of variable x ( y = f(x) ) form is an intersection fo the x-axis and the curve of the function. The x-intercept for a function y = f(x) is a solution to the equation f(x) = 0 because at that value of x, the function f(x) lies on x-axis, where y is 0. Values of x-intercept for a function f(x) are also called roots or solution of f(x) = 0 equation.

For x intercept, y = 0

x + y = 18

x + 0 = 18

x = 18

Hence, the x-intercept is (18, 0)

For y intercept, x = 0

x + y = 18

0 + y = 18

y = 18

Hence, the y-intercept is (0, 18)

The x- and y-intercepts of the graph of x+y=18 are; (18, 0) and (0, 18) respectively.

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The correct answer is option D

3(c) - 2 represents the total cost of three dance tickets at a cost of c each, less a one-time $2 discount.

         y = mx+b, where m is the slope and b is the y-intercept.

Based on the question. We have the parameters listed below.

The total cost of three dance tickets is 3c (at c for each)

One-time offer = $2

Because discounts are always subtracted from the total cost,

the equation represents,

the total cost of three dance tickets at a cost of c each, less a one-time discount $2

=  3(c) - 2

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Answer

Option C is correct.

8.0 × 10³ miles = 8 thousand miles.

Explanation

The number given in scientific notation is

8.0 × 10³ miles

= 8.0 × 1000 miles

= 8000 miles

= 8 thousand miles.

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The expression for f(x) is: [tex]f(x)=(x+4) , (x-2) , (x-9) ,(x+5),(x+5),(x+5)[/tex]

We know that for any polynomial equation with roots:

[tex]a_{1}, a_{2}, a_{3} ,...[/tex]

with multiplicity:

[tex]m_{1}, m_{2}...[/tex]

the equation for the polynomial is given by:

[tex]f(x)=(x-a_{1}) ^{m_{1} }, (x-a_{2}) ^{m_{2} }...[/tex]

If the leading coefficient is negative we may take '-' sign in the starting of the expression.

Here we are given that, f(x) has a leading coefficient of 1, roots -4, 2, and 9 with multiplicity  1, and root -5 with multiplicity 3

Hence, f(x) is given by:

= [tex]f(x)=(x-(-4)) ^{1 }, (x-2) ^{1}, (x-9) ^{1},(x-(-5)) ^{3}[/tex]

= [tex]f(x)=(x+4) , (x-2) , (x-9) ,(x+5),(x+5),(x+5)[/tex]

Hence, the expression for f(x) is: [tex]f(x)=(x+4) , (x-2) , (x-9) ,(x+5),(x+5),(x+5)[/tex]

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Answer:

3rd Graph = 1st box

2nd Graph = 2nd Box

4th Graph = 3rd Box

Answer:

:]

Step-by-step explanation:

x, x+2

Equation: 2x+4=2x+4

All real numbers

b) it is an identity, it has infinite solutions.

Answer:

where is the question? plssss so im sorrry but where is the question i don't see a question?

The answers (C) and (D) are accurate:.

F(x) = 4; 0 = x 2 and F(x) = -2x + 9; 2 = x 4 respectively.

A piecewise function's graph has a large number of curve elements. It means that, depending on the value of the input, it has a wide range of definitions. To put it another way, a piecewise function reacts differently to the input.

It follows that:

The image displays the piecewise function:

Observing the piecewise function's graph

Every value in the domain is associated to exactly one value in the range according to the function, which may be thought of as a unique kind of connection with a predefined domain and range.

F(x) = 4; 0< = x < 2

F(x) = -2x + 9; 2 < = x < 4

Thus, F(x) = 4; 0< = x < 2 and F(x) = -2x + 9; 2 < = x < 4 the option (C) and (D) are correct.

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The correct question is:

" 2) Select the algebraic definition for the piecewise function graph.

F(x){_____ 0< = x < 2

{_____ 2 < = x < 4

A. 2x-8

B. 2

C. -2x+8

D. 4

E. 2x-4"

Answer

It will take 3 hours to get to your cousin's house.

Explanation

Firstky, note that Speed is given as

For this question, we are told that the distance to your cousin's house is 150 miles.

The speed is an average rate of 50 miles per hour.

We are then asked to calculate how long it will take to get to your cousin's house.

Speed = 50 miles/hour

Distance = 150 miles

Time = ?

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Translation that has the same effect as the composition of translations is

(x, y)→ ( x+2 , y+7 )

Composition of two reflections can be expressed as translation. Composition of reflections over parallel lines always has the same effect as a translation. Combination of two or more transformations is called composition of translation.

In this case :

As given in the question , 9 units are added from the x-coordinate in the first transformation and then 7 units are subtracted. So, the sum is:

+9-7 = +2

Observe that, in the first transformation, 1 units are added to the y-coordinate and then 6 units are added. The sum is:

+6+1 = +7

Then, the single Translation that has the same effect as the given Composition of translation is calculated to be:

(x, y)→ ( x+2 , y+7 )

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Root 13 is a non-recurring, infinite decimal. Since 13 is not a perfect square, its square root cannot be determined precisely. 13 cannot be expressed as a fraction, which is the definition of a rational number, because it cannot be expressed as a ratio of integers.

An illustration of a rational number?

If p and q are integers and q is not equal to 0, then the number is in the form of p/q and is said to be rational. Rational number examples include 1/3, 2/4, 1/5, 9/3, and so on.

Irrational number examples include: Any real number that cannot be expressed as a fraction is considered to be illogical.

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Answer:

11. -3/2

12. -1

Step-by-step explanation:

To find slope, subtract the y's and put that on top of a fraction. Then subtract the x's and put that on the bottom of the fraction. Simplify if you can.

Subtract y's 2 - -4 is

2+4 which is 6, put that on top.

0 - 4 is -4 put it on the bottom.

Slope is 6/-4. Simplified, this is -3/2

The other question, same thing:

y-y over x-x

-4 - -3 / -2 - - 3

= -4+3 / -2 + 3

= -1 / 1

= -1

Answer:

45 large dogs

Step-by-step explanation:

Step 1:

60 x 3 = 180

180 ÷ 4 = 45