Twelve new students are standing in a line. How many different ways can the first seven students in line order themselves

Answer:

To find an inverse function, reflect a graph of a function across the line y=x (and find the resulting equation)

To reflect a linear function in the line y=x, find points on f(x) and then swap their x and y coordinates.

Points on f(x):  (0, -4)  (2, 0)  (5, 6)

Points reflected in line y=x:  (-4, 0)  (0, 2)  (6, 5)

Plot points (-4, 0)  (0, 2)  (6, 5) and connect to form a straight line - this is the inverse of the function:  [tex]f^{-1}(x)[/tex]

To determine the equation of f(x):

Choose 2 points on f(x):  (5, 6) and (0, -4)

Calculate the slope (gradient) by using:

[tex]m=\dfrac{\triangle y}{\triangle x}=\dfrac{y_2-y_1}{x_2-x_1}=\frac{6--4}{5-0}=2[/tex]

Using the slope-intercept form:  y = mx + b

(where m is the slope and b is in the y-intercept)

From inspection of the graph, we can see the line crosses the y-axis at -4,

⇒ f(x) = 2x - 4

As the line is actually a line segment (with endpoints (0, -4) and (5, 6), then

f(x) = 2x - 4,   0 ≤ x ≤ 5

To determine the equation of [tex]f^{-1}(x)[/tex]:

Rewrite f(x)  as  [tex]y = 2x - 4[/tex]

Swap the x and y:  [tex]x = 2y - 4[/tex]

Rearrange to make y the subject: [tex]y= \dfrac{1}{2}(x + 4)[/tex]

Replace y with [tex]f^{-1}(x)[/tex]

So the equation of the inverse is:   [tex]f^{-1}(x)= \dfrac{1}{2}(x + 4)[/tex]

As the original function is a segment, then

[tex]f^{-1}(x)= \dfrac{1}{2}(x + 4), \ \ \ -4\leq x\leq 6[/tex]

(shown in blue on the attached diagram)

** I can't see any points labelled E and F on the original function. If they are the endpoints of the line segment of f(x), then they are (0, -4) and (5, 6) **

Answer:

156

Step-by-step explanation:

While solving we will have to use the area formula of the rectangle, which is :A=w*l ; length*width=A.

Steps:
1)let’s consider that the shape is a full rectangle. => 16*12=192.

2)9*2=18 -> 18*2=36

3)192-36=156.

Area of the shape is 156 cm².

For explanation, please check the attached image.

Answer:

52

Step-by-step explanation:

a/13=4

a=13x4

So, a = 52

Answer:

B

Step-by-step explanation:

q and u are the only congruent angles

Answer:

point-slope form: [tex]y-8=\frac{4}{5}(x+2)[/tex]

Step-by-step explanation:

hope this helps :)

Answer:

D. 27 square feet per hour

Step-by-step explanation:

Step 1:

Find the unit rate. Since 18 tiles are per 2/3 of an hour, we can divide 18 by 2 to get 9 tiles layed per third hour.

Step 2:

Multiply the 9 per third of an hour by 3 to find how many are per hour,

[tex]9*3=27[/tex] square feet per hour

This is called finding the unit rate of a scenario.

The y-intercept of g(x) is equal to 2 plus the y-intercept of f(x).

The functions are given as:

f(x) = -2(1.07)^x

Table of values for g(x)

x    g(x)

−4    −10

−2 −    7

0        −4

2         1

The y-intercept is when x = 0.

So, we have:

g(0) = -4

Also, we have:

f(0) = -2(1.07)^0

f(0) = -2

-2 is greater than -4 by 2

Hence, the y-intercept of g(x) is equal to 2 plus the y-intercept of f(x).

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Answer:

hope this helps...

answer in the diagram

Tyler needs 28 feet of fencing to enclose his rectangular garden.

We have,

The perimeter of a rectangle is given by the formula:

Perimeter = 2 * (Length + Width)

In this case,

The length of the garden is 8 ft and the width is 6 ft.

Substituting these values into the formula

Perimeter = 2 * (8 ft + 6 ft)

= 2 * 14 ft

= 28 ft

Therefore,

Tyler needs 28 feet of fencing to enclose his rectangular garden.

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Answer:

576 adult tickets were sold at the school play.

Step-by-step explanation:

638 - 62 = 576

Answer:

576

Step-by-step explanation:

you would do 638-62 and get 576

Answer:

  y = 130(24/13)^(x -10)

Step-by-step explanation:

The y-value changes by a factor of 240/130 = 24/13 for a unit change in the x-value. This means we can write the function as though it had an initial value of 130 and a growth factor of 24/13, translated 10 units to the right.

  y = 130(24/13)^(x -10)

_____

Additional comment

This can also be written in the form ...

  y = a·e^(kx)

where a=130·(24/13)^(-10) ≈ 0.28266, and k=ln(24/13) ≈ 0.61310

Answer:

standard showerhead in Andrew's house dispenses 8 gallons of water per minute. Andrew changed this shower head to an energy-saving one. The equation shows the amount of water dispensed, y, as a function of the number of minutes, x, for the new shower head.

y = 3x

Answer:

40 gallons :)

Step-by-step explanation:

Answer:

57 °

Step-by-step explanation:

Complementary angles = 90 °

Since, Your angle don't have ∠ [  ] Then Let let "C" and "y"

Thurs, C = 12x- 3  and y = 7x - 2

It is given that angles r and s are complementary  angles. Two angles are complementary  if they add up to 90 degrees. This means the sum of measures of angle r and angle s must be 90 degrees. So,

c + y = 90

12x - 3 + 7x - 2 = 90

19x - 5 = 90

19x = 95

x = 95/19

x = 5

Using the value of x in expression or r, we get:

c = 12x - 3 = 12(5) - 3 = 60 -3 = 57 degrees.

So measure of angle c is 57 degrees.

Hence, the ∠ is 57 °

[RevyBreeze]

Answer:

50

Step-by-step explanation:

45+62+43= 150

150/3= 50

Answer: 150km

Step-by-step explanation:

The question says that the car required 9 litres of gasoline to cover 108km which means we and then derive that:

9L = 108km

And we are trying to find out how much distance can cover:

12.5L =?

Therefore, in order to find out the distance, we need to figure out how much distance can 1L take the car

therefore:

1L = [tex]\frac{108km}{9L}[/tex] = 12km

So if we know how far 1L can take us, we can just multiply 12.5 litres by the 12km to find out the distance:

12.5L × 12km = 150km

So, therefore, 12.5 litres can cover 150km.

Answer:

Correct answer is C

Step-by-step explanation:

The blue graph is translated down 3 which would give you the minus 3 and translated left 4 giving you the plus 4..

The equation of the blue graph is G ( x ) = ( x + 4 )² - 3

Graphs behave differently at various x-intercepts. Sometimes the graph will cross over the x-axis at an intercept. Other times the graph will touch the x-axis and bounce off.

Identify the even and odd multiplicities of the polynomial functions' zeros.

Using end behavior, turning points, intercepts, and the Intermediate Value Theorem, plot the graph of a polynomial function.

The graphs cross or are tangent to the x-axis at these x-values for zeros with even multiplicities. The graphs cross or intersect the x-axis at these x-values for zeros with odd multiplicities

Given data ,

Let the equation of the graph be represented as A

Now , the value of A is

Since the graph is that of a parabolic curve ,

It is a quadratic equation of the form y = ( x + a )² - b

And , the graph is shifted right to 4 units and down by 3 units

So , the equation of graph is G ( x ) = ( x + 4 )² - 3

Hence , the equation of graph is G ( x ) = ( x + 4 )² - 3 and plotted

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Sum of two interiors=exterior

[tex]\\ \tt\longrightarrow 69+3x+12=6x+27[/tex]

[tex]\\ \tt\longrightarrow 3x+81=6x+27[/tex]

[tex]\\ \tt\longrightarrow 3x=54[/tex]

[tex]\\ \tt\longrightarrow x=18[/tex]

Answer:

The total weight is 1593 lbs.

Step-by-step explanation:

177*9 = 1593

Answer:its right

Step-by-step explanation:Just remember inorder for a relationship to function  y dont repeat its eX

Answer: 130

Step-by-step explanation:

Answer:

Use F.O.I.L method
First, Outter, Inner, Last

So:

5x*7x= 35x^2

5x*-6= -30x

7x*2= 14x
2*-6= -12

So just add it all up, combine like terms and you have your answer.

35x^2 -16x -12

Answer:

12x - 4

Step-by-step explanation:

Add like terms.

5x + 7x = 12x

2 + (-6) = -4

Therefore, (5x + 2) + (7x - 6) = 12x - 4.

Answer:

14[tex]x^{2}[/tex] - 98x - 25774

Step-by-step explanation:

1- Reorder

  Reduce

  Calculate

2- Rewrite

   Calculate

3- Calculate

4- Remove the parentheses

5- Calculate

Answer:

3/14

Step-by-step explanation:

if he has 14 baseballs 5 of them are a so:

14-5=9

if he has 6 the are b then:

9-6=3

so 3 divided 14= 3/14

The standard equation of an ellipse is [tex]\frac{x^2}{144} +\frac{y^2}{95} =1[/tex]

The standard equation of an ellipse is given by:

[tex]\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} =1[/tex]

Where (h, k) is the center of the ellipse, 2a is the length of the major axis and 2b is the length of the minor axis.

Given the center = (0, 0), a = 12, b = 9.75, hence:

[tex]\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} =1\\\\\frac{(x-0)^2}{12^2} + \frac{(y-0)^2}{9.75^2} =1\\\\\frac{x^2}{144} + \frac{y^2}{95} =1[/tex]

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Answer: 17u

Step-by-step explanation:

(9+9+6-7)u=17u

Answer:

17u

Step-by-step explanation:

9u+6u+9u =24u

24u-7u=17u

Answer:

No

Step-by-step explanation:

These are NOT equivalent. If you expand the 2nd expression you get 27+23k which is close, but not the same.

Answer:

you are correct.

if you multiply the base and height with 3

height: 3 * 4 = 12

base: 3 * 8 = 24

area = 1/2 * base * height = 1/2 * 24 * 12 = 144

change in dimensions: 3 * 1 =  * 3

change in area is (144/16) = 9

Answer:

(3, 0)

Step-by-step explanation:

So with the 2 equations you can either choose which to start with but you need to make the X or Y the opposite from the other equation.

1.

3x + y = 9 (keep as is)
x + 2y = 3 --> -3( x + 2y = 3) In this case I chose to make the X the opposite of each other

--

3x - 3x = 0 (forced to get rid of)

y - 6y = -5y (Get the -6 by -3 x 2)

9 - 9 (Get the -9 by -3 x 3)

Left with:

-5y = 0 (Divide both sides by -5 to get X alone)

y = 0

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

(Choose any ORIGINAL equation)

x + 2y = 3

x + 2(0) = 3 (substitute)

Left with:

x = 3  (x + 0 = 3)

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

Optional:

Chose the other equation (the opposite from above)

Substitute X and Y in 3x + y = 9

3(3) + (0) = 9

Left with: 9 = 9 (check)

Hope this helps!

Answer:

What is the question?

Step-by-step explanation: