The function $f : \mathbb{r} \rightarrow \mathbb{r}$ satisfies $f(x) f(y) - f(xy) = x + y$ for all $x$, $y \in \mathbb{r}$. find $f(x)$.

Answer:

The required probability is 5/18.

Step-by-step explanation:

Total number of total students = 10

Number of girls = 5

Number of boys = 5

Formula for probability:

[tex]Probability=\frac{\text{Favorable outcome}}{\text{Total outcome}}[/tex]

The probability that the first student chosen will be a girl = [tex]\frac{5}{10}=\frac{1}{2}[/tex]

After selecting 1 student, the total number of student is

[tex]10-1=9[/tex]

The probability that the second student chosen will be a boy = [tex]\frac{5}{9}[/tex]

The probability that the first student chosen will be a girl and the second will be a boy is

[tex]P=\frac{1}{2}\times \frac{5}{9}[/tex]

[tex]P=\frac{5}{18}[/tex]

Therefore the required probability is 5/18.

The value of the rational expression of equation is A = -1/5

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

A = ( 2x - 1 ) / ( x + 5 )

when x = 0

Substituting the values in the equation , we get

A = ( 2 ( 0 ) -1 ) / ( 0 + 5 )

On simplifying , we get

A = -1/5

Hence , the equation is solved and A = -1/5 when x = 0

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Answer:

thx for points man

Step-by-step explanation:

Answer:

The reason why any angles coming out from D and C are congruents is  because of the geometry coungruence's concept of 2 items having the same pattern, shape or form and size as the mirror image of the other.

2 angles would be congruent by being the same angle in degrees or radians.

Thereby any angle coming out from C as vertex would be congruent with any other vertex point angle mirroring the resulting figure shaped by the radiants or degrees of such angle.

Step-by-step explanation:

Answer: y= 630 is the horizontal asymptote for the given function.

Step-by-step explanation:

Horizontal asymptotes are horizontal lines that the graph of the function approaches as x tends to [tex]+\infty[/tex] or [tex]-\infty[/tex].

Thus, If there is a function f(x),

Then Its horizontal asymptote,  y = [tex]\lim_{x\rightarrow \infty} f(x)[/tex]

Here the given function is, [tex]f(x) = \frac{560+630x}{x}[/tex]

Thus its horizontal asysmptote is, y = [tex]\lim_{x\rightarrow \infty} \frac{560+630x}{x}[/tex]

⇒ y = [tex]\lim_{x\rightarrow \infty}560/x+630[/tex]

⇒ y = 0+ 630

⇒ y= 630 is the horizontal asymptote of the given function f(x).

The horizontal asymptote of y = (630x + 560)/x is y = 630.

A linear function is given by:

y = mx + b

where y, x are variables, m is the rate of change and b is the y intercept.

Given the total cost as y = 630x + 560.

For the function y = (630x + 560)/x, the horizontal asymptote is at:

y = 630x/ x = 630

The horizontal asymptote of y = (630x + 560)/x is y = 630.

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Answer:

The answer is 13.23

Step-by-step explanation:

In order to determine the median of the set of data, we have to know about median and how applicate it.

The median of a set of data is the middlemost number in the set. The median is also the number that is halfway into the set. To find the median, the data should first be arranged in order from least to greatest.

Also, if there is an even number of items in the data set, then the median is found by taking the mean (average) of the two middlemost numbers.

So, we arrange the set of data:

11.20

12.50

12.50

13.23

13.23

14.50

15.60

15.75

The data set is an even number.

The two middlemost numbers are: 13.23; 13.23.

So, the mean (average) is:

(13.23+13.23)/2=13.23

Finally, the median of the set of data is 13.23

The interior angle of a regular hexagon is 120 degrees, and the exterior angle is 60 degrees.

To find the measures of an interior angle and an exterior angle of a regular polygon with 6 sides, we will use the fact that the sum of interior angles of a polygon is given by (n-2)×180°, where 'n' is the number of sides of the polygon. Thus, a regular hexagon will have its interior angles sum to (6-2)×180° = 720°. Since all interior angles in a regular polygon are equal, each interior angle will be 720° ÷ 6 = 120°. The exterior angle of a regular polygon is calculated as 360° ÷ n. Therefore, an exterior angle of a regular hexagon will be 360° ÷ 6 = 60°.

So, the interior angle of a regular hexagon is 120°, and the exterior angle is 60°.

10. 4x = 1

x = 1/4

 since there is no y if you graph x = 1/4 you would get a straight vertical line at x = 1/4

 since it is a vertical line it is symmetric about the x axis ( it looks the same on both sides of the x axis)

Answer:

[tex]\bf\textbf{Probability of selecting exactly two $5 bill }=\frac{1}{7}[/tex]

Step-by-step explanation:

Total number of bills in the wallet = 7

Total number of $5 bills in the wallet = 3

Total number of $10 bills in the wallet = 2

Total number of $20 bill in the wallet = 1

Total number of $100 bill in the wallet = 1

We need to find the probability that he selects exactly two $5 bills.

Number of favorable outcomes = 3

[tex]\text{Probability of selecting one $5 bill }\frac{3}{7}[/tex]

[tex]\text{Probability of selecting second $5 bill }\frac{2}{6}[/tex]

[tex]\bf\textbf{Probability of selecting exactly two $5 bill = }\frac{3}{7}\times \frac{2}{6}=\frac{1}{7}[/tex]

they would be similar since they have the same angles, but different length sides

they are different sizes

 the sides are different lengths

 congruent, means same size and shape

 the only answer that applies is A

The answer is -11 - 6x + 2x^2 + 8x^3 <==

she hikes 1/6 a day, to get 11/6 , she would have to hike 11 days

to hike 1/3 of a mile

1/3 / 1/6 = 1/3 * 6/1 = 6/3 = 2

 so she would have to hike 2 days

Answer:

11 days and 2 days

Step-by-step explanation:

Molly hikes every day = [tex]\frac{1}{6}[/tex] miles

She would take days to hike total [tex]\frac{11}{6}[/tex] miles = [tex]\frac{\frac{11}{6} }{\frac{1}{6} }[/tex]

= [tex]\frac{11}{6}[/tex] ×  [tex]\frac{6}{1}[/tex] = 11 days.

To hike a total  [tex]\frac{1}{3}[/tex] of a mile she would have to hike = [tex]\frac{\frac{1}{3} }{\frac{1}{6} }[/tex]

[tex]\frac{1}{3}[/tex] ×  [tex]\frac{6}{1}[/tex] = 2 days

To hike a total of  [tex]\frac{11}{6}[/tex], she would have to hike for 11 days. To hike a total of  [tex]\frac{1}{3}[/tex] of a mile, she would have to hike for 2 days

Answer:

the given statement is true.

Step-by-step explanation:

The given lines are

2x - 3y = 1 and 2x + 3y = 2

Write these equations in slope intercept form of a line y = mx +b

For the first equation

[tex]2x-3y=1\\\\3y=2x-1\\\\y=\frac{2}{3}x-\frac{1}{3}[/tex]

For the first equation

[tex]2x+3y=2\\\\3y=-2x+2\\\\y=-\frac{2}{3}x+\frac{2}{3}[/tex]

The slope and y-intercepts of first line are 2/3 and -1/3 respectively.

The slope and y-intercepts of second line are -2/3 and 2/3 respectively.

Since, the slopes and y-intercepts of these lines are different.

Hence, these lines are intersecting.

Therefore, the given statement is true.

ne S is the blue line, where does it contact circle B?

 it touches at Point K,

 so that would be the tangency.

 Answer Point K

Answer:

Graph B

Step-by-step explanation:

Given is a function as

[tex]f(x) = \frac{3}{2} (\frac{1}{3} )^x[/tex]

There are 4 graphs given.

Out of the 4 options we have to select one which suits this graph

Let us study about f graph

X intercept is at infinity.

Or y=0 is asymptote for this curve

y intercept is when x =0

i.e. y intercept =3/2 (1) = 3/2

Only A and B satisfy this value of y intercept

Out of A and B we have to select one option

When x=1, we get

f(1) = 3/2 (1/3) = 1.5

This is satisfied only by Graph B.

Hence answer is graph B.

When x tends to -infinity y

81 x 31 = 2 511 (area of a brick)

2511 x 400 = 1 004 400 (area of the wall)

Convert 1 004 400" to ft. [1ft. = 12"]

1 004 400 / 12 = 83 700 ft.

Now this is what we have.

-Hight 42 ft.

-Length X ft.

-Area 83 700ft.

Algebra time.

42 x X = 83 700 (to get X you would devide 83 700 by 42)

83 700 / 42 = 1 992.85ft. (X = 1 992.85ft.)

So the length of the wall would be 1992.85ft.

The height of the wall is 166.07 ft.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given that, 400 bricks, each measuring 81" by 31", are required to build a wall 42 feet high.

Here, Area of a one brick 81"×31"

6.75×2.58=17.44 ft²

Total area of 400 bricks = 400×17.44=6975 ft²

Total brick area divided by 42' height of wall

=6975÷42=166.07 ft

Therefore, the height of the wall is 166.07 ft.

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Part A:



The first thing of completing the square is writing the expression   as   which expands to  .

We have the first two terms exactly alike with the function we start with:  and   but we need to add/subtract from the last term, 49, to obtain 41. 

So, the second step is to subtract -8 from the expression 

The function in finalizing the square form is


Part B:

The vertex is acquired by equating the expression in the bracket from part A to zero




It means the curve has a turning point at x = -7

This vertex is a minimum since the function will make a U-shape. 
A quadratic function   can either make U-shape or ∩-shape depends on the value of the constant   that goes with  . When   is (+), the curve is U-shape. When   (-), the curve is ∩-shape

Part C:

The symmetry line of the curve will go through the vertex, hence the symmetry line is 

This function is shown in the diagram below

Answer:

Part A: The vertex form is h(x) = (x+7)^2  - 8 .

Part B: The vertex is a minimum. The vertex is (-7,-8).  

Part C: The axis of symmetry is x=-7. (axis of symmetry is the x value of the vertex)

Step-by-step explanation:

This video will help you understand how I got the function into vertex form.

Search: How do you convert from standard form to vertex form of a quadratic Brian McLogan

This will help you find the vertex

Search: Finding the vertex of a parabola in standard form khan academy