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The set {2, 4, 6, ..., n} contains the positive consecutive even integers from 2 through n.  When one of the integers from the set is removed, the average of the remaining integers in the set is 28.

What is the least possible value of  n ?

Die Menge {2, 4, 6, ..., n} enthält die positiven fortlaufenden geraden ganzen Zahlen von 2 bis n. Wenn eine der Ganzzahlen, (x), aus der Menge entfernt wird, beträgt der Durchschnitt der verbleibenden Ganzzahlen in der Menge 28. Was ist der kleinstmögliche Wert von n?

Hello Guest!

\((2+n-x)/2=28\\ n-x=54\\ x=n-54\)

               \(x=n-54 \)   |   2     4     6      .   .   .   20

                   n = x + 54    |  56  58    60                74

\(\varnothing = (n+2-x)/2\)    |  28  28    28                28

The least possible value of  n is 56.

  !

AX  = 12

AX  =  4 CX  

So....CX  = 3

And we have this relationship

AX/ BX  = BX / CX

AX * CX  =  BX^2

12 * 3  =  BX^2

36   =  BX^2        take both roots

6  =   BX

We can form a rectangle that is 12 ft high  and has a width of 4* 2ft  = 8 ft

The rope will form the diagonal of this rectangle and will have a length of

√[12^2 + 8^2]  =

√[144 + 64 ] =

√[ 16 ( 9 + 4) ]  =

4√13  ft

g(x)  =  5x  - 4

g(x)  = f^-1(x) - 3

g(x) + 3  = f^-1(x)

If f(x)  = ax + b

Then

y =ax + b

y - b  = ax

(y - b)  / a  = x

(x - b)  / a  =  y  = f^-1(x)

So

g(x)  + 3  =  (x - b) / a

5x - 4 + 3  =  (1/a)x - b/a

5x - 1  =  (1/a)x - b/a

So

5  = 1/a

a  =1/5

And

-1  = -b/a

-1  = -b / (1/5)

1  = b / (1/5)

b  =1/5

So

5a + 5b  =

5(1/5) + 5(1/5)  =

1  + 1  =

2

[2, 4, 6, .....54]     has an average of 28

Removing 28  will also produce an average of 28

Correct Good Job! How did you figure it out?

8^6 / 4+3.7(42.3-24.6)

Hello Guest!

\(8^6 / 4+3.7(42.3-24.6)=\color{blue} 65601.49 \)

  !

One house has the address of 91

The other has the address of 19

By similar triangles, the answer is 6 sqrt(2).

that member give you the answer that i want to say you 

13   17   19   = 49  ?

Step 1: Simplify both sides of the equation.

0.4x+16+0.3(x−(0.4+16)+20)+0.75(x−(0.4x+16))−(0.3(x−0.4x+16)+20)+30=x

0.4x+16+(0.3)(x)+(0.3)(−0.4)+(0.3)(−16)+(0.3)(20)+(0.75)(x)+(0.75)(−0.4x)+(0.75)(−16)+(−0.3)(x)+(−0.3)(−0.4x)+(−0.3)(16)+−20+30=x(Distribute)

0.4x+16+0.3x+−0.12+−4.8+6+0.75x+−0.3x+−12+−0.3x+0.12x+−4.8+−20+30=x

(0.4x+0.3x+0.75x+−0.3x+−0.3x+0.12x)+(16+−0.12+−4.8+6+−12+−4.8+−20+30)=x(Combine Like Terms)

0.97x+10.28=x

0.97x+10.28=x

Step 2: Subtract x from both sides.

0.97x+10.28−x=x−x

−0.03x+10.28=0

Step 3: Subtract 10.28 from both sides.

−0.03x+10.28−10.28=0−10.28

−0.03x=−10.28

Step 4: Divide both sides by -0.03.

−0.03x

−0.03

=

−10.28

−0.03

x=342.666667

Largest integer = x      smallest    < 1/2x        

smallest integer is  x - 3 

x-3 <1/2x

-3 < -1/2 x

3> 1/2 x

6 > x      or x < 6     the GREATEST x would be 5     (edited)

At Y intercept x = 0  (right?)   put 0 in for x   6(0) + 8y = 24     y intercept = 3      0,3

At X intercept y= 0                  put 0 in for y to find x intercept  = ?                        ?,0

    Plot those two points and draw a line through both of them......done !      

1 qrt covers TWO x 9 x 10 = 180 sq ft

10ft x 12 ft   x 1qt/180ft^2 = 120/180 qt = 2/3 qt

thank you 

This basically means, solve the system of equations for x and y....you CAN do it graphically

  or algebraically:

2x+3y=7         Multiply by -3 ==> -6x - 9y = -21

3x+4y= -8       Multiply by 2 ==>   6x + 8y = -16     See what I did there?  Now add the two equations together and the 'x' part disappears

                                                          -y = - 37    y = 37    now sub this value of y into oneof the equations to find the 'x' value and you're done.

x^3 + 8x^2 + 6x + 48    factor by grouping

x^2( x + 8)  + 6(x + 8)

(x + 8)(x^2 + 6)

First, lets see if the tiles fit evenly.....

  disregarding grout lines

2 feet x 5 feet   is   24 inches x 60 inches 

24 is a multiple of 3 and 4

60 is a multiple of 3 and 4

  so the tiles should fit evenly

     8 x 3 = 24    so 8 rows

     15 x 4 = 60  so 15 columns         15 x 8 =120 tiles

Check:  24 x 60 = 1440 sq inches

               120 tiles x 3x4 = 1440 sq inches    Check!

thank you so much 

The line goes up '4' for every one x  means slope is 4    slope is rise /run    it rises  4  for 'run' of one   = 4

how you know that the slope is 4 ?

The equation of a line is

y=mx+b   where m is the slope  

In your example the slope is given as '4'

y = 4x +b     Now put in the point you were given   x,y   2, -3

-3 = 4(2)+b    and solve to find b = -11   for your question

the line equation becomes

y=4x-11